#### How light a higgsino or a wino dark matter can become in a compressed scenario of MSSM

HJE
How light a higgsino or a wino dark matter can become in a compressed scenario of MSSM
Manimala Chakraborti 0 1 2 5
Utpal Chattopadhyay 0 1 2 3
Sujoy Poddar 0 1 2 4
0 170/436 , N.S.C. Bose Road, Kolkata - 700092 , India
1 2A & B Raja S.C. Mullick Road, Jadavpur, Kolkata 700 032 , India
2 Nu allee 12 , 53115 Bonn , Germany
3 Department of Theoretical Physics, Indian Association for the Cultivation of Science
4 Department of Physics, Netaji Nagar Day College
5 Bethe Center for Theoretical Physics & Physikalisches Institut der Universitat Bonn
Higgsinos and Wino have strong motivations for being Dark Matter (DM) candidates in supersymmetry, but their annihilation cross sections are quite large. For thermal generation and a single component DM setup the higgsinos or wino may have masses of around 1 or 2{3 TeV respectively. For such DM candidates, a small amount of slepton coannihilation may decrease the e ective DM annihilation cross section. This, in turn reduces the lower limit of the relic density satis ed DM mass by more than 50%. Almost a similar degree of reduction of the same limit is also seen for squark coannihilations. However, on the contrary, for near degeneracy of squarks and higgsino DM, near its generic upper limit, the associated coannihilations may decrease the relic density, thus extending the upper limit towards higher DM masses. detection signals. Here, because of the quasi-mass degeneracy of the squarks and the LSP, we come across a situation where squark exchange diagrams may contribute signi cantly or more strongly than the Higgs exchange contributions in the spin-independent direct detection cross section of DM. For the higgsino-DM scenario, we observe that a DM mass of 600 GeV to be consistent with WMAP/PLANCK and LUX data for sfermion coannihilations. The LUX data itself excludes the region of 450 to 600 GeV, by a half order of magnitude of the cross-section, well below the associated uncertainty. The similar combined lower limit for a wino DM is about 1.1 TeV. There is hardly any collider bound from the LHC for squarks and sleptons in such a compressed scenario where sfermion masses are close to the mass of a higgsino/wino LSP.
1 Introduction 2 3 4
5
1
Results for relic density
3.1
3.2
3.3
Quasi degeneracy of electroweakino masses
Higgsino dominated LSP
Wino dominated LSP
Direct and indirect detection of DM
4.1
Direct detection
4.2 Indirect detection
Conclusion
Introduction
Sfermion coannihilations with Higgsino and wino types of LSP
One of the most interesting features of low energy supersymmetry (SUSY) [1{8] is that it
can provide with a viable candidate for dark matter (DM) [9, 10]. The lightest
supersymmetric particle (LSP), typically the lightest neutralino, in R-parity conserving scenarios
of the Minimal Supersymmetric Standard Model (MSSM) [1{8] is a strong candidate for
DM. In MSSM, the neutralinos are composed of gauginos (bino and wino) and
higgsinos.
Whether the LSP in a particular MSSM scenario is able to satisfy the right relic
abundance, depends crucially on its gaugino-higgsino compositions. For example, in the
minimal supergravity model (mSUGRA) [7, 8, 11{16] that assumes SUSY breaking at a
high scale, the LSP is bino-like for most of the parameter space. Bino being a gauge singlet,
its annihilation occurs mainly through t-channel exchange of sfermions, giving rise to the
bulk annihilation region [4{6]. With the discovery of a 125 GeV Higgs boson at the Large
Hadron Collider (LHC) of CERN [17{19], the sfermion masses are pushed towards higher
values, particularly for the universal models like mSUGRA. This makes bulk annihilation
rather an ine cient mechanism for obtaining the right relic density [20{25]. It is however
possible to have a bino-LSP giving the correct abundance of DM in some speci c regions
of parameter space of mSUGRA, like the stau coannihilation, funnel (resonant Higgs
annihilation) or hyperbolic branch (HB) [26{28]/ focus point (FP) [29{35] regions. While most
of the former two regions of parameter space are ruled out by the Higgs data [17{19], a
large part of the HB/FP region, which corresponds to a signi cant degree of bino-higgsino
mixing, is disfavored by DM direct detection experiments [36{39]. There is also a higgsino
LSP region in mSUGRA but this comes with a baggage of a very large gluino mass and a
{ 1 {
or models with non-holomorphic soft terms [
71, 72
].
Apart from bino, one may have the right relic abundance in MSSM if the LSP is a
higgsino, wino or a well-managed admixture of bino, wino and higgsinos [
73
]. For the
higgsino-like LSP scenario, the lightest neutralino ( e01
higgsino mixing parameter . In this case the lightest chargino e1 and the second lightest
neutralino e20 are almost mass degenerate with e10 with their masses are close to . For
a thermally generated single component dark matter, it has been typically accepted that
the LSP mass for obtaining the right DM abundance is around 1 TeV for a higgsino-like
and e1 are too strong causing the DM relic density to become underabundant.
0 0
LSP [27, 28, 36{39]. Below this limit the annihilation and coannihilations among e1, e2
On the other hand, a wino-like LSP may be possible to realize if M2 < (M1; ) where
M2 and M1 are the SU(2)L and U(1)Y gaugino mass parameters respectively. A wino may
be the candidate for LSP in many theoretically well-motivated models like the Anomaly
Mediated Supersymmetry Breaking (AMSB) [74{77]. For a wino LSP, me01 and m
very close to M2 allowing strong coannihilations. A thermally generated wino dark matter
lie
e1
is underabundant up to
2 TeV. It satis es the relic density data for a wino mass of
) mass is close to the value of the
scenario, have imposed stringent bounds on the masses of strong sector sparticles [89{
100]. The strong sector scalar masses are increasingly pushed above a TeV regime that is
even superseded by the gluino mass limits. On the other hand, the direct mass bounds
on the electroweak (EW) sector sparticles from the LHC searches are rather mild [101{
111]. In the context of mass limits of sparticles, we must however remember that the
LHC searches are restricted to the so-called \simpli ed models" that are characterized
e1
by certain assumptions on sparticle masses and compositions of the EW sector gauginos
(electroweakinos). The searches in the 3l + E=T channel [112] for example consider e10 to
be purely a bino and e1 = e02 to be completely wino dominated. Imposing basic constraints
like the Higgs mass, dark matter relic density and muon g
2 there have been studies that
e ectively probed the SUSY parameter space for the above types of electroweakinos [113{
132]. However, it turns out that the collider limits get signi cantly degraded once we start
varying the composition of the electroweakinos. This may be seen in ref. [133] where the
authors considered e1 to be higgsino dominated or a mixture of a wino and higgsinos in a
bino dominated LSP ( 0) situation. Similar to the above, changed composition of the LSP
itself may signi cantly alter the collider limits. For example, the trilepton search limits are
, e02 and e1 are
almost mass degenerate. This is simply because the resulting leptons come out to be very
1The spread of results depends on purity of wino, the extent of decoupling of the squark masses as well
soft. For collider studies of benchmark points that satisfy the observed relic density range,
one may however use monojet + E=T analysis [134, 135]. However, the bounds are seen
to be very weak [136]. Apart from all the above, collider bounds of sfermions including
also squarks get severely diluted if one considers a compressed scenario of sparticle masses
where the LSP is higgsino/wino dominated in its composition with its mass close to that
of sleptons and/or squarks as appropriate in a LSP-sfermion coannihilation study.
In this analysis we use a compressed SUSY scenario in a phenomenological MSSM
(pMSSM) [137] framework so as to explore how light the higgsinos and wino can become
while having relic density values within the phenomenologically accepted range. We will
consider appropriate coannihilations of the LSP separately with sleptons and squarks or
is generally bino (B~)-dominated in its composition [7, 8]. Except the t-channel slepton
exchange that requires very light sleptons or the s-channel Higgs modes, a bino typically
undergoes a tiny amount of self-annihilation that leads to overabundance in most of the
mSUGRA parameter space.
The situation changes when bino-slepton or in particular
bino-stau coannihilation comes into the picture. Here the non-relativistic threshold S-wave
coannihilation cross-sections such as
B~ lR and lR lR , lR being the right handed stau,
are not suppressed by fermionic mass factors. The above coannihilation cross-sections are
much larger than the self-annihilation cross-section of a highly bino-dominated LSP [139].
Thus, in mSUGRA, the coannihilation of e10 with ~1 is able to reduce the relic density
to fall within the WMAP/PLANCK [140, 141] speci ed range. A detailed analysis was
made in ref. [
142
] where all possible kinds of coannihilations were considered in a
binodominated LSP scenario in an mSUGRA setup. However, we must remember that masses
of sparticles in mSUGRA are correlated that causes mostly LSP-stau coannihilations to be
relevant. Thus, a signi cant amount of change in the DM relic density via coannihilations,
leads to an acceptable value, but this is possible only in a limited zone of parameter space.
Models with essentially unconstrained sparticle masses such as pMSSM when
considered in a compressed scenario are able to probe the true potential of coannihilations.
Here, the LSP may nd several coannihilating partners almost mass-degenerate with itself
that would overcome the associated exponential suppression encountered in computing the
e ective annihilation cross section. In this analysis, we will focus on higgsino and wino
dominated LSPs that undergo coannihilations with sfermions, both sleptons and squarks,
separately or together. We will see that there may be rather uncommon occurrences when
coannihilations may potentially cause a decrease in the e ective annihilation cross-sections,
thereby causing an increase in the DM relic density. This was discussed in refs. [143, 144]
where the latter reference named the coannihilating species as parasite degree of freedom
{ 3 {
in which the authors investigated the role of sleptons coannihilating with the LSP. In this
work, we will systematically analyze the e ects of coannihilations with all the sfermions
in a compressed scenario and probe the mass reach of the LSP as a higgsino/wino in
relation to the latest phenomenological constraints involving dark matter, Higgs mass and the
relevant bounds from collider data.
We emphasize that the e ect of considering a coannihilating particle, in particular
whether it would cause a decrease or increase of the relic density depends on several
factors [138, 143], namely, i) the annihilation cross section
0
i
0 of the coannihilating particle
0i with the LSP ( 0), ii) the cross section
0i 0i for the coannihilating particle annihilating
0i 0j , where i and j refer to di erent species of coannihilating particles,
iv) the relative mass gap between the sparticles namely, i =
thereby on the extent of exponential suppression, v) appropriate weight factors arising out
of the degrees of freedom of the associated particles undergoing coannihilations.
m 0i m 0 or ij =
m 0i m j
m i
We must remember that while a bino does not have any gauge charge, a higgsino (wino)
is associated with isospin 12 (1) . This translates into a larger internal degrees of freedom,
namely 8 for a higgsino and 6 for a wino type of LSP considering its Majorana nature.
Expectedly, a large number of internal degrees of freedom contributes more toward the
self-annihilation cross section of the LSP. In addition to the above, one must also consider
large coannihilations involving candidates like e1 , e02 for a higgsino type of LSP and
a wino type of the same. All the above lead to a substantially large e ective annihilation
e1 for
cross-section for the above two types of LSP. Among the coannihilating sfermions, the left
handed ones have larger internal degrees of freedom. This further gets multiplied by the
color degrees of freedom for squarks. In computing the e ective annihilation rates out of
individual cross-sections, one notes that the associated weight factors for di erent
coannihilating species play very important roles in either decreasing or increasing the total rate
itself. As mentioned before, unlike a bino LSP, a higgsino or a wino LSP is intrinsically
associated with a larger amount of self-annihilation as well as LSP-electroweakino
coannihilations. We will refer this as a generic higgsino or wino DM scenario. It turns out that in
a compressed sfermion scenario all the appropriate degrees of freedom of the coannihilating
sfermions may contribute to the averaging process toward <
e v > in such a way that
the latter becomes smaller than the case of having no sfermion coannihilations over most
of the parameter space satisfying the DM relic density limits. Thus, for a given LSP mass
the relic density increases. This on the other hand is synonymous with a decreased lower
limit of the mass of LSP satisfying the WMAP/PLANCK data. However, apart from the
typical trend mentioned above, we will come across a parameter region corresponding to
a higgsino as LSP where the outcome due to squark-squark coannihilations may become
dominant over the electroweakino part of the LSP depletion cross section.
We will also study the direct and indirect detection prospects for the types of DM
considered in this analysis. The LUX [145] experiment puts strong bounds on spin-independent
(SI) DM direct detection cross-sections. The e01 nucleon scattering cross-section that LUX
relies on is enhanced for su cient gaugino-higgsino mixing [146]. However, in our scenario
the cross section is supposed to be small for LSP being so pure, either a higgsino or a
{ 4 {
wino. On the other hand, the DM indirect detection experiments [147, 148] look for signals
coming from stable nal state particles of DM annihilation processes in the solar or galactic
cores. Since the sfermion-coannihilations make the smaller DM mass zones to become valid
in relation to the relic density data, it is important to
nd whether the indirect detection
rates can also be large for much smaller values of higgsino or wino masses satisfying the
DM relic density limits.
The paper is organized as follows. In section 2 we brie y discuss the e ect of sfermion
coannihilations in the calculation of the e ective cross-section. In section 3 we present
the relic density computation results for higgsinos and wino types of LSP by considering
slepton and squark coannihilations separately or together. We will start the section by
discussing the roles of the relevant electroweakino mass di erences that potentially a ect
the higgsino and wino relic density results. Constraints coming from the direct and indirect
DM detection experiments on our results are discussed in section 4. Finally, we conclude
in section 5.
2
Sfermion coannihilations with Higgsino and wino types of LSP
Let us consider the evolution of a class of particles i, i = 1; :::N , in the Early Universe. We
assume the particles are di erent from SM candidates by assuming an R-parity conserved
scenario of SUSY. The Boltzmann equation governing the number density ni of the i-th
kind of particle at any instant of time t is given by [143],
dn
dt
=
3Hn
h e vi n
2
ne2q ;
h e vi =
P
ij h ij vij inieqneq
neq2
j :
{ 5 {
dni =
dt
3Hni
X h
j6=i
X h
j6=i
N
X
j=1
h ij vij i ninj
nieqnjeq
h X0ij vij i ninX
ij (ni
nieq)
nieqneq
X
ji nj
neq i
j
;
h X0jivij i nj nX
njeqneq i
X
where the rst term is due to the expansion of the universe and H is the Hubble
parameter [10]. The second term arises because of coannihilations between i-th and j-th sparticles
leading to SM particles in the nal state i.e. for processes like i j ! X. The total
crosssection for scattering o the cosmic thermal background, iX !
j Y is given by X0ij ,
where X and Y are SM type of particles. The last term describes the decay of i and ij
refers to the total decay width for the processes i !
j X. Since in an R-parity conserving
neq
thermal equilibrium value i.e. nni ' nieq , eq. (2.1) leads to,
scenario all the existing sparticles will eventually decay into the LSP, its number density
is given as n = PiN=1 ni. Now, an assumption for the distribution of e01 maintaining its
where,
(2.1)
(2.2)
(2.3)
In the non-relativistic approximation, one has,
neq
nieq =
gi exp( x i)(1 + i)3=2
ge
;
(2.4)
where gi is the number of internal degrees of freedom of the i-th particle, i = mi m1 (for
i > 1), x = mT1 , m1 being the mass of the LSP and ge = PiN=1 gi exp( x i)(1 + i
)3=2.
m1
In this analysis with slepton and squark coannihilations each i corresponding to a
sfermion type i is allowed to vary up to a chosen limit
max. Thus, each sfermion mass
m ~ will have an upper limit of me01 (1 + max). max is chosen as 20% keeping in mind the
fi
exponential suppression within eq. (2.4). Considering a slepton coannihilation scenario in
pMSSM, as an example, we note that the rst two generations of sleptons do not di er much
in their mass values among themselves and these will be close to M~l (= M~lR ), the pMSSM
common slepton mass parameter.2 First, let us consider only the sleptons of the rst two
generations to undergo coannihilations. For a given me01 and max, the sleptons will have a
maximum mass value of me01 (1 + max) and this will be close to the maximum value of M~.
l
For a given LSP mass, calling the average of all the associated i values as , one nds that
the highest possible
becomes close to max, the chosen degree of maximum relative mass
deviation, irrespective of tan . Next, we allow the third generation of sleptons to have
mass values in the coannihilation zone. Consequent of the L-R mixing e ect (which is more
prominent for a larger tan ), m~1 and m~2 are largely separated among themselves. Only
the heavier stau will have its maximum mass value near me01 (1+ max) and all other sleptons
will have much smaller masses. Thus, the reach of M~l becomes smaller and so is the average
value of all the three generations of slepton masses. Hence, the average relative deviation
will have its maximum value signi cantly smaller than max, an e ect that would increase
with tan . Additionally, when LSP mass is in the smaller zone meaning a stronger degree
of electroweakino coannihilations, the requirement of slepton coannihilations increases so
as the satisfy the relic density limits. Thus, the slepton masses are needed to stay within
the close vicinity of me01 . Consequently,
smaller for a given mass of the LSP. Here, the aforesaid range becomes smaller because
of the stau L-R mixing since coannihilation e ects of both the staus are quite required
in the process. In other words, the stau masses cannot be too far away from me01 , or
the associated i values can not be large, thus avoiding an exponential suppression. It
follows that the minimum mass of the LSP satisfying eq. (3.1) becomes larger for a larger
tan . Similarly, squark coannihilations, in principle, will also show qualitatively identical
behaviour3 based on the availability of the all the generation of squarks for coannihilations.
However, we will consider only the rst two generations of squarks in this study keeping the
top-squarks in a decoupled zone because of a very large L-R mixing, particularly arising
as well as its range of variation both become
from the requirement of satisfying the Higgs mass data.
In regard to a book-keeping of the internal degrees of freedom (d.o.f.) we note that for
a given generation of the right and left handed sleptons like ~R;L there are 2 internal d.o.f.
2Only small di erences come from the D-term contributions of the left and the right sleptons as well as
sneutrinos.
3We will however point out a di erence for the higgsino LSP case in the heavier limit of the LSP.
{ 6 {
available for each R and L while the sneutrino ~ along with its anti-particle would have
one internal d.o.f. each. Thus, for a compressed slepton spectra undergoing coannihilations
with the LSP the total number of internal d.o.f. for all the three generations of sleptons
would be 18. For the squark coannihilations with only two generations are considered in
the analysis, the resulting internal d.o.f. amounts to 48 after accounting for the color d.o.f..
3
Results for relic density
In spite of the fact that the PLANCK [141] data for the DM relic density has a very
small uncertainty ( CDM h2 = 0:1199
0:0022), we note that there is about a 10% level
of theoretical uncertainty in computing the SUSY DM relic density [149, 150]. This is
approximately six times the observational uncertainty, as concluded in refs. [149, 150]. It
was shown that higher order SUSY-QCD corrections may cause a signi cant degree of shift
of the relic density in some scenarios and the uncertainty arising out of renormalization
scheme and scale variations can be quite signi cant. Several recent analyses used such a
degree of theoretical error or even more (see for example refs. [151, 152]). Thus, we will
use
e1
0:012 that leads to the following bounds.
micrOMEGAs version 3.2 [154]. We have also veri ed agreement with the code DarkSUSY [155]
by choosing various representative points over the parameter space.
Throughout the analysis we impose the Higgs mass range of 122 to 128 GeV considering
the uncertainty in computing SUSY Higgs mass mh with radiative corrections [156{161].
3.1
Quasi degeneracy of electroweakino masses
Since the electroweakino coannihilations play a dominant role in computing the DM relic
density both for higgsino and wino types of LSPs, it is important to discuss brie y the role
of the appropriate electroweakino mass di erences [162{168]. In regard to a higgsino type
of LSP, both the mass di erences m
e1
me01 and me02
me01 are important. Typically the
latter is about double the former at the tree level [164]. For a higgsino type of LSP, with
M2 > ; MW , an expansion in 1=M2 leads to the following tree level mass di erence [166].
m
e1
In the wino limit of the LSP, one has M2 < j j; jM1j causing the di erence m
become small. An expansion in 1= leads to the following tree level relationship [166].
m
e1
{ 7 {
Additional suppression comes for large tan
since sin2 (2 )
4=tan2 . Thus, the terms
up to the order 1= 3 are suppressed indicating the lowest contributing order to be 1= 4
which is given as follows [167].
m
e1
One nds that the above mass splitting is small even for moderate values of . Thus, the
radiative corrections for the two electroweakino masses or rather that of their di erence
become important [169{173]. The dominant corrections to the masses come from top-stop
and
(Z)-higgsino loops [169, 170]. On the other hand, the renormalization of the mass
di erence is controlled by the gauge boson loops as pointed out in refs. [165, 168]. However,
in our analysis we nd a non-negligible reduction in the mass gap when
and/or squark
masses are taken to be very large (
10 TeV) and we agree with the conclusion of ref. [164]
in this regard. In this analysis, since we are looking for slepton and squark coannihilations
with the LSP while trying to probe the lower mass limit of the latter, we undertake a
minimalistic approach of considering not too much di erent mass values for the scalars
among themselves. We also limit
so as to have only an adequate degree of wino purity
of the LSP while trying to respect naturalness [26{35, 174{176] as far as possible. Hence,
we will prefer not to take very large values for the scalar masses or .
3.2
Higgsino dominated LSP
A higgsino dominated LSP with mass close to
can be made out of the choice M2 > M1 >
. We will quantify the degree of higgsino content of the LSP via Zh de ned as Zh =
(N123 +N124), where Nij ; i; j = 1; 2; 3; 4 are the elements of the neutralino-mass diagonalizing
matrix [7, 8]. In particular, we have used the following choice: M1 = 2
and M2 = 2:4 .
We then vary
in the range of 100 GeV <
< 2 TeV that covers the typical relic density
satis ed higgsino mass zone of 1 TeV. In a correlated scanning setup, for each value of
we
vary the common slepton mass parameter for all the three generations of sleptons within
the range 50% below and above the value of . The common squark mass parameters are
chosen to be large (3 TeV). For squarks, we allow coannihilations only with the rst two
generations for reasons described in section 2 while taking sleptons as well as the third
generation of squarks to be heavy (3 TeV). As before, we vary
in the range of 100 GeV
<
< 2 TeV. Then, for each value of
we vary the common squark mass parameters for
the rst two generations within the range 50% below and above the value of .
Furthermore, while
being varied, we scan the trilinear soft breaking parameter At
from
7 TeV, so as to satisfy the higgs mass data. However, we must emphasize
that the choice of At has a very small impact in our study of sfermion coannihilations.
The squark mass parameters of the third generation as well as the electroweak symmetry
breaking (EWSB) scale are taken as 3 TeV throughout the slepton and squark
coannihilation studies. The SU(3)C gaugino mass parameter M3 is also chosen to be 3 TeV whereas
the mass of the CP-odd Higgs (MA) is set at 5 TeV. The latter avoids a Higgs resonance
annihilation region. In order to study the e ect of slepton coannihilations on the relic
density of DM, we make sure that the physical slepton masses stay within 20% of the LSP
{ 8 {
coannihilates with sleptons and sneutrinos of all the three generations apart from the usual LSP- e1
and LSP-e02 coannihilations for tan
LSP. The plot is obtained by varying
= 10 and 30 as appropriate to the case of a higgsino-type of
in a correlated higgsino-gaugino mass setup as explained in
the text. The black and red points refer to tan
= 10 and 30 respectively. The reference results with
no slepton coannihilations are shown in green and blue points for tan
All the points in the plot satisfy the lower and upper limits of DM relic density (eq. (3.1)). Clearly,
the above sfermion coannihilations reduce the lower limit of the LSP mass satisfying eq. (3.1) to
me01 ' 450 GeV from about 1 TeV. b) Similar plot with LSP-squark coannihilations along with
reference cases where squarks refer only to the rst two generations. The color codes are same as
those of (a). Reduction of the lower limit and enhancement of the upper limit of the LSP mass
are notable.
mass irrespective of the generation. The same is true for the case of rst two generations of
squarks while we analyze the e ects of squark coannihilations. We like to emphasize that
with the above nearly degenerate squark masses close to that of the LSP, the commonly
discussed LHC limits [177] for squarks would not apply to our scenario.
the LSP e ciently coannihilates with sleptons and sneutrinos of all the three generations.
We note that the LSP-sfermion coannihilations take place in the background of strong
electroweakino coannihilations. The signi cance of higgsino purity level in turn is directly
The squarks are taken to be very heavy (3 TeV). The reference results for the generic
higgsino LSP or the case of no sfermion coannihilations are shown in green and blue points
= 10 and 30 respectively. The black and red points refer to tan
= 10 and
30 respectively for the cases with slepton coannihilations. All the points in the scatter
plot satisfy the lower and upper limits of DM relic density. Clearly as seen in gure 1(a),
the slepton coannihilations reduce the lower limit of the LSP mass satisfying eq. (3.1) to
me01 ' 450 GeV for tan
1 TeV corresponding to the generic higgsino DM result. There is hardly any change in the
upper limit of the mass of LSP in this regard. The di erence of the lower limits for the
two values of tan
for the case of slepton coannihilations arises from the L-R mixing of
= 10 and
640 GeV for tan
= 30 respectively from about
{ 9 {
with respect to the mass of the LSP for the LSP-slepton coannihilation scenarios including also
sneutrinos, where the LSP is highly higgsino dominated in its composition. For a given slepton
mass labeled as m~li the relative deviation is given as i =
values of i for all the three generations of sleptons including all the internal degrees of freedom
of sleptons as mentioned in section 1. The two di erent colors namely cyan (circle) and brown
(square) refer to the cases of tan
= 10 and 30 respectively. b) The results of considering the
coannihilations of LSP with the rst two generations of squarks for tan
= 10 and 30. The color
the third generation of sleptons (section 2). A relatively larger spread of stau masses via
exponential suppression e ectively reduces the corresponding coannihilation contributions
toward the e ective cross section. The cases of no slepton coannihilations hardly depend
on tan . This is consistent with the discussion made in section 2. We extend the results
to LSP-squark coannihilations in gure 1(b). All the internal degrees of freedom are taken
into account including the colors. The sleptons, on the other hand, are chosen to be very
heavy (3 TeV) as mentioned before. The color codes are same as those of gure 1(a). Here,
squarks refer only to the rst two generations for reasons mentioned in section 2. For the
lower limit of the LSP mass, one
nds me01 ' 840 GeV irrespective of tan . In any case,
the above is rather a modest reduction from about 1 TeV corresponding to the case of a
generic higgsino DM. We must also note that for squark coannihilations the upper limit of
me01 is stretched by about 200 GeV corresponding to the no sfermion coannihilation case.
In this zone of large LSP mass, the relic density decreases compared to the generic higgsino
DM case due to the dominance of squark-squark coannihilations. We will come back to it
for further discussion while describing gure 2(b).
Figure 2 shows scattered points in the me01
gure 1. Figure 2(a) shows the scatter plot in the (me01
with sleptons. The points that correspond to satisfying the DM relic density limits of
eq. (3.1) have two di erent colors namely cyan (circle) and brown (square) representing
the cases of tan
= 10 and 30 respectively. The left and right hand side white regions
indicate LSP to be underabundant and overabundant respectively. The regions with large
plane corresponding to the analysis of
) plane for LSP coannihilating
are associated with smaller degrees of coannihilation. The brown region corresponding
to tan
= 30 has a larger degree of stau L-R mixing. This follows from the discussion
made in section 2. Thus, compared to tan
= 30, the e ect of slepton coannihilations is
more prominent, thereby meaning the lower limit of the LSP mass to become smaller for
tan
= 10. As seen in the gure, this leads to a higgsino dominated LSP with mass as
low as 450 GeV satisfying eq. (3.1). The associated coannihilating sleptons correspond to
less than 2%. We also note that as explained in section 2 as well as in the description of
gure 1(a), an analysis with only the rst two generations of sleptons would hardly show any
dependence on tan
concerning the lower limit of the LSP mass satisfying the relic density
constraint of eq. (3.1). Figure 2(b) shows the result for the LSP-squark coannihilations
where we have considered only the rst two generations of squarks for which the outcome
is essentially independent of tan . On the lower side, the LSP mass satisfying eq. (3.1)
is reduced to around 840 GeV from 1 TeV corresponding to the generic higgsino DM case.
On the other end, the higgsino LSP mass may extend to about 1300 GeV, about a 20%
increase than the generic higgsino DM upper limit. There is a \notch" region corresponding
to
0:05 spreading across the values of the LSP mass. In this quasi degenerate
LSPsquark setup, the above arises due to a relatively rapid change of the DM relic density
coming out of the enhancement of qq~~01;2 e ective couplings. We will discuss this at the
end of section 4.1.
In the zone of relatively large LSP mass and for nearly degenerate squarks and the
LSP i.e. small values of , a detail check of the outgoing products of annihilation and
coannihilations con rms that the squark-squark coannihilations dominate over the generic
higgsino DM e ective annihilation cross-section.
We note that the latter, which is
inversely proportional to the DM relic density, decreases with increase in higgsino mass.4
Additionally, for larger values of
and larger LSP mass, in spite of a smaller degree of
generic electroweakino annihilation/coannihilations due to heavier LSP, the squark-squark
coannihilations are more and more exponentially suppressed. Thus, even for slightly larger
values of
we get overabundance of DM.
The result of a combined analysis of the above slepton (three generations) and squark
coannihilations (two generations) is given in gure 3. The colors refer to the same
convention as that of gure 2. The top-squark masses are chosen to be very heavy (3 TeV). The
left and right hand side blanck regions indicate LSP to be underabundant and
overabundant respectively. Here, a large number of sfermions participate in coannihilations and the
region with small LSP mass that would have otherwise underabundant DM gets the right
amount of relic density even for relatively larger values of . The relic density is clearly
enhanced thus satisfying eq. (3.1). However, among a variety of participating
coannihilation channels, predominant contributions still come from electroweakino coannihilations.
4For the generic higgsino LSP case one has
relation for a wino LSP with mass mW~ reads
e1
0 h2 = 0:10( 1 TeV )2 [
73
], where is given in TeV. A similar
W~ h2 = 0:13( 2:5 TeV )2 = 0:021m2W~ [
73
], denoting a factor of 5
mW~
stronger e ective annihilation cross section compared to the higgsino case. As we will see the squark-squark
coannihilation contributions are not large enough to supersede the generic wino DM depletion cross section.
Hence, the wino dominated LSP scenario with squark coannihilations will not encounter any stretching of
the LSP mass region satisfying the relic density data on the higher side.
as mentioned in the text. The cyan (circle) and brown (square) points refer to tan
respectively. All the points in the scatter plot satisfy the lower and upper limits of DM relic density
of eq. (3.1). The lower limit of the higgsino LSP mass satisfying the DM relic density constraint is
around 500 GeV.
The lower limit of the higgsino LSP mass satisfying the DM relic density constraint is
around 500 GeV.
3.3
Wino dominated LSP
A wino-like LSP in MSSM implies nearly degenerate e10 and e1 , both of whose masses
being essentially determined by the SU(2) gaugino mass parameter M2. The smallness
of mass di erence between me01 and m
a relic density too low to satisfy the obsee1rved limits unless the mass of wino is too large
leads to intense coannihilations resulting into
(above 2 TeV). A choice like M1 >
> M2 would give rise to a wino dominated LSP. In
particular, we choose
= 2M2 and M1 > 2:4M2, so as to make the LSP predominantly
a wino. M2 is then varied in the range 100 GeV < M2 < 2.5 TeV. For slepton
coannihilations and a given value of M2, the common mass parameter for the slepton masses of
all the three generations are varied within the range 50% below and above the value of
M2. The common squark mass parameters are pushed to 4 TeV. On the other hand, for
squark coannihilations, the common squark mass parameter of the rst two generations are
similarly chosen around the value of M2, while the latter being scanned as before. Here,
the slepton mass parameters are large (4 TeV). The squark masses of the third generation
and the SU(3) gaugino mass parameter M3 are kept at 4 TeV while the CP-odd Higgs
mass is set at 6 TeV throughout our analysis, thus ensuring no s-channel Higgs resonance
annihilations. Once again, owing to the variation of M2 that results into varying
we scan
At between
2 TeV to
7 TeV so as to have the higgs mass mh in the correct range. It
can be observed from
gure 4 that in the absence of any slepton coannihilation the relic
coannihilations. The cyan (circle) and brown (square) points refer to tan
coannihilates with sleptons and sneutrinos of all the three generations apart from the usual LSP- e1
All the points that are generated by varying M2 satisfy the lower and upper limits of DM relic density
of eq. (3.1). Clearly, the slepton coannihilations reduce the lower limit of the LSP mass satisfying
the WMAP/PLANCK data to me01 ' 1:1 TeV. b) Similar plot with LSP-squark coannihilations
along with reference cases with no LSP-squark coannihilations where squarks refer only to the rst
two generations. The color codes are same as those of (a).
e1
density becomes viable for m 0
1.8 TeV.5 The presence of sleptons with masses close to
e1
m 0 leads to many new coannihilation channels and a ects the averaging procedure toward
the e ective cross section and as we will see this increases the DM relic density so that
eq. (3.1) is satis ed for much smaller masses of the LSP.
The amount of the wino component in the LSP is expressed in terms of the wino
fraction de ned as, ZW = N122. The wino fractions for di erent LSP masses with/without
sfermion coannihilations are shown in
gure 4. We only show the parameter points that
satisfy eq. (3.1) for the limits of DM relic density. Figure 4(a) shows the scatter plot of
the wino fraction ZW vs LSP mass when the LSP e ciently coannihilates with sleptons
and sneutrinos of all the three generations. We note that the LSP-sfermion coannihilations
take place in the background of strong electroweakino coannihilations. The signi cance
of wino purity level in turn is directly related to the level of coannihilations between the
5We must note that a wino mass of 1.8 TeV satisfying the relic density data is low compared to what is
seen in the literature, typically above 2 TeV. Obtaining a heavier wino that satis es the DM relic density
limits is possible i) via considering larger sfermion mass and
as explained in the text in section 3.1 and ii)
most importantly, via including non-perturbative e ects like Sommerfeld correction. Sommerfeld correction
is known to increase the wino mass that satis es the relic density limits. We have not included such an
e ect particularly for the fact that a low wino mass like 1.1 TeV would hardly have an appreciable degree
of Sommerfeld e ect. We would like to mention ref. [81] (their
gure 2) and ref. [82] (their
gure 2) in
support of the smallness of the correction for our relevant zone of wino mass. Considering the fact that
the relic density / M22, using ref. [82] we estimate a 10-12 % level of enhancement of M2 for its lower
bound that would satisfy the observational relic density limits. Thus, the lower limit of the wino mass is
estimated to change from 1.1 TeV to around 1.2 TeV (as we will come across in
gure 4) if we include the
Sommerfeld e ect.
electroweakino states e10 and e1 . As before, we have considered a maximum of 20%
deviation in masses for the coannihilating particles with respect to the mass of the LSP.
The squark masses of the rst two generations are kept at 4 TeV . The reference results
with no slepton coannihilations are shown in green and blue points for tan
respectively. The black and red points refer to tan
= 10 and 30 respectively for the cases
with slepton coannihilations. Clearly, as seen in
gure 4(a), the slepton coannihilations
respectively for tan
reduce the lower limit of the LSP mass satisfying eq. (3.1) to me01 ' 1:1 TeV and 1.3 TeV
= 10 and 30. There is a dissimilarity in the lower limits in the
results for the two di erent values of tan
for similar reasons as in the case of higggsino
LSP mentioned in section 3.2.
We extend the results to LSP-squark coannihilations in
gure 4(b). Here the sleptons are chosen to be very heavy (4 TeV). The color codes are same
as those of gure 4(a). The squarks again refer only to the rst two generations for reasons
mentioned earlier. One nds the lower limit as me01 ' 1:1 TeV for both values of tan .
while considering the coannihilations of LSP separately with sleptons or squarks where the
LSP is wino dominated in its composition. This refers to the scanning corresponding to
gure 4. The colored points belong to parameter space that satisfy eq. (3.1). Figure 5(a)
shows the scatter plot in the (me01 - ) plane. Apart from the sleptons we also include the
three generations of sneutrinos in this analysis.
is similarly de ned as in the higgsino
case of section 3.2. The color codes are same as those of gure 2. The left and right hand
side white regions indicate LSP to be underabundant and overabundant respectively. The
regions with large
refer to smaller degrees of coannihilation because of larger exponential
suppression. The brown region corresponding to tan
= 30 is associated with a larger
degree of stau L-R mixing. Demanding both ~1 and ~2 along with the rst two generations
of sleptons to have masses within 20% of the LSP mass restricts the reach of
for reasons
mentioned in section 2. The e ect of slepton coannihilations is more prominent for tan
=
10 and this leads to a wino dominated LSP having the right abundance with mass as low
as 1.1 TeV when the coannihilating sleptons have
less than 2%. Similar to the higgsino
analysis, the tan
exist if we had excluded the third generation of sleptons to take part in coannihilations.
dependence of the lower limit of me01 satisfying eq. (3.1) would cease to
Figure 5(b) shows a similar result for the LSP-squark coannihilations where we consider
only the rst two generations of squarks as before. Clearly, being devoid of any top-squark
coannihilations the result is essentially independent of tan . The lowest LSP mass that
satis es the DM relic density constraint is around 1.1 TeV. Unlike the higgsino case, there
is no dominance of squark-squark coannihilations over the parameter space that satis es
the DM relic density constraint. This is indeed related to the large annihilation cross
section that a wino has compared to that of a higgsino for a given mass of the LSP (see
footnote# 4). Similar to the higgsino case, there is a \notch" region corresponding to
0:05 spreading across the values of the LSP mass. In this quasi degenerate LSP-squark
setup, the above arises due to a relatively rapid change of the DM relic density coming out
of the enhancement of qq~~01 e ective coupling. We will discuss this at the end of section 4.1.
The results of a combined analysis of the above slepton (three generations) and squark
coannihilations (two generations) is given in gure 6. The two di erent colors namely cyan
respect to the mass of the LSP for LSP-slepton coannihilation scenarios including also sneutrinos,
where the LSP is highly wino dominated in its composition. For a given slepton mass labeled as
(ml~
m 0
i me01 ) .
e1
m~li the relative deviation is given as i =
refers to the average of the values of i
for all the three generations of sleptons including all the internal degrees of freedom of sleptons as
mentioned in section 1. The two di erent colors namely cyan (circle) and brown (square) refer to
= 10 and 30 respectively. b) The results of considering the coannihilations of LSP
with the rst two generations of squarks for tan
= 10 and 30. The color scheme is similar to (a).
(circle) and brown (square) refer to the cases of tan
= 10 and 30 respectively. The left
and right hand side white regions indicate LSP to be underabundant and overabundant
respectively. The regions with large
refer to smaller degrees of coannihilation. The lower
limit of the wino LSP mass satisfying the DM relic density constraint is around 900 GeV.
We would like to mention here that the ATLAS and CMS collaborations presented
their results for chargino searches in the high transverse momentum (pT ) disappearing
tracks [178, 179] and long lived particle search channels for nearly degenerate e1 and
e10 [180, 181]. The mass range of e1 considered in this analysis is well within these bounds.
4
Direct and indirect detection of DM
In this section we will probe the prospect of direct and indirect detection of the lightest
neutralino. We will particularly come across the importance of squark exchange diagrams
in computing the SI direct detection cross section. The squark exchange diagrams are
usually less important since the Higgs exchange diagrams typically dominate. As we will
see, in this analysis we are in a di erent situation because of considering quasi-degenerate
squarks and LSP for the requirement of coannihilations.
4.1
Direct detection
Direct detection of DM involves
nding the recoil energy deposited when a DM
particle scatters o
a detector nucleus [9, 10]. Spin-independent LSP-proton scattering may
take place through s-channel squark exchange and t-channel Higgs exchange diagrams.
as mentioned in the text. The cyan (circle) and brown (square) points refer to tan
respectively. All the points in the scatter plot satisfy the lower and upper limits of DM relic density
of eq. (3.1). The lower limit of the wino LSP mass satisfying the DM relic density constraint is
around 900 GeV.
nate [
182, 183
].6
form [146]:
When the squarks are considerably heavy, the Higgs exchange diagrams typically
domiThe Higgs- e01- e10 coupling for the higgsino-LSP case can be written down in the
1
1
2
Ch ~ ~ '
MZ cW 1
sin 2
CH ~ ~ ' 2
MZ cW cos 2
t
2
W
M1
j j
M1
t
2
W
+
j j
M2
+
1
M2
j j
1
;
j j
;
where tW = tan W etc. with
W being the Weinberg angle. Similarly, for the wino-LSP
case, the couplings are as follows [146]:
(4.1)
(4.2)
Ch ~ ~ '
CH ~ ~ '
MZ cW
M22
2
MZ cW
M22
2
M2 +
sin 2 ;
cos 2 :
From the above expressions it is clear that the couplings and hence the scattering
cross-section would be large if there is a large degree of mixing between the gaugino and
the higgsino components of the LSP. We also note that couplings become weaker for
increased gaugino masses and . On the other hand, a pure higgsino or a wino LSP with
6On the contrary, we will soon discuss the scenario when the squark exchange diagrams may even
dominate over the Higgs exchange diagrams.
for higgsino dominated LSPs undergoing LSP-slepton coannihilations. The cyan and brown points
= 10 and 30 respectively that satisfy eq. (3.1). The red line (solid) is the LUX 2016
exclusion contour and the maroon dashed line shows the expected limit from the future XENON1T
experiment. (b) Same as (a) except LSP undergoing LSP-squark coannihilations. (c) Same as (a)
except LSP undergoing slepton plus squark coannihilations.
very little mixing can hardly be able to produce large values of spin-independent
crosssection. Figure 7 shows our results for DM direct SI detection cross-section where only the
points satisfying eq. (3.1) are shown for a higgsino type of LSP undergoing LSP-slepton
coannihilations ( gure 7(a)) and LSP-squark coannihilations ( gure 7(b)). The cyan and
brown points correspond to tan
= 10 and 30 respectively. The red line (solid) is the
LUX 2016 exclusion contour [145] and the maroon dashed line shows the expected limit
from the future XENON1T experiment [
184
]. Clearly, the recent LUX data rules out low
higgsino mass region below 600 GeV ( gure 7(a)). We must also remember the existence of
uncertainty, around one order in magnitude, in the computation of the SI direct detection
cross-section. Factors like strangeness content of nucleon, local DM density, velocity
distribution pro les, all contribute toward such uncertainty amount (see ref. [113] and references
therein). As seen in gure 7(a) the higgsino LSP scenario may be e ectively probed via
XENON1T. Figure 7(b) shows similar results for the LSP-squark coannihilations. Here,
the lowest LSP mass that survives after the LUX 2016 data is about 840 GeV. Additionally,
a large region of parameter space7 is discarded via the same experiment without however
a ecting the lowest possible value of the LSP mass. Compared to the case of gure 7(a)
here the SI direct detection cross-sections are generally large. This is a signature of having
a quasi-degenerate squark and LSP scenario that comes into our study of the LSP-squark
coannihilations. Here the e ective coupling constant for quark-LSP scattering drastically
increases [185] causing the cross-section to be larger, often much more than the LUX limit
for a signi cant zone of the LSP mass. Thus, the squark exchange diagrams are potentially
able to compete with or even dominate over the Higgs exchange diagrams while
contributing to the total direct detection cross-section.8 This is of course true for some region of
parameter space where the degree of the LSP-squark mass degeneracy is higher. We remind
that the above is unlike the usually encountered MSSM parameter regions where Higgs
exchange diagrams dominate over the squark exchange diagrams in the SI direct detection
cross-section. Coming back to gure 7(b) we see that a lot of parameter space is eliminated
via LUX 2016 data. The remaining parameter space can fully be probed in the XENON1T
experiment. The e ect of including both slepton and squark coannihilations is shown in
gure 7(c). The lowest LSP mass limit satisfying the LUX data is around 680 GeV.
Figure 8 shows our results for DM direct SI detection cross-section where only the
points satisfying eq. (3.1) are shown for a wino type of LSP undergoing slepton
coannihilations ( gure 8(a)) and squark coannihilations ( gure 8(b)). The cyan and brown points
correspond to tan
= 10 and 30 respectively. The red line (solid) is the LUX 2016
exclusion contour [145] and the maroon dashed line shows the expected limit from the future
XENON1T experiment [
184
]. Clearly, as seen in gure 8(a) the cross-section is too low so
that even XENON1T would not be able to probe this scenario except around the 1.1 TeV
region for LSP mass. We must additionally clarify that a comparison of gure 7(a) and
gure 8(a) shows that contrary to what we would naively expect, the SI cross-section in
the latter case is in general smaller. The reason lies in the fact that the values of me01
that satisfy the relic density limits for a wino like LSP are much higher than that of a
higgsino dominated LSP. Figure 8(b) shows similar results for the LSP-squark
coannihilations. Here, the lowest LSP mass that survives after the LUX 2016 data is about 1.27 TeV.
Additionally, a large region of parameter space is discarded via the same experiment while
eliminating a window of 1.1 TeV to 1.27 TeV of LSP mass. XENON1T would not be able
to probe this scenario except the region close to 1.2 TeV of the LSP mass. Similar to the
case of higgsino-squark coannihilations, the SI direct detection cross-section is much larger
for wino-squark coannihilation scenario compared to the wino-slepton results. The squark
exchange contributions can be signi cantly large for the parameter points associated with
near degeneracy of the squark and LSP masses as explained before. Here, we observe that
the cross-section can be quite large even for squark masses > 1.2 TeV. The Higgs-exchange
contributions are sub-dominant in this case of wino-dominated LSP that has a very small
7By parameter space one really means here a smeared region of squark masses around a given LSP mass.
8The extent of any cancellation e ect on the contrary is small, unlike the wino scenario that we will
see soon.
HJEP09(217)64
for wino dominated LSPs undergoing LSP-slepton coannihilations. The cyan and brown points
represent tan
= 10 and 30 respectively that satisfy eq. (3.1). The red line (solid) is the LUX 2016
exclusion contour and the maroon dashed line shows the expected limit from the future XENON1T
experiment. (b) Same as (a) except LSP undergoing LSP-squark coannihilations. (c) Same as (a)
except LSP undergoing slepton plus squark coannihilations.
higgsino content. We must also note that for a xed value of me01 we get a wide degree of
variation in cross-section with some points exceeding the LUX limit whereas some points
having values below the limit. In the latter case there is a cancellation among the
contributions from the squark and Higgs exchange diagrams that pushes the cross-section to
very low values. Similar to what happens for the higgsino LSP case as in
gure 7(b), this
is a signature of quasi-degenerate squarks and LSP that leads to a large increase in the
e ective coupling constant for quark-LSP scattering [185].
Finally, the e ect of including both slepton and squark coannihilations is shown in
gure 8(c). The lowest LSP mass limit satisfying the LUX data is about 1 TeV.
We will come to the discussion of the notch regions of gure 2(b) and gure 5(b). Apart
from direct detection, enhancement of qq~~ e ective coupling near the degenerate zone of
squarks and LSP masses has its important signature also on the DM relic density. For a
(c)
wino dominated LSP that does not have a quasi degenerate neutralino state, the notch
region is found to coincide with the mentioned cancellation region of SpI (i.e. cancellation
between the higgs exchange and the squark exchange diagrams). Corresponding to a given
mass of the LSP, this is the region of
where the above e ective coupling becomes large.
The situation for a higgsino-LSP case is more involved. This is principally because on the
top of the coannihilations a wino LSP would undergo, there are additional coannihilation
0 0
processes like e2 e1
, e02q~ contributing toward the higgsino relic density. As a result, in
spite of a cancellation zone of SpI for certain values of , coannhilation e ects potentially
smear the abrupt change in the higgsino relic density coming out of the e ect of enhanced
correspond to a cancellation or an enhancement zone in
e01q~q and e20q~q coupling strengths. Consequently, for a higgsino DM the values of
SpI are not the same where the
that
anomalous \notch" zone of the relic density occurs. However, the enhancement of coupling
remains a valid fact. It is seen that for a given me01 there is an abrupt decrease of the DM
relic density corresponding to some range of . Once a lower and a upper limit of the relic
density are imposed, the above decrease in relic density irrespective of the LSP mass, leads
to the formation of the notch regions for some e ective range of values of . Details may
be explained by examining the relevant coupling enhancements as given in ref. [185].9
DM particles may get trapped due to gravity inside astrophysically dense objects like the
Sun or the Earth by losing energy through repeated scattering with the nucleons. Inside
the core of these objects DM particles may undergo pair annihilations leading to SM
particles like fermion-antifermion pairs, gauge bosons etc. in the nal state. The resulting
antiparticles, neutrinos and gamma rays can o er interesting indirect signals of DM in
the galaxy.
The high energy neutrinos produced as end products of DM pair annihilation in the
solar core can produce muons through charged current interactions. The IceCube
experiment [147] provides bounds on the muon
ux for the pair annihilation channel DM DM
! W +W . Figure 9(a) shows a scatter plot of the values of muon
ux as a function of
satisfying eq. (3.1). The cyan and brown points correspond to tan
me01 for higgsino dominated LSPs undergoing slepton coannihilations for parameter points
= 10 and 30
respectively. The green and blue lines are the current and projected limits from the IceCube
experiment [147, 148] in the e1 e1 ! W +W
0 0
results for LSP-squark coannihilations. Clearly, the uxes in both the above gures are in
channel. Similarly, gure 9(b) shows the
general too small to be probed.
The results of muon
ux for the case of a wino dominated LSP is shown in gure 10.
Figure 10(a) shows the results for LSP-slepton coannihilations for parameter points that
satisfy eq. (3.1) for wino dominated LSPs undergoing slepton coannihilations. The color
convention and the details of the limits from IceCube data are similar to gure 9(a). Clearly,
the
ux is too small to be probed for the LSP-slepton coannihilation scenario. Similarly,
gure 10(b) shows the results for LSP-squark coannihilations. The result does not show
9Speci cally we refer eqs. 15 to 17 and A8 to A14 of the paper.
HJEP09(217)64
nihilations for tan
= 10 (cyan) and 30 (brown) while satisfying eq. (3.1). Present and future
IceCube limits are shown as green and blue lines respectively. (b) same as (a) except the LSP is
undergoing LSP-squark coannihilations.
lations for tan
= 10 (cyan) and 30 (brown) while satisfying eq. (3.1). Present and future IceCube
limits are shown as green and blue lines respectively. (b) same as (a) except the LSP is undergoing
LSP-squark coannihilations.
any more exclusion of low mass LSP region compared to what is seen in gure 8(b) for the
SI direct detection cross section.
Let us now discuss the constraints on spin-dependent DM-nucleon interaction
crosssection as derived from the IceCube data. Inside the solar core, the number density N of
DM particles at any instant of time t is obtained from the following [9],
dN
dt
= Cc
CAN 2;
(4.3)
where, Cc is the capture rate of DM by interaction with the nucleons present at the surface
of the Sun whereas CA is related to the annihilation rate
A as:
of eq. (4.3) leads to
A = 12 Cc tanh2(t= ), with
= pC1cCA . Hence, the capture rate is
A = 21 CAN 2. Solution
LSPs undergoing LSP-slepton coannihilations for tan
= 10 (cyan) and 30 (brown) while satisfying
eq. (3.1). Present and future IceCube limits are shown as green and blue lines respectively. (b)
Same as (a) except the LSP is undergoing LSP-squark coannihilations.
determined by the annihilation rate and when the age of the universe is much greater than
(which occurs for large Cc and CA), an equilibrium is reached so that A = 12 Cc. Thus,
it is possible to put bounds on the annihilation and capture cross-sections by looking at
the indirect DM signals from the Sun. Since, capture of the DM particles occurs through
spin-independent/dependent (SI/SD) DM interactions with the nucleons, these bounds get
translated into the bounds on DM SI/SD interaction cross-sections.
e01 can have spin-dependent interaction with the quarks via s-channel squark exchange
and t-channel Z-boson exchange processes. Similar to the SI case, while considering
LSPslepton coannihilations, we can safely ignore the contributions from the squark exchange
by cZ e01 e10 =
processes since the squarks are taken to be heavy. The tree level Z e01 e01 coupling is given
N123
N124 . For the higgsino LSP case the coupling is given as [146],
cZ e01 e10 '
1
2
tW M1
2 m2W +
m2W
M2
cos 2 + O
;
M1 M2
;
with
> 0( < 0). The same coupling for the wino case takes the form [146],
cZ e01 e10 ' M22
m2W
2 cos 2 :
Thus, in general the couplings get suppressed as the LSP, irrespective of a higgsino or
a wino becomes heavy. Figure 11(a) shows the results for the SD cross section for the
higgsino dominated LSP scenario for LSP-slepton coannihilation. Figure 11(b) shows the
LSP-squark coannihilation case for which the degeneracy between squark and the LSP
masses (similar to what was described in the SI case) may push up the SD cross section.
In general the IceCube limits would be inadequate to probe such higgsino models.
Figure 12 shows the results for the SD cross section for the wino dominated LSP
scenario for LSP-slepton coannihilation ( gure 12(a)) and LSP-squark coannihilation (
gure 12(b)) cases. Although the IceCube limits may eliminate some region of parameter
(4.4)
(4.5)
undergoing LSP-slepton coannihilations for tan
= 10 (cyan) and 30 (brown) while satisfying
eq. (3.1). Present and future IceCube limits are shown as green and blue lines respectively. (b)
Same as (a) except the LSP is undergoing LSP-squark coannihilations.
space where the LSP undergoes squark coannihilations, the result does not show any more
exclusion of low mass LSP region compared to what is seen in gure 8(b) for the SI direct
detection cross section.
In table 1 we show two benchmark points (BP) satisfying WMAP/PLANCK relic
density limits of eq. (3.1) as well as the direct and indirect detection limits from the LUX and
IceCube experiments respectively. BP1 and BP2 correspond to the case of a higgsino-LSP
undergoing slepton and squark coannihilations for masses 617 GeV and 760 GeV
respectively for tan
= 10.
Monojet searches at the 14 TeV LHC can probe pure higgsino
410 GeV [186]. However, the situation looks more
scenario only upto the mass of me01
promising for a 100 TeV collider where higgsinos may be probed upto 1.2 TeV. Existing
disappearing track searches at the LHC do not have much sensitivity to a higgsino LSP.
However, with modi cations in search strategy, as suggested in refs. [187, 188], higgsinos
upto
600 GeV and
1.1 TeV could be probed by the 14 TeV high luminosity (HL)-LHC
and a 100 TeV collider respectively. BP3 and BP4 refer to wino-like LSP participating in
slepton and squark coannihilations with masses 1011 GeV and 1188 GeV respectively for
the same value of tan . Although a HL-LHC at 14 TeV seems to be unable to probe these
benchmark points, a 100 TeV collider, with an exclusion reach of
1.8 TeV in the monojet
search channel can decisively explore such scenarios [186]. These benchmark scenarios for
wino-like DM is likely to evade the HL-LHC even with disappearing track searches.
However, the same searches at a 100 TeV collider can conclusively probe these cases. Apart
from collider searches, all the four BPs will be probed in near future with the XENON1T
experiment. However, they are unlikely to produce any signal in future indirect detection
experiments.
Higgsino DM
Wino DM
BP1
me02 (GeV)
me03 (GeV)
M~(e; )L (GeV)
M~(e; )R (GeV)
e
e
m 1 (GeV)
m 2 (GeV)
M~ (GeV)
Mu~L (GeV)
Md~L (GeV)
Mu~R (GeV)
Md~R (GeV)
Mt~1
mh
~h2
SI
SD
10 9 (pb)
10 6 (pb)
(km 2yr 1)
HJEP09(217)64
direct detection bounds from the LUX and indirect detection constraints from the IceCube. All
the benchmark points are for tan
= 10. BP1 (BP3) and BP2 (BP4) correspond to the case of a
higgsino (wino)-LSP undergoing slepton and squark coannihilations respectively. The relevant SM
parameters used are mtpole = 173:2 GeV, mbMS = 4:19 GeV and m
= 1:77 GeV.
A bino-dominated LSP generally produces overabundant DM. A bino-like LSP relies mostly
on the bulk-annihilation or t-channel slepton exchange mechanism, a disfavored scenario
in the context of LHC data. A bino can also be a DM candidate with the help of
coannihilations with sleptons (typically staus), or coannihilations with suitable electroweakinos
as in the Focus Point/Hyperbolic Branch region, or it can take the help of s-channel Higgs
mediation for pair annihilation in order to satisfy the DM relic density limits. On the
other hand, in MSSM there are theoretical as well as phenomenological motivations to
study higgsino and wino-dominated LSPs. When the LSP turns out to be a higgsino, these
for a wino-LSP situation include coannihilations between e10 and
0 0
processes include pair-annihilation and coannihilations among e1; e1 and e2
e1 . It is known that
. The same
these processes are too strong to cause the LSP to become an underabundant component
of DM unless its mass is around 1 TeV for a higgsino or a little above 2 TeV for a wino type
of LSP. We consider a compressed scenario of pMSSM where sfermions may take a very
signi cant role as coannihilating sparticles. Our purpose is to examine how light the LSP
as a higgsino or a wino can be while it satis es both the lower and the upper limit of the
DM relic density as given by the WMAP/PLANCK data. We choose two representative
values of tan , namely 10 and 30 and consider both sleptons and squarks as coannihilating
partners. In regard to the LSP-slepton coannihilations we consider all the three
generations of sleptons including also the sneutrinos while keeping the squark masses heavy. We
perform the analysis by requiring a maximum of 20% mass di erence between that of the
LSP and each of its coannihilating partners. Consideration of the slepton coannihilations
reduces the e ective cross section leading to an increase in the relic density. This is how
the relic density gets modi ed or in other words this is how the lower limit of the LSP
mass satisfying the relic density limits decreases. We
nd that for a higgsino dominated
LSP the lowest LSP mass that satis es the relic density limits is about 450 GeV, about
a 60% reduction corresponding to the case of no sfermion coannihilations and this occurs
for tan
= 10. The dependence on tan
comes via the L-R mixing of tau-sleptons and
the exponential suppression generically associated with coannihilation toward the e ective
annihilation cross-section. The same reduction in the lower limit for a wino type of LSP
occurs for tan
= 10 and it is about 1.1 TeV, more than a 100 percent reduction in the
value corresponding to the case of no sfermion coannihilations. For squarks, we allowed
coannihilations with only the rst two generations of squarks while imposing a similar 20%
limit as before for the deviation of masses of the coannihilating particles from the LSP
mass keeping the third generation of squarks as well as sleptons of all the generations very
heavy. The reason of omitting the third generation lies in the fact that a large splitting
between the two top-squark masses as required by a 125 GeV Higgs boson would take away
a lot of parameter space if we need a uniform 20% limit for the di erence of each of the
squarks and the LSP masses. In the absence of coannihilating third generation of squarks,
our results become essentially independent of tan . The lowest LSP mass satisfying the
relic density limits is about 840 GeV for the higgsino case, only a modest reduction by
10-15% from the generic higgsino LSP scenario. For the higgsino-squark coannihilation
scenario we additionally obtain a region of parameter space where the relic density is
decreased when squark coannihilations come to the picture, thus increasing the upper limit
of the LSP mass satisfying the relic density data. This happens only in a very limited zone
of parameter space with nearly degenerate squark and LSP masses and toward the end of
the upper limit of the LSP mass satisfying the DM relic density data. Coming to wino,
the lower limit of the LSP mass with the above squark coannihilations is around 1.1 TeV.
Additionally, computation for a scenario of combined slepton and squark coannihilations
shows that the lower limit of higgsino-LSP is about 500 GeV whereas for a wino-LSP the
same is about 900 GeV. We also note that throughout our study we consider the CP-odd
Higgs boson (A) to be su ciently heavy so as to avoid an s-channel A-pole.
We further analyze the direct and indirect detection prospects of DM for the above
types of LSPs for the two kinds of sfermion coannihilations considered in this work. In
the part of the analysis that involves squark-LSP coannihilations, because of the near
degeneracy of squarks with the LSP, the squark exchange diagrams in the direct detection
cross section can be very important. These may even exceed the contributions from the
Higgs exchange diagrams which typically dominate the generic MSSM parameter space.
The SI direct detection cross section may exceed the recent LUX data for a higgsino
type of LSP undergoing slepton coannihilations for a mass below 600 GeV. For squark
coannihilations, the above number is about 840 GeV. The corresponding number for the
case of slepton plus squark coannihilations is around 680 GeV. The same occurs at around
1.27 TeV for a wino-LSP undergoing squark coannihilations whereas there is no direct
detection constraint for the part of the study involving slepton coannihilations. The case
of combined slepton and squark coannihilations gives a lower mass limit of a wino DM
as 1 TeV. However, in spite of the appearance of the above limits we must keep in mind
that there can be an order of magnitude of uncertainty in the computation of the SI direct
detection cross-section. This may potentially lower the above mass limits by 10 to 15%.
The indirect detection data such as that from the IceCube for the muon ux do not put any
additional constraint than whatever is given by the relic density and the SI direct detection
cross section data in combination. Regarding future experiments, XENON1T would be
able to probe only the higgsino LSP scenario with both kinds of sfermion coannihilations.
Finally, with relevant bounds from ATLAS and CMS being satis ed, we pointed out that
for LSP and e1 either being a higgsino or a wino dominated in nature there is hardly any
collider bound to worry about while considering the compressed pMSSM scenario where
the sfermion masses would be suitable for DM coannihilations.
Acknowledgments
UC is thankful to receive the hospitality from CERN Theory division where a major part
of this work was completed. MC would like to thank TRR33 \The Dark Universe" project
for nancial support.
Open Access.
This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
HJEP09(217)64
[INSPIRE].
HJEP09(217)64
supersymmetry breaking Lagrangian: Theory and applications, Phys. Rept. 407 (2005) 1
(1983) 542 [INSPIRE].
Singapore (1984).
[7] M. Drees, P. Roy and R.M. Godbole, Theory and Phenomenology of Sparticles, World
[8] H. Baer and X. Tata, Weak scale supersymmetry: From super elds to scattering events,
Cambridge University Press, Cambridge U.K. (2006).
267 (1996) 195 [hep-ph/9506380] [INSPIRE].
[9] G. Jungman, M. Kamionkowski and K. Griest, Supersymmetric dark matter, Phys. Rept.
[10] G. Bertone, D. Hooper and J. Silk, Particle dark matter: Evidence, candidates and
constraints, Phys. Rept. 405 (2005) 279 [hep-ph/0404175] [INSPIRE].
[11] A.H. Chamseddine, R.L. Arnowitt and P. Nath, Locally Supersymmetric Grand Uni cation,
Phys. Rev. Lett. 49 (1982) 970 [INSPIRE].
Supersymmetry, Phys. Lett. B 119 (1982) 343 [INSPIRE].
[12] R. Barbieri, S. Ferrara and C.A. Savoy, Gauge Models with Spontaneously Broken Local
[13] L.J. Hall, J.D. Lykken and S. Weinberg, Supergravity as the Messenger of Supersymmetry
Breaking, Phys. Rev. D 27 (1983) 2359 [INSPIRE].
Nucl. Phys. B 227 (1983) 121 [INSPIRE].
[14] P. Nath, R.L. Arnowitt and A.H. Chamseddine, Gauge Hierarchy in Supergravity Guts,
[15] N. Ohta, Grand uni ed theories based on local supersymmetry, Prog. Theor. Phys. 70
[16] P. Nath, R. Arnowitt and A.H. Chamseddine, Applied N =1 Supergravity, World Scienti c,
[hep-ph/9709356] [INSPIRE].
[hep-ph/0312378] [INSPIRE].
Scienti c, Singapore (2005).
[17] ATLAS collaboration, Observation of a new particle in the search for the Standard Model
Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1
[arXiv:1207.7214] [INSPIRE].
[18] CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS
experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
[19] ATLAS, CMS collaborations, Combined Measurement of the Higgs Boson Mass in pp
Collisions at p
114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].
s = 7 and 8 TeV with the ATLAS and CMS Experiments, Phys. Rev. Lett.
Constraining Supersymmetry using the relic density and the Higgs boson, Phys. Rev. D 89
(2014) 055017 [arXiv:1309.6958] [INSPIRE].
[23] P. Bechtle et al., Constrained Supersymmetry after the Higgs Boson Discovery: A global
analysis with Fittino, PoS(EPS-HEP 2013)313 [arXiv:1310.3045] [INSPIRE].
HJEP09(217)64
[24] J. Ellis, Supersymmetric Fits after the Higgs Discovery and Implications for Model
Building, Eur. Phys. J. C 74 (2014) 2732 [arXiv:1312.5426] [INSPIRE].
[25] L. Roszkowski, E.M. Sessolo and A.J. Williams, What next for the CMSSM and the NUHM:
Improved prospects for superpartner and dark matter detection, JHEP 08 (2014) 067
[arXiv:1405.4289] [INSPIRE].
[26] K.L. Chan, U. Chattopadhyay and P. Nath, Naturalness, weak scale supersymmetry and the
prospect for the observation of supersymmetry at the Tevatron and at the CERN LHC,
Phys. Rev. D 58 (1998) 096004 [hep-ph/9710473] [INSPIRE].
[27] U. Chattopadhyay, A. Corsetti and P. Nath, WMAP constraints, SUSY dark matter and
implications for the direct detection of SUSY, Phys. Rev. D 68 (2003) 035005
[hep-ph/0303201] [INSPIRE].
[28] S. Akula, M. Liu, P. Nath and G. Peim, Naturalness, Supersymmetry and Implications for
LHC and Dark Matter, Phys. Lett. B 709 (2012) 192 [arXiv:1111.4589] [INSPIRE].
[29] J.L. Feng, K.T. Matchev and T. Moroi, Focus points and naturalness in supersymmetry,
Phys. Rev. D 61 (2000) 075005 [hep-ph/9909334] [INSPIRE].
[30] J.L. Feng, K.T. Matchev and T. Moroi, Multi - TeV scalars are natural in minimal
supergravity, Phys. Rev. Lett. 84 (2000) 2322 [hep-ph/9908309] [INSPIRE].
[31] J.L. Feng, K.T. Matchev and F. Wilczek, Neutralino dark matter in focus point
supersymmetry, Phys. Lett. B 482 (2000) 388 [hep-ph/0004043] [INSPIRE].
[32] U. Chattopadhyay, A. Datta, A. Datta, A. Datta and D.P. Roy, LHC signature of the
minimal SUGRA model with a large soft scalar mass, Phys. Lett. B 493 (2000) 127
[hep-ph/0008228] [INSPIRE].
[33] U. Chattopadhyay, T. Ibrahim and D.P. Roy, Electron and neutron electric dipole moments
in the focus point scenario of SUGRA model, Phys. Rev. D 64 (2001) 013004
[hep-ph/0012337] [INSPIRE].
[34] J.L. Feng and F. Wilczek, Advantages and distinguishing features of focus point
supersymmetry, Phys. Lett. B 631 (2005) 170 [hep-ph/0507032] [INSPIRE].
[35] S.P. Das, A. Datta, M. Guchait, M. Maity and S. Mukherjee, Focus Point SUSY at the
LHC Revisited, Eur. Phys. J. C 54 (2008) 645 [arXiv:0708.2048] [INSPIRE].
[36] H. Baer, V. Barger and A. Mustafayev, Implications of a 125 GeV Higgs scalar for LHC
SUSY and neutralino dark matter searches, Phys. Rev. D 85 (2012) 075010
[arXiv:1112.3017] [INSPIRE].
[37] J. Ellis and K.A. Olive, Revisiting the Higgs Mass and Dark Matter in the CMSSM, Eur.
[38] O. Buchmueller et al., The CMSSM and NUHM1 in Light of 7 TeV LHC, Bs !
XENON100 Data, Eur. Phys. J. C 72 (2012) 2243 [arXiv:1207.7315] [INSPIRE].
and
(2014) 2922 [arXiv:1312.5250] [INSPIRE].
Uni cation, Phys. Lett. B 155 (1985) 381 [INSPIRE].
[40] J.R. Ellis, K. Enqvist, D.V. Nanopoulos and K. Tamvakis, Gaugino Masses and Grand
[41] M. Drees, Phenomenological Consequences of N = 1 Supergravity Theories With
Nonminimal Kinetic Energy Terms for Vector Super elds, Phys. Lett. B 158 (1985) 409
strings and D-brane models, Phys. Rev. D 64 (2001) 125010 [hep-ph/0003186] [INSPIRE].
[43] U. Chattopadhyay and P. Nath, b
uni cation, g
2, the ~bs +
constraint and
nonuniversalities, Phys. Rev. D 65 (2002) 075009 [hep-ph/0110341] [INSPIRE].
for and implications of nonuniversal GUT scale boundary conditions for soft SUSY breaking
parameters, eConf C 960625 (1996) SUP107 [hep-ph/9609457] [INSPIRE].
[45] K. Huitu, Y. Kawamura, T. Kobayashi and K. Puolamaki, Phenomenological constraints on
SUSY SU(5) GUTs with nonuniversal gaugino masses, Phys. Rev. D 61 (2000) 035001
[hep-ph/9903528] [INSPIRE].
[46] G. Anderson, H. Baer, C.-h. Chen and X. Tata, The Reach of Fermilab Tevatron upgrades
for SU(5) supergravity models with nonuniversal gaugino masses, Phys. Rev. D 61 (2000)
095005 [hep-ph/9903370] [INSPIRE].
[47] J. Chakrabortty and A. Raychaudhuri, A Note on dimension-5 operators in GUTs and
their impact, Phys. Lett. B 673 (2009) 57 [arXiv:0812.2783] [INSPIRE].
[48] S.P. Martin, Non-universal gaugino masses from non-singlet F-terms in non-minimal
uni ed models, Phys. Rev. D 79 (2009) 095019 [arXiv:0903.3568] [INSPIRE].
[49] U. Chattopadhyay and D.P. Roy, Higgsino dark matter in a SUGRA model with
nonuniversal gaugino masses, Phys. Rev. D 68 (2003) 033010 [hep-ph/0304108] [INSPIRE].
[50] U. Chattopadhyay, A. Corsetti and P. Nath, Supersymmetric dark matter and Yukawa
uni cation, Phys. Rev. D 66 (2002) 035003 [hep-ph/0201001] [INSPIRE].
[51] U. Chattopadhyay, D. Choudhury and D. Das, Large evolution of the bilinear Higgs
coupling parameter in SUSY models and reduction of phase sensitivity, Phys. Rev. D 72
(2005) 095015 [hep-ph/0509228] [INSPIRE].
[52] K. Huitu, J. Laamanen, P.N. Pandita and S. Roy, Phenomenology of non-universal gaugino
masses in supersymmetric grand uni ed theories, Phys. Rev. D 72 (2005) 055013
[hep-ph/0502100] [INSPIRE].
[53] G. Belanger, F. Boudjema, A. Cottrant, A. Pukhov and A. Semenov, WMAP constraints
on SUGRA models with non-universal gaugino masses and prospects for direct detection,
Nucl. Phys. B 706 (2005) 411 [hep-ph/0407218] [INSPIRE].
[54] S.F. King, J.P. Roberts and D.P. Roy, Natural dark matter in SUSY GUTs with
non-universal gaugino masses, JHEP 10 (2007) 106 [arXiv:0705.4219] [INSPIRE].
Signal-based analysis for the Large Hadron Collider, JHEP 10 (2007) 080
[arXiv:0708.2427] [INSPIRE].
Bosons in SUSY Cascades in CMS and Dark Matter with Non-universal Gaugino Masses,
[57] S. Bhattacharya and J. Chakrabortty, Gaugino mass non-universality in an SO(10)
supersymmetric Grand Uni ed Theory: Low-energy spectra and collider signals, Phys. Rev.
D 81 (2010) 015007 [arXiv:0903.4196] [INSPIRE].
[58] U. Chattopadhyay, D. Das and D.P. Roy, Mixed Neutralino Dark Matter in Nonuniversal
Gaugino Mass Models, Phys. Rev. D 79 (2009) 095013 [arXiv:0902.4568] [INSPIRE].
[59] M. Guchait, D.P. Roy and D. Sengupta, Probing a Mixed Neutralino Dark Matter Model at
the 7 TeV LHC, Phys. Rev. D 85 (2012) 035024 [arXiv:1109.6529] [INSPIRE].
[60] S. Mohanty, S. Rao and D.P. Roy, Predictions of a Natural SUSY Dark Matter Model for
Direct and Indirect Detection Experiments, JHEP 11 (2012) 175 [arXiv:1208.0894]
[INSPIRE].
[INSPIRE].
[61] S. Mohanty, S. Rao and D.P. Roy, Reconciling the muon g
2 and dark matter relic density
with the LHC results in nonuniversal gaugino mass models, JHEP 09 (2013) 027
[arXiv:1303.5830] [INSPIRE].
[62] J. Chakrabortty, S. Mohanty and S. Rao, Non-universal gaugino mass GUT models in the
light of dark matter and LHC constraints, JHEP 02 (2014) 074 [arXiv:1310.3620]
[63] S.P. Martin, Nonuniversal gaugino masses and seminatural supersymmetry in view of the
Higgs boson discovery, Phys. Rev. D 89 (2014) 035011 [arXiv:1312.0582] [INSPIRE].
[64] S.P. Das, M. Guchait and D.P. Roy, Testing SUSY models for the muon g-2 anomaly via
chargino-neutralino pair production at the LHC, Phys. Rev. D 90 (2014) 055011
[arXiv:1406.6925] [INSPIRE].
[65] I. Gogoladze, F. Nasir, Q. Sha and C.S. Un, Nonuniversal Gaugino Masses and Muon g-2,
Phys. Rev. D 90 (2014) 035008 [arXiv:1403.2337] [INSPIRE].
[66] U. Chattopadhyay, D. Choudhury, M. Drees, P. Konar and D.P. Roy, Looking for a heavy
Higgsino LSP in collider and dark matter experiments, Phys. Lett. B 632 (2006) 114
[hep-ph/0508098] [INSPIRE].
[67] M. Chakraborti, U. Chattopadhyay, S. Rao and D.P. Roy, Higgsino Dark Matter in
Nonuniversal Gaugino Mass Models, Phys. Rev. D 91 (2015) 035022 [arXiv:1411.4517]
[INSPIRE].
[68] L. Roszkowski, R. Ruiz de Austri, R. Trotta, Y.-L.S. Tsai and T.A. Varley, Global ts of the
Non-Universal Higgs Model, Phys. Rev. D 83 (2011) 015014 [Erratum ibid. D 83 (2011)
039901] [arXiv:0903.1279] [INSPIRE].
[69] H. Baer, A. Mustafayev, S. Profumo, A. Belyaev and X. Tata, Direct, indirect and collider
detection of neutralino dark matter in SUSY models with non-universal Higgs masses,
JHEP 07 (2005) 065 [hep-ph/0504001] [INSPIRE].
[70] J.R. Ellis, K.A. Olive and Y. Santoso, The MSSM parameter space with nonuniversal Higgs
JHEP 12 (1998) 027 [hep-ph/9810442] [INSPIRE].
[74] G.F. Giudice, M.A. Luty, H. Murayama and R. Rattazzi, Gaugino mass without singlets,
[75] L. Randall and R. Sundrum, Out of this world supersymmetry breaking, Nucl. Phys. B 557
[76] J.A. Bagger, T. Moroi and E. Poppitz, Anomaly mediation in supergravity theories, JHEP
(1999) 79 [hep-th/9810155] [INSPIRE].
04 (2000) 009 [hep-th/9911029] [INSPIRE].
(2000) 115001 [hep-ph/0006049] [INSPIRE].
[77] U. Chattopadhyay, D.K. Ghosh and S. Roy, Constraining anomaly mediated supersymmetry
breaking framework via on going muon g-2 experiment at Brookhaven, Phys. Rev. D 62
[INSPIRE].
[INSPIRE].
[INSPIRE].
Matter and Future dSph Observations, JHEP 07 (2014) 080 [arXiv:1405.4914] [INSPIRE].
density of wino-like dark matter in the MSSM, JHEP 03 (2016) 119 [arXiv:1601.04718]
[82] M. Cirelli, A. Strumia and M. Tamburini, Cosmology and Astrophysics of Minimal Dark
Matter, Nucl. Phys. B 787 (2007) 152 [arXiv:0706.4071] [INSPIRE].
[83] A. Masiero, S. Profumo and P. Ullio, Neutralino dark matter detection in split
supersymmetry scenarios, Nucl. Phys. B 712 (2005) 86 [hep-ph/0412058] [INSPIRE].
[84] T. Cohen, M. Lisanti, A. Pierce and T.R. Slatyer, Wino Dark Matter Under Siege, JCAP
10 (2013) 061 [arXiv:1307.4082] [INSPIRE].
[85] M. Baumgart, I.Z. Rothstein and V. Vaidya, Constraints on Galactic Wino Densities from
Gamma Ray Lines, JHEP 04 (2015) 106 [arXiv:1412.8698] [INSPIRE].
[86] H. Baer, V. Barger, P. Huang, D. Mickelson, M. Pade ke-Kirkland and X. Tata, Natural
SUSY with a bino- or wino-like LSP, Phys. Rev. D 91 (2015) 075005 [arXiv:1501.06357]
[INSPIRE].
[87] M. Ibe, S. Matsumoto, S. Shirai and T.T. Yanagida, Wino Dark Matter in light of the
AMS-02 2015 Data, Phys. Rev. D 91 (2015) 111701 [arXiv:1504.05554] [INSPIRE].
[88] A. Hryczuk, I. Cholis, R. Iengo, M. Tavakoli and P. Ullio, Indirect Detection Analysis:
Wino Dark Matter Case Study, JCAP 07 (2014) 031 [arXiv:1401.6212] [INSPIRE].
[89] ATLAS collaboration, Search for supersymmetry at ps=8 TeV in nal states with jets and
two same-sign leptons or three leptons with the ATLAS detector, JHEP 06 (2014) 035
[90] ATLAS collaboration, Search for squarks and gluinos with the ATLAS detector in nal
states with jets and missing transverse momentum using p
s = 8 TeV proton-proton
collision data, JHEP 09 (2014) 176 [arXiv:1405.7875] [INSPIRE].
[91] ATLAS collaboration, Search for strong production of supersymmetric particles in nal
states with missing transverse momentum and at least three b-jets at ps= 8 TeV
proton-proton collisions with the ATLAS detector, JHEP 10 (2014) 024 [arXiv:1407.0600]
and missing transverse momentum at p
(2015) 116 [arXiv:1501.03555] [INSPIRE].
[92] ATLAS collaboration, Search for squarks and gluinos in events with isolated leptons, jets
s = 8 TeV with the ATLAS detector, JHEP 04
[93] ATLAS collaboration, Search for supersymmetry in events containing a same- avour
opposite-sign dilepton pair, jets and large missing transverse momentum in p
s = 8 TeV pp
collisions with the ATLAS detector, Eur. Phys. J. C 75 (2015) 318 [Erratum ibid. C 75
(2015) 463] [arXiv:1503.03290] [INSPIRE].
[94] CMS collaboration, Search for supersymmetry in pp collisions at ps=8 TeV in events with
a single lepton, large jet multiplicity and multiple b jets, Phys. Lett. B 733 (2014) 328
[95] CMS collaboration, Search for new physics in events with same-sign dileptons and jets in
s = 8 TeV, JHEP 01 (2014) 163 [Erratum ibid. 1501 (2015) 014]
[96] CMS collaboration, Search for new physics in the multijet and missing transverse
momentum
nal state in proton-proton collisions at ps= 8 TeV, JHEP 06 (2014) 055
[97] CMS collaboration, Searches for supersymmetry based on events with b jets and four W
bosons in pp collisions at 8 TeV, Phys. Lett. B 745 (2015) 5 [arXiv:1412.4109] [INSPIRE].
[98] CMS collaboration, Search for Supersymmetry Using Razor Variables in Events with
s = 8 TeV, Phys. Rev. D 91 (2015) 052018
[99] CMS collaboration, Searches for Supersymmetry using the MT 2 Variable in Hadronic
Events Produced in pp Collisions at 8 TeV, JHEP 05 (2015) 078 [arXiv:1502.04358]
[arXiv:1311.4937] [INSPIRE].
pp collisions at p
[arXiv:1311.6736] [INSPIRE].
[arXiv:1402.4770] [INSPIRE].
b-Tagged Jets in pp Collisions at p
[arXiv:1502.00300] [INSPIRE].
[100] CMS collaboration, Search for Physics Beyond the Standard Model in Events with Two
Leptons, Jets and Missing Transverse Momentum in pp Collisions at p
s = 8 TeV, JHEP
04 (2015) 124 [arXiv:1502.06031] [INSPIRE].
[101] ATLAS collaboration, Search for direct production of charginos and neutralinos in events
with three leptons and missing transverse momentum in p
ATLAS detector, JHEP 04 (2014) 169 [arXiv:1402.7029] [INSPIRE].
s = 8TeV pp collisions with the
momentum in pp collisions at p
nal states with tau leptons in p
ATLAS-CONF-2016-093 (2016).
transverse momentum in the
ATLAS-CONF-2016-096 (2016).
[102] ATLAS collaboration, Search for direct production of charginos, neutralinos and sleptons
in
nal states with two leptons and missing transverse momentum in pp collisions at p
s =
8 TeV with the ATLAS detector, JHEP 05 (2014) 071 [arXiv:1403.5294] [INSPIRE].
[103] ATLAS collaboration, Search for the direct production of charginos, neutralinos and staus
in
nal states with at least two hadronically decaying taus and missing transverse
s = 8 TeV with the ATLAS detector, JHEP 10 (2014) 096
[104] ATLAS collaboration, Search for direct pair production of a chargino and a neutralino
decaying to the 125 GeV Higgs boson in p
Eur. Phys. J. C 75 (2015) 208 [arXiv:1501.07110] [INSPIRE].
s = 8 TeV pp collisions with the ATLAS detector,
[105] ATLAS collaboration, Search for electroweak production of supersymmetric particles in
s = 13TeV pp collisions with the ATLAS detector,
[106] ATLAS collaboration, Search for supersymmetry with two and three leptons and missing
nal state at p
s = 13 TeV with the ATLAS detector,
[107] CMS collaboration, Searches for electroweak production of charginos, neutralinos and
sleptons decaying to leptons and W, Z and Higgs bosons in pp collisions at 8 TeV, Eur.
Phys. J. C 74 (2014) 3036 [arXiv:1405.7570] [INSPIRE].
[108] CMS collaboration, Searches for electroweak neutralino and chargino production in
channels with Higgs, Z and W bosons in pp collisions at 8 TeV, Phys. Rev. D 90 (2014)
092007 [arXiv:1409.3168] [INSPIRE].
pp collisions at p
s = 13 TeV with 12.9/fb, CMS-PAS-SUS-16-024 (2016).
[109] CMS collaboration, Search for electroweak SUSY production in multilepton nal states in
tau leptons in pp collisions at p
s = 8 TeV, CMS-PAS-SUS-14-022.
[110] CMS collaboration, Search for electroweak production of charginos in nal states with two
[111] CMS collaboration, Search for electroweak production of charginos and neutralinos in the
WH nal state at 13 TeV, CMS-PAS-SUS-16-026 (2016).
p
s = 8 TeV with the ATLAS detector, ATLAS-CONF-2013-035 (2013).
[112] ATLAS collaboration, Search for direct production of charginos and neutralinos in events
with three leptons and missing transverse momentum in 21 fb 1 of pp collisions at
[113] M. Chakraborti, U. Chattopadhyay, A. Choudhury, A. Datta and S. Poddar, The
Electroweak Sector of the pMSSM in the Light of LHC - 8 TeV and Other Data, JHEP 07
(2014) 019 [arXiv:1404.4841] [INSPIRE].
[114] D. Ghosh, M. Guchait and D. Sengupta, Higgs Signal in Chargino-Neutralino Production at
the LHC, Eur. Phys. J. C 72 (2012) 2141 [arXiv:1202.4937] [INSPIRE].
[115] K. Howe and P. Saraswat, Excess Higgs Production in Neutralino Decays, JHEP 10 (2012)
[116] A. Arbey, M. Battaglia and F. Mahmoudi, Higgs Production in Neutralino Decays in the
065 [arXiv:1208.1542] [INSPIRE].
MSSM - The LHC and a Future e+e
[arXiv:1212.6865] [INSPIRE].
Collider, Eur. Phys. J. C 75 (2015) 108
[117] A. Choudhury and A. Datta, Neutralino dark matter confronted by the LHC constraints on
Electroweak SUSY signals, JHEP 09 (2013) 119 [arXiv:1305.0928] [INSPIRE].
[118] A. Bharucha, S. Heinemeyer and F. von der Pahlen, Direct Chargino-Neutralino Production
at the LHC: Interpreting the Exclusion Limits in the Complex MSSM, Eur. Phys. J. C 73
(2013) 2629 [arXiv:1307.4237] [INSPIRE].
88 (2013) 115010 [arXiv:1309.5966] [INSPIRE].
[arXiv:1404.2924] [INSPIRE].
[122] J. Eckel, M.J. Ramsey-Musolf, W. Shepherd and S. Su, Impact of LSP Character on
Slepton Reach at the LHC, JHEP 11 (2014) 117 [arXiv:1408.2841] [INSPIRE].
[123] C. Han, L. Wu, J.M. Yang, M. Zhang and Y. Zhang, New approach for detecting a
compressed bino/wino at the LHC, Phys. Rev. D 91 (2015) 055030 [arXiv:1409.4533]
[124] C. Han, Probing light bino and higgsinos at the LHC, arXiv:1409.7000 [INSPIRE].
[125] J. Bramante, P.J. Fox, A. Martin, B. Ostdiek, T. Plehn, T. Schell et al., Relic Neutralino
Surface at a 100 TeV Collider, Phys. Rev. D 91 (2015) 054015 [arXiv:1412.4789]
[126] A. Choudhury, K. Kowalska, L. Roszkowski, E.M. Sessolo and A.J. Williams,
Less-simpli ed models of dark matter for direct detection and the LHC, JHEP 04 (2016)
182 [arXiv:1509.05771] [INSPIRE].
[127] J. Bramante, N. Desai, P. Fox, A. Martin, B. Ostdiek and T. Plehn, Towards the Final
Word on Neutralino Dark Matter, Phys. Rev. D 93 (2016) 063525 [arXiv:1510.03460]
[128] K. Hamaguchi and K. Ishikawa, Prospects for Higgs- and Z-resonant Neutralino Dark
Matter, Phys. Rev. D 93 (2016) 055009 [arXiv:1510.05378] [INSPIRE].
[129] J. Cao, Y. He, L. Shang, W. Su and Y. Zhang, Testing the light dark matter scenario of the
MSSM at the LHC, JHEP 03 (2016) 207 [arXiv:1511.05386] [INSPIRE].
[130] A. Choudhury and S. Mondal, Revisiting the Exclusion Limits from Direct
Chargino-Neutralino Production at the LHC, Phys. Rev. D 94 (2016) 055024
[arXiv:1603.05502] [INSPIRE].
[131] A. Datta, N. Ganguly and S. Poddar, New Limits on Heavier Electroweakinos and their
LHC Signatures, Phys. Lett. B 763 (2016) 213 [arXiv:1606.04391] [INSPIRE].
[132] D. Chowdhury, K.M. Patel, X. Tata and S.K. Vempati, Indirect Searches of the Degenerate
MSSM, Phys. Rev. D 95 (2017) 075025 [arXiv:1612.06471] [INSPIRE].
[133] M. Chakraborti, U. Chattopadhyay, A. Choudhury, A. Datta and S. Poddar, Reduced LHC
constraints for higgsino-like heavier electroweakinos, JHEP 11 (2015) 050
[arXiv:1507.01395] [INSPIRE].
[134] CMS collaboration, Search for dark matter, extra dimensions and unparticles in monojet
events in proton{proton collisions at p
[arXiv:1408.3583] [INSPIRE].
s = 8 TeV, Eur. Phys. J. C 75 (2015) 235
[135] ATLAS collaboration, Search for new phenomena in nal states with an energetic jet and
s =8 TeV with the ATLAS
Supersymmetry via the interplay between the LHC and Direct Dark Matter Detection, JHEP
07 (2015) 066 [arXiv:1504.02472] [INSPIRE].
[137] MSSM Working Group collaboration, A. Djouadi et al., The Minimal supersymmetric
standard model: Group summary report, hep-ph/9901246 [INSPIRE].
[138] K. Griest and D. Seckel, Three exceptions in the calculation of relic abundances, Phys. Rev.
D 43 (1991) 3191 [INSPIRE].
coannihilation channels and the cosmologically relevant region of MSSM parameter space,
Astropart. Phys. 13 (2000) 181 [Erratum ibid. 15 (2001) 413] [hep-ph/9905481] [INSPIRE].
[140] WMAP collaboration, G. Hinshaw et al., Nine-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations: Cosmological Parameter Results, Astrophys. J. Suppl. 208
(2013) 19 [arXiv:1212.5226] [INSPIRE].
chargino and sfermion coannihilations in mSUGRA, JCAP 04 (2003) 001
[hep-ph/0301106] [INSPIRE].
[143] J. Edsjo and P. Gondolo, Neutralino relic density including coannihilations, Phys. Rev. D
56 (1997) 1879 [hep-ph/9704361] [INSPIRE].
[144] S. Profumo and A. Provenza, Increasing the neutralino relic abundance with slepton
coannihilations: Consequences for indirect dark matter detection, JCAP 12 (2006) 019
[hep-ph/0609290] [INSPIRE].
[145] LUX collaboration, D.S. Akerib et al., Results from a search for dark matter in the
complete LUX exposure, Phys. Rev. Lett. 118 (2017) 021303 [arXiv:1608.07648] [INSPIRE].
[146] J. Hisano, S. Matsumoto, M.M. Nojiri and O. Saito, Direct detection of the Wino and
Higgsino-like neutralino dark matters at one-loop level, Phys. Rev. D 71 (2005) 015007
[hep-ph/0407168] [INSPIRE].
[147] IceCube collaboration, R. Abbasi et al., Multi-year search for dark matter annihilations in
the Sun with the AMANDA-II and IceCube detectors, Phys. Rev. D 85 (2012) 042002
[arXiv:1112.1840] [INSPIRE].
[148] IceCube collaboration, M.G. Aartsen et al., Search for dark matter annihilations in the
Sun with the 79-string IceCube detector, Phys. Rev. Lett. 110 (2013) 131302
[arXiv:1212.4097] [INSPIRE].
[149] J. Harz, B. Herrmann, M. Klasen, K. Kovarik and P. Steppeler, Theoretical uncertainty of
the supersymmetric dark matter relic density from scheme and scale variations, Phys. Rev.
D 93 (2016) 114023 [arXiv:1602.08103] [INSPIRE].
[150] M. Klasen, K. Kovarik and P. Steppeler, SUSY-QCD corrections for direct detection of
neutralino dark matter and correlations with relic density, Phys. Rev. D 94 (2016) 095002
[arXiv:1607.06396] [INSPIRE].
pMSSM in light of the Fermi GeV excess: prospects for the LHC Run-II and astroparticle
experiments, JCAP 04 (2016) 037 [arXiv:1507.07008] [INSPIRE].
[152] M. Badziak, M. Olechowski and P. Szczerbiak, Spin-dependent constraints on blind spots for
thermal singlino-higgsino dark matter with(out) light singlets, JHEP 07 (2017) 050
[arXiv:1705.00227] [INSPIRE].
[153] A. Djouadi, J.-L. Kneur and G. Moultaka, SuSpect: A Fortran code for the supersymmetric
and Higgs particle spectrum in the MSSM, Comput. Phys. Commun. 176 (2007) 426
[hep-ph/0211331] [INSPIRE].
[154] G. Belanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs3: A program for
calculating dark matter observables, Comput. Phys. Commun. 185 (2014) 960
[arXiv:1305.0237] [INSPIRE].
[155] P. Gondolo, J. Edsjo, P. Ullio, L. Bergstrom, M. Schelke and E.A. Baltz, DarkSUSY:
Computing supersymmetric dark matter properties numerically, JCAP 07 (2004) 008
[astro-ph/0406204] [INSPIRE].
[156] G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich and G. Weiglein, Towards high precision
predictions for the MSSM Higgs sector, Eur. Phys. J. C 28 (2003) 133 [hep-ph/0212020]
[INSPIRE].
[INSPIRE].
[157] B.C. Allanach, A. Djouadi, J.L. Kneur, W. Porod and P. Slavich, Precise determination of
the neutral Higgs boson masses in the MSSM, JHEP 09 (2004) 044 [hep-ph/0406166]
[158] S.P. Martin, Three-loop corrections to the lightest Higgs scalar boson mass in
supersymmetry, Phys. Rev. D 75 (2007) 055005 [hep-ph/0701051] [INSPIRE].
[159] R.V. Harlander, P. Kant, L. Mihaila and M. Steinhauser, Higgs boson mass in
supersymmetry to three loops, Phys. Rev. Lett. 100 (2008) 191602 [Erratum ibid. 101
(2008) 039901] [arXiv:0803.0672] [INSPIRE].
[160] S. Heinemeyer, O. Stal and G. Weiglein, Interpreting the LHC Higgs Search Results in the
MSSM, Phys. Lett. B 710 (2012) 201 [arXiv:1112.3026] [INSPIRE].
[161] A. Arbey, M. Battaglia, A. Djouadi and F. Mahmoudi, The Higgs sector of the
phenomenological MSSM in the light of the Higgs boson discovery, JHEP 09 (2012) 107
[arXiv:1207.1348] [INSPIRE].
[162] M. Drees, M.M. Nojiri, D.P. Roy and Y. Yamada, Light Higgsino dark matter, Phys. Rev.
D 56 (1997) 276 [Erratum ibid. D 64 (2001) 039901] [hep-ph/9701219] [INSPIRE].
[163] G.D. Kribs, A. Martin and A. Menon, Natural Supersymmetry and Implications for Higgs
physics, Phys. Rev. D 88 (2013) 035025 [arXiv:1305.1313] [INSPIRE].
[164] G.F. Giudice and A. Pomarol, Mass degeneracy of the Higgsinos, Phys. Lett. B 372 (1996)
253 [hep-ph/9512337] [INSPIRE].
[165] H.-C. Cheng, B.A. Dobrescu and K.T. Matchev, Generic and chiral extensions of the
supersymmetric standard model, Nucl. Phys. B 543 (1999) 47 [hep-ph/9811316] [INSPIRE].
[166] N.E. Bomark, A. Kvellestad, S. Lola, P. Osland and A.R. Raklev, Long lived charginos in
Natural SUSY?, JHEP 05 (2014) 007 [arXiv:1310.2788] [INSPIRE].
[167] T. Gherghetta, G.F. Giudice and J.D. Wells, Phenomenological consequences of
supersymmetry with anomaly induced masses, Nucl. Phys. B 559 (1999) 27
[hep-ph/9904378] [INSPIRE].
[169] R. Schofbeck and H. Eberl, Two-loop SUSY QCD corrections to the chargino masses in the
MSSM, Eur. Phys. J. C 53 (2008) 621 [arXiv:0706.0781] [INSPIRE].
the MSSM, Phys. Lett. B 649 (2007) 67 [hep-ph/0612276] [INSPIRE].
[170] R. Schofbeck and H. Eberl, Two-loop SUSY QCD corrections to the neutralino masses in
[171] D. Pierce and A. Papadopoulos, Radiative corrections to neutralino and chargino masses in
the minimal supersymmetric model, Phys. Rev. D 50 (1994) 565 [hep-ph/9312248]
[172] A.B. Lahanas, K. Tamvakis and N.D. Tracas, One loop corrections to the neutralino sector
and radiative electroweak breaking in the MSSM, Phys. Lett. B 324 (1994) 387
[hep-ph/9312251] [INSPIRE].
[173] D. Pierce and A. Papadopoulos, The Complete radiative corrections to the gaugino and
Higgsino masses in the minimal supersymmetric model, Nucl. Phys. B 430 (1994) 278
[hep-ph/9403240] [INSPIRE].
[175] R.K. Kaul and P. Majumdar, Cancellation of Quadratically Divergent Mass Corrections in
Globally Supersymmetric Spontaneously Broken Gauge Theories, Nucl. Phys. B 199 (1982)
[176] R. Barbieri and G.F. Giudice, Upper Bounds on Supersymmetric Particle Masses, Nucl.
[177] ATLAS collaboration, Further searches for squarks and gluinos in
nal states with jets and
s =13 TeV with the ATLAS detector,
[178] ATLAS collaboration, Search for charginos nearly mass degenerate with the lightest
neutralino based on a disappearing-track signature in pp collisions at p
s = 8 TeV with the
ATLAS detector, Phys. Rev. D 88 (2013) 112006 [arXiv:1310.3675] [INSPIRE].
[179] CMS collaboration, Search for disappearing tracks in proton-proton collisions at ps = 8
TeV, JHEP 01 (2015) 096 [arXiv:1411.6006] [INSPIRE].
[180] ATLAS collaboration, Searches for heavy long-lived charged particles with the ATLAS
s = 8 TeV, JHEP 01 (2015) 068
[181] CMS collaboration, Search for Decays of Stopped Long-Lived Particles Produced in
s = 8 TeV, Eur. Phys. J. C 75 (2015) 151
36 [INSPIRE].
Phys. B 306 (1988) 63 [INSPIRE].
missing transverse momentum at p
ATLAS-CONF-2016-078 (2016).
detector in proton-proton collisions at p
[arXiv:1411.6795] [INSPIRE].
Proton-Proton Collisions at p
[arXiv:1501.05603] [INSPIRE].
3483 [hep-ph/9307208] [INSPIRE].
[182] M. Drees and M. Nojiri, Neutralino - nucleon scattering revisited, Phys. Rev. D 48 (1993)
resonance annihilation of dark matter in the light of XENON100 and CDMS-II
experiment, JCAP 04 (2016) 027 [arXiv:1512.07501] [INSPIRE].
Phys. Rev. D 64 (2001) 015001 [hep-ph/0011082] [INSPIRE].
161 [arXiv:1404.0682] [INSPIRE].
with disappearing charged tracks, JHEP 06 (2017) 119 [arXiv:1703.05327] [INSPIRE].
Disappearing Track Searches at the LHC and Future Colliders, arXiv:1703.09675
[1] H.P. Nilles , Supersymmetry, Supergravity and Particle Physics, Phys. Rept . 110 ( 1984 ) 1 [2] J.D. Lykken , Introduction to supersymmetry, hep-th/9612114 [INSPIRE].
[3] J. Wess and J. Bagger , Supersymmetry and Supergravity, second edition, Princeton ( 1991 ).
[4] H.E. Haber and G.L. Kane , The Search for Supersymmetry: Probing Physics Beyond the Standard Model , Phys. Rept . 117 ( 1985 ) 75 [INSPIRE].
[5] S.P. Martin , A Supersymmetry primer , Adv. Ser. Direct. High Energy Phys . 21 ( 2010 ) 1 [6] D.J.H. Chung , L.L. Everett , G.L. Kane , S.F. King , J.D. Lykken and L.-T. Wang, The Soft [20] M. Citron , J. Ellis , F. Luo , J. Marrouche , K.A. Olive and K.J. de Vries , End of the CMSSM coannihilation strip is nigh , Phys. Rev. D 87 ( 2013 ) 036012 [arXiv: 1212 .2886] [INSPIRE].
[21] K. Kowalska , L. Roszkowski and E.M. Sessolo , Two ultimate tests of constrained supersymmetry , JHEP 06 ( 2013 ) 078 [arXiv: 1302 .5956] [INSPIRE].
[22] S. Henrot-Versille , R. Lafaye , T. Plehn , M. Rauch , D. Zerwas , S. Plaszczynski et al., [39] O. Buchmueller et al., The CMSSM and NUHM1 after LHC Run 1, Eur . Phys. J. C 74 [44] G. Anderson , C.H. Chen , J.F. Gunion , J.D. Lykken , T. Moroi and Y. Yamada , Motivations [55] S. Bhattacharya , A. Datta and B. Mukhopadhyaya , Non-universal gaugino masses: A [56] K. Huitu , R. Kinnunen , J. Laamanen , S. Lehti , S. Roy and T. Salminen , Search for Higgs masses , Phys. Lett. B 539 ( 2002 ) 107 [ hep -ph/0204192] [INSPIRE].
[71] G.G. Ross , K. Schmidt-Hoberg and F. Staub , On the MSSM Higgsino mass and ne tuning , Phys. Lett. B 759 ( 2016 ) 110 [arXiv: 1603 .09347] [INSPIRE].
[72] U. Chattopadhyay and A. Dey , Probing Non-holomorphic MSSM via precision constraints, dark matter and LHC data , JHEP 10 ( 2016 ) 027 [arXiv: 1604 .06367] [INSPIRE].
[73] N. Arkani-Hamed , A. Delgado and G.F. Giudice , The Well-tempered neutralino , Nucl.
[78] U. Chattopadhyay , D. Das , P. Konar and D.P. Roy , Looking for a heavy wino LSP in collider and dark matter experiments , Phys. Rev. D 75 ( 2007 ) 073014 [ hep -ph/0610077] [79] J. Hisano , S. Matsumoto , M. Nagai , O. Saito and M. Senami , Non-perturbative e ect on thermal relic abundance of dark matter , Phys. Lett. B 646 ( 2007 ) 34 [ hep -ph/0610249] [80] B. Bhattacherjee , M. Ibe , K. Ichikawa , S. Matsumoto and K. Nishiyama , Wino Dark [81] M. Beneke , A. Bharucha , F. Dighera , C. Hellmann , A. Hryczuk , S. Recksiegel et al., Relic [119] T. Han , S. Padhi and S. Su , Electroweakinos in the Light of the Higgs Boson , Phys. Rev . D [120] A. Papaefstathiou , K. Sakurai and M. Takeuchi , Higgs boson to di-tau channel in Chargino-Neutralino searches at the LHC , JHEP 08 ( 2014 ) 176 [arXiv: 1404 .1077] [121] F. Yu , Anatomizing Exotic Production of the Higgs Boson , Phys. Rev. D 90 ( 2014 ) 015009 detector , Eur. Phys. J. C 75 ( 2015 ) 299 [arXiv: 1502 .01518] [INSPIRE]. [136] D. Barducci , A. Belyaev , A.K.M. Bharucha , W. Porod and V. Sanz , Uncovering Natural [139] J.R. Ellis , T. Falk , K.A. Olive and M. Srednicki , Calculations of neutralino-stau [141] Planck collaboration, P.A.R. Ade et al., Planck 2013 results . XVI. Cosmological parameters , Astron. Astrophys . 571 ( 2014 ) A16 [arXiv: 1303 .5076] [INSPIRE].
[142] J. Edsjo , M. Schelke , P. Ullio and P. Gondolo , Accurate relic densities with neutralino , [168] J.L. Feng , T. Moroi , L. Randall , M. Strassler and S.-f. Su, Discovering supersymmetry at the Tevatron in wino LSP scenarios , Phys. Rev. Lett . 83 ( 1999 ) 1731 [ hep -ph/9904250] [174] N. Sakai , Naturalness in Supersymmetric GUTs, Zeit. Phys. C 11 ( 1981 ) 153 .
[183] U. Chattopadhyay , D. Das , D.K. Ghosh and M. Maity , Probing the light Higgs pole observations , Phys. Rev. D 82 ( 2010 ) 075013 [arXiv: 1006 .3045] [INSPIRE].
[184] XENON collaboration, E. Aprile et al., Physics reach of the XENON1T dark matter [186] M. Low and L.-T. Wang, Neutralino dark matter at 14 TeV and 100 TeV, JHEP 08 ( 2014 )