Natural SUSY at LHC with rightsneutrino LSP
Revised: March
Natural SUSY at LHC with rightsneutrino LSP
Arindam Chatterjee 0 1
Juhi Dutta 0 1
Santosh Kumar Rai 0 1
HarishChandra Research Institute, HBNI,
0 203 B. T. Road, Kolkata700108 , India
1 Chhatnag Road, Jhusi , Allahabad211019 , India
We study an extension of the minimal supersymmetric standard model (MSSM) with additional righthanded singlet neutrino super elds. tension incorporates a mechanism for the neutrino mass, it also opens up the possibility of having the rightsneutrinos ( ) as the lightest supersymmetric particle (LSP). In this work, we focus on the viability of rather small (. 500 GeV) higgsino mass parameter ( ), an important ingredient for \naturalness", in the presence of such a LSP. For simplicity, we assume that the bino and wino mass parameters are much heavier; thus we only consider (almost) pure and compressed higgsinolike states, with small O(10 2) gaugino admixture which nevertheless still a ect the decay of the lowlying higgsinolike states, thus signi  cantly a ecting the proposed signatures at colliders. Considering only prompt decays of the higginolike states, especially the lightest chargino, we discuss the importance of leptonic channels consisting of up to two leptons with large missing transverse energy to probe this scenario at the Large Hadron Collider (LHC). In addition we also comment on the dark matter predictions for the studied scenario.
Supersymmetry Phenomenology

2.1
2.2
2.3
4.1
4.3
4.4
4.5
4.6
5
Conclusion
1
Introduction
1 Introduction 2 The model 4
Survey of the relevant parameter space
Constraints on electroweakino sector from LHC
4.2 Impact of additional related searches at LHC
Benchmarks
Collider analyses
impressing the fact that low j j is of more essence to the \natural" scenarios at EW scale.
While the constraints on stop squarks and gluinos are rather stringent due to their
large production crosssection at the LHC, the weakly interacting sector with rather light
{ 1 {
electroweakinos in general, and higgsinos in particular, remain viable [11, 12]. There have
been several analyses on light electroweakinos, assuming a simpli ed spectra with one or
more speci c decay channels [13{26]. Further, the constraints on the mass of the light
higgsinolike states have been studied in detail because of their importance in a \natural"
supersymmetric scenario [19, 27{33]. However, note that these analyses assume the lightest
neutralino as the lightest supersymmetric particle (LSP). In scenarios with conserved
Rparity, the search strategies, and therefore the limits of various sparticle masses, depend on
the nature of the LSP. This is because in such scenarios the LSP appears at the end of the
decay chain of each sparticle, therefore dictating the possible search channels. This
warrants investigation of supersymmetric scenarios with di erent types of LSP. While within
neutrino mass generation issue, has been widely studied in supersymmetric extensions.
While the leftsneutrinos have been ruled out as a Dark Matter (DM) candidate long
ago, thanks to the stringent limit from direct detection experiments [71], rightsneutrinos
continue to be widely studied as a candidate for DM in simple extensions of the MSSM [59{
63, 65{68, 72]. In its simplest incarnation as ours, the rightsneutrinos at EW scale remain
very weakly interacting, thanks to the small Yukawa coupling O(10 6{10 7) determining
their coupling strength to other particles. However, as in the case of charged sfermions,
a rather large value of the corresponding trilinear soft supersymmtry breaking parameter
can induce signi cant leftadmixture in a dominantly rightsneutrino and therefore can
substantially increase the interaction strengths [66, 67, 72]. In both of these scenarios, DM
aspects as well as search strategies at LHC have been studied for certain choices of the
SUSY spectra [64, 73{79].
We note that in the light of \naturalness", it becomes equally important to investigate
the supersymmetric spectrum in such a scenario. In particular we focus on a minimalistic
spectrum, motivated by \naturalness" at the EW scale, with light higgsinolike states and
a rightsneutrino LSP. However, analysing collider signatures from the third generation
squarks and gluinos will be beyond the scope of the present work and will be addressed in
a subsequent extension. For the present case, the strongly interacting sparticles have been
assumed to be very heavy adhering to the \naturalness" scheme proposed in refs. [9, 10].
Further, we will also assume the gaugino mass parameters to be large enough (& O(
1
) TeV).
Thus the light electroweakinos are higgsinodominated states.
Note that the presence
of a mixed rightsneutrino as the LSP can lead to a very di erent signature from the
compressed higgsinolike states, mostly due to the leptonic decay of the light chargino.
Although leptonic channels provide a cleaner environment for new physics searches at a
{ 2 {
hadron machine such as the LHC, one expects that the level of compression in the mass
spectra of the electroweakinos would also play a major role in determining the e cacy of
the leptonic channels. We investigate the prospects of discovery of such channels at the
13 TeV run of LHC. We focus on the following apsects in our study:
We consider a rightsneutrino LSP along with a compressed electroweakino sector
sitting above the LSP, where the lighter states are almost Higgsinolike with a very
small admixture of gauginos.
We give a detailed account of how the decay of the light electroweakinos depend on
the various supersymmetric parameters that govern the mixing, mass splitting and,
in which region of the parameter space the decays are prompt. We also highlight how
even the smallest gaugino admixture plays a signi cant role in their decays.
We comment on the DM predictions for a thermal as well as nonthermal nature of
the rightsneutrino DM candidate in regions of parameter space of our interest.
We then look at possible leptonic signals that arise from such a spectrum and analyze
the signal at LHC.
The article is organized as follows. In section 2 we discuss the model and the underlying
particle spectrum of interest in detail. In the following section 3 we focus on identifying the
parameter space satisfying relevant constraints as well as implications on neutrino sector
and a sneutrino as DM. In section 4 we discuss the possible signatures at LHC and present
our analysis for a few representative points in the model parameter space. We nally
conclude in section 5.
2
The model
We consider an extension to the Minimal Supersymmetric Standard Model (MSSM) by
introducing a rightchiral neutrino super eld for each generation. This extension addresses
the important issue of neutrino mass generation which is otherwise absent in the MSSM.
In particular, we adopt a phenomenological approach for \TeV typeI seesaw mechanism".
The superpotential, suppressing the generation indices, is given by [59, 72, 80]:
W
WMSSM + y L^H^uN^c +
MRN^cN^c
1
2
where y is the neutrino Yukawa coupling, L^ is the leftchiral lepton doublet super eld,
H^u is the Higgs uptype chiral super eld and N^ is the rightchiral neutrino super eld.
Besides the usual MSSM superpotential terms denoted by WMSSM, we now have an added
Yukawa interaction term involving the leftchiral super eld L^ coupled to the uptype Higgs
super eld H^u, and N^ . SM neutrinos obtain a Dirac mass mD after electroweak symmetry
breaking once the neutral Higgs eld obtains a vacuum expectation value (vev) vu, such that
mD = y vu. The third term 12 MRN^cN^c is a leptonnumber violating (L= ) term (4L = 2).
{ 3 {
In addition to the MSSM contributions, the softsupersymmetry breaking scalar
potential receives additional contributions as follows:
1
2
V
soft
VMSSM + m2RjNe j2 +
soft
BM Ne cNe c + T Le:HuNe c + h.c.
where m2R is the softsupersymmetry breaking mass parameter for the sneutrino, BM
is the soft masssquared parameter corresponding to the leptonnumber violating term
and T is the softsupersymmetry breaking LR mixing term in the sneutrino sector. We
have suppressed the generation indices both for the superpotential as well as for the soft
supersymmetrybreaking terms so far.
Note that a small parameter is critical to ensure the absence of any
netuning at
the EW scale ( EW) [5{8]. Finetuning arises if there is any large cancellation involved at
the EW scale in the right hand side of the following relation [1, 2]:
MZ2 =
2
m2Hd +
d
(m2Hu +
tan 2
1
u) tan 2
2
;
(2.1)
where m2Hu ; m2Hd denote the softsupersymmetry breaking terms for the uptype and the
downtype Higgses at the supersymmetry breaking mass scale (which is assumed to be
the geometric mean of the stop masses in the present context) and tan
denotes the
ratio of the respective vevs while
u and
d denote the radiative corrections. Note that,
since we are not considering any speci c highscale framework in the present context,
we are only concerned about the EW
netuning. Typically
EW . 30 is achieved with
j j . 300 GeV [5{8]. The assurance of EW naturalness is the prime motivation in exploring
small
scenarios. However it is quite possible that obtaining such a spectrum from a
highscale theory may require larger netuning among the highscale parameters and the
corresponding running involved, especially considering that mHu evolves signi cantly to
ensure radiative EW symmetry breaking. Therefore,
EW can be interpreted as a lower
bound on netuning measure [5{8]. Note that, stop squarks and gluinos contribute to the
radiative corrections to mHu at one and twoloop levels respectively. It has been argued [9,
10] that an EW
netuning of less than about 30 can be achieved with
. 300 GeV and
with stop squarks and (gluinos) as heavy as about 3 TeV (4 TeV). It is, therefore, important
to probe possible scenarios with low
EW and therefore with low j j.
2.1
The (s)neutrino sector
e
o = feL; eRogT are given by,
o
e
2
e
2
In presence of the softsupersymmetrybreaking terms BM , a split is generated between
the CPeven and the CPodd part of righttype sneutrino elds. In terms of CP eigenstates
we can write: L = eLep+ieLo ; R = eRep+ieRo , where superscripts e, o denote \even" and \odd"
respectively. The sneutrino (e) masssquared matrices in the basis ee = feL; eRegT and
e
M
0m2LL
mjLR2
mjL2R1
mjRR2 A
C ;
{ 4 {
(2.2)
1
2
m2LL = m2L +
m2Z cos 2 + m2D;
mjLR2 = (T
mjRR2 = m2R + m2D + MR2
BM ;
y MR)v sin
mD cot ;
(2.3)
(2.4)
(2.5)
(2.6)
and v =
with j 2 fe; og and the `+' and the `' signs correspond to j = e and j = o respectively,
qvu2 + vd2 = 174 GeV, where vu; vd denotes the vevs of the uptype and the
downtype CPeven neutral Higgs bosons. Further, we have assumed T to be real and
with no additional CPviolating parameters in the sneutrino sector. The physical masses
and the mass eigenstates can be obtained by diagonalizing these matrices. The eigenvalues
The corresponding mass eigenstates are give by,
The mixing angle
= 2
' is given by,
e1j = cos 'j eLj
sin 'j eRj
e2j = sin 'j eLj + cos 'j eRj:
sin 2 j =
(T
y MR)v sin
mD cot
mj22
mj12
;
where j denotes CPeven (e) or CPodd (o) states.
The o diagonal term involving T is typically proportional to the coupling y , ensuring
that the leftright (LR) mixing is small. However, the above assumption relies on the
mechanism of supersymmetrybreaking and may be relaxed. The phenomenological choice
of a large T
O(1)GeV leads to increased mixing between the left and right components
of the sneutrino
avor eigenstates in the sneutrino mass eigenstates [66, 67, 72]. Further,
if the denominator in eq. (2.6) is suitably small, it can also lead to enhanced mixing.
As for the neutrinos, at treelevel with MR
1 eV, their masses are given by m
as in the case of TypeI seesaw mechanism [81{83].
Thus, with MR
neutrino masses of O(0:1) eV requires y
10 6{10 7. Although we have ignored the avor
indices in the above discussion of the sneutrino sector, the neutrino oscillation experiments
indicate that these will play an important role in the neutrino sector. We will assume
that the leptonic Yukawa couplings are avor diagonal, and that the only source of avor
mixing arises from y [84]; see also [85, 86]. Further, at oneloop, avor diagonal BM
can also contribute to the neutrino mass matrix [80, 87] which can be quite signi cant in
the presence of large T in particular.1 The dominant contribution to the Majorana mass
of the active neutrino arises from the sneutrinogaugino loop as shown in gure 1. The
1Note that avor o diagonal terms in BM can lead to avor mixing in the neutrino sector via higher
order e ects which we avoid in our discussions for simplicity.
' MR
y2vu2 ,
O(100) GeV,
{ 5 {
additional contributions to the neutrino mass give signi cant constraints in the fT ; BM g
parameter space.
mass, then, requires a very small y
' 10 11.
Finally, some comments on the scenario with MR = 0 and BM = 0 are in order. With
MR = 0 (and BM = 0), only Dirac mass terms would be present for neutrinos, which is
given by y vu. The oscillation data for neutrinos can only be satis ed by assuming y
(and/or T , at oneloop order) to be avor o diagonal. In addition, O(0:1) eV neutrino
In the sneutrino sector, the relevant mass eigenstates may be obtained simply by
substituting MR = 0 = BM in equations (2.2), (2.3), (2.4). Since the mass matrices for both
CPeven and the CPodd sneutrinos are identical in this scenario, any splitting between
the corresponding mass eigenstates would be absent. Consequently there will be only two
complexscalar mass eigenstates ~1; ~2. Also, there will be no large oneloop contribution
to the Majorana neutrino mass, relaxing the constraint on large T signi cantly.
2.2
The electroweakino sector
The other relevant sector for our study is the charginoneutralino sector, in particular the
higgsinolike states. This sector resembles the charginoneutralino sector of the MSSM.
The treelevel mass term for the charginos, in the gauge eigenbasis, can be written as [88]
are column vectors whose components are Weyl spinors. The mass matrix M c is given by
c
Lmass =
T M c + + h:c:
+ = (Wf+; h~2+)T ;
= (Wf ; h~1 )
T
M c =
p
M2
2MW cos
p
2MW sin
!
:
(2.7)
(2.8)
(2.9)
In the above equation, M2 is the supersymmetry breaking SU(
2
) gaugino (wino) mass
parameter,
is the supersymmetric higgsino mass parameter, MW is the mass of the W
{ 6 {
boson, and tan
is the ratio of vevs as described before. The nonsymmetric M c can
be diagonalized with a biunitary transformation using the unitary matrices U and V to
obtain the diagonal mass matrix,
M Dc = U M cV 1 = Diagonal(m ~+ m ~+ ):
1 2
The eigenstates are ordered in mass such that m ~+
1
m ~+ . The left and righthanded
com2
ponents of the corresponding Dirac mass eigenstates, the charginos ~i+ with i 2 f1; 2g, are
PL ~i+ = Vij j+; PR ~i+ = Uij j ;
where PL and PR are the usual projectors, j =
j y, and summation over j is implied.
In the above mass matrix sW ; s ; cW and c stand for sin W ; sin ; cos W and cos
respectively while
W is the weak mixing angle. MZ is the mass of the Z boson, and M1 is the
supersymmetry breaking U(
1
)Y gaugino (bino) mass parameter. M n can be diagonalized
by a unitary matrix N to obtain the masses of the neutralinos as follows,
MDn = N M nN 1 = Diagonal(m ~01 m ~02 m ~03 m ~04 )
m ~03
m ~04 .
Again, without loss of generality, we order the eigenvalues such that m ~01
The lefthanded components of the corresponding mass eigenstates, described by
fourcomponent Majorana neutralinos ~i0 with i 2 f1; 2; 3; 4g, may be obtained as,
PL ~i0 = Nij j0
;
0 =
B~0; Wf3; h~01; h~02 T
The neutralino mass matrix M n can be written as
, the tree level mass term is given by [88]
n
Lmass =
2
1 0T M n 0 + h:c:
M n = BBB
0
M1
0
MZ sW c
MZ sW s
0
M2
MZ cW c
MZ cW s
MZ sW c
MZ cW c
0
MZ sW s
MZ cW s C
0
1
C :
C
A
where summation over j is again implied; the righthanded components of the neutralinos
are determined by the Majorana condition ~
charge conjugation.
ic = ~i, where the superscript c stands for
Since the gaugino mass parameters do not a ect \naturalness", for simplicity we have
assumed M1; M2
like states, ~01, ~
j j. In this simple scenario there are only three lowlying
higgsino02 and ~1 . The EW symmetry breaking induces mixing between the
gaugino and the higgsinolike states, via the terms proportional to MZ ; MW in the mass
matrices above. The contributions of the rightchiral neutrino super elds to the chargino
{ 7 {
and neutralino mass matrices are negligible, thanks to the smallness of y (' 10 6). Thus
lightest neutralino and charginos are expected to be nearly the same as in the MSSM.
Following [89] (see also [90]), in the limit M1; M2
for the masses below,
j j, we give the analytical expression
m ~
1
= j j 1
m ~0a;s =
M W2 sin 2
M2
MZ2 (1
2
sin 2 )
+ O(M2 2) + rad:corr:
sin W2 +
M1
cos W2
M2
+ rad:corr:
(2.16)
where the subscripts s (a) denote symmetric (antisymmetric) states respectively, and the
sign of the eigenvalues have been retained. For the symmetric state Ni3; Ni4 share the
same sign, while for the antisymmetric state there is a relative sign between these two
receives di erent radiative corrections in M n and M c), M1; M2 and tan
terms. Although the leading contribution to the mass eigenvalues are given by j j (which
a ects the mass
splitting between the three light higgsinolike states due to nonnegligible gauginohiggsino
mixing. The radiative corrections, mostly from the third generation (s)quarks, contribute
di erently for m ~
1
and m ~01;2 and have been estimated in [89, 91{93]. As we are interested
in a spectrum where the lighter chargino and the neutralinos play a major role and the
knowledge of their mass di erences would become crucial, it is necessary to explore what
role the relevant SUSY parameters have in contributing to the masses of the higgsino
dominated states. It is quite evident from our choice of large M1 and M2 that the three
states according to eq. (2.16) would be closely spaced.
We now look at how the variation of the above gaugino parameters a ect the shift
variation of the mass di erences
in mass of m ~
1
and m ~01;2 . Assuming
have used SARAH [94, 95] to generate model les for SPheno [96, 97], and have used the same
to estimate the masses. Since SLHA [98] convention has been followed, the input parameters,
as shown in the gures above, are interpreted as DR parameters at
1:6 TeV. Note that
the same model and spectrum generators have been used for all subsequent gures. The
me01 and
m2 = me02
m
as a function
= 300 GeV, tan
= 5, in
gure 2 we show the
following features are noteworthy from
gure 2:2
For
> 0; M1; M2
: here ~02 is the heaviest higgsinolike state while ~1 remains
between the two neutralinos. For a xed M1
j j, the mass di erence
m1 increases
as M2 decreases. This feature can be simply understood from eq. (2.16). A similar
conclusion also holds for
m2. Further, as shown in panels (a) and (b) of gure 2,
the variation in
m2 is larger compared to
m1 in this case.
For
> 0;M1 < 0: we nd that negative M1 can lead to negative
m1, since the
lightest chargino can become lighter than this state for a wide range of M2 [29, 30, 38].
2Although our numerical analysis, as shown in gure 2, includes radiative corrections, the generic features
also appear at the treelevel for j j = 300 GeV, M1; M2
j j and tan
= 5.We have checked this using a
Mathematica code.
{ 8 {
the palette.
me01 ( m2 = me02
2
1
3
2
1
] 3
eV 2
G
2
1
3
2
1
2
M
?3
?2
?1
1
2
3
?3
?2
?1
As shown in gure 2(a), such a scenario occurs for large M2 values (& 2 TeV) with
jM1j . 1 TeV. Further, for jM1j
M2, as jM1j decreases one observes an upward
kink in the
attributed to the change in nature of the lightest neutralino state from antisymmetric
to the symmetric state.
< 0; M1 > 0: as shown in gures 2(c) and 2(d), similar to the
> 0 case,
mi
smoothly increases with decreasing M2 in this region as well.
< 0; M1 < 0: in gure 2(c) we again see (due to the change in nature of LSP)
a sharp rise of
m1 for large M2 & 2 TeV and jM1j . 1:5 TeV. Note that in this case
the ~1 can be the heaviest higgsinolike state in a substantial region of the parameter
space for M2 & 2 TeV, as shown in gure 2(d).
2.3
Compressed Higgsino spectrum and its decay properties
As we have already emphasized, the focus of this work is on higgsinolike NLSPs in a
scenario with a rightsneutrino LSP where the choice of small j j is motivated by the
\naturalness" criteria [6, 8, 9]. Thus we will restrict our discussions to scenarios where the
higgsino mass parameter j j . 500 GeV. The gaugino mass parameters have been assumed
{ 9 {
j j, and m~1 < j j. Here
to be heavy for simplicity; thus the light higgsinolike states are quite compressed in mass
( gure 2).
Note that since the gaugino mass parameters are much heavier, the gaugino fraction
in the higgsinolike states are small (O(10 2)). However, M1 and M2 play signi cant role
in determining
m2 and also the hierarchy between the higgsinolike states.
While for most parameter space the spectra shown in the left panel of gure 3 is realized,
for M1 < 0 (i.e. sign(M1M2) =
1), it is possible to achieve the chargino as the lightest
higgsinolike state which leads to a spectra as shown in the right panel of gure 3. Further,
with ; M1 < 0 one can also have the chargino as the heaviest of the three higgsinolike
state. However, as we will discuss subsequently in section 4, this does not contribute to
any new signature. Figure 3 schematically shows the mass hierarchies of our interest. For
the electroweakinos which are dominantly higgsinolike, their production rates and
subsequent decay properties would have serious implications on search strategies at accelerator
machines like LHC. This in turn would play an important role in constraining the higgsino
mass parameter
in the natural SUSY framework.
~
1 ! ~01W
We now try to brie y motivate the compositions of the LSP as well as the
higgsinolike states of our interest and their decay properties. In the presence of ~01 as the
lightest higgsinolike state, the decay modes available to the chargino are ~
1 ! l ~kj and
, where j; k corresponds to a particular lighter sneutrino species. The partial
width to the 3body decay modes, mostly from the o shell W boson mediated processes,
are suppressed by the small mass di erence while small y (. 10 6) suppresses the
2body decay mode. In such a scenario, the gaugino fraction in ~1 , can contribute to the
2body mode signi cantly in the presence of small leftright mixing (
O(10 5)) in the
sneutrino sector.
We illustrate the decay properies of ~
1 based on the composition of the LSP in
gure 4.3 As shown in
gure 4, for small T and therefore for small left admixture in
3The particular choice of gaugino mass parameters correspond to
m1 . 1 GeV, and the partial width
in the corresponding hadronic channel is quite small (' 10 16 GeV). Thus, the leptonic partial width
resembles the total width of ~1 .
?9
?10
?11
)
?
epL ?12
to T , the soft leftright mixing parameter in the sneutrino sector. The plot shows the required T
and mixing angle sin( j) for prompt decay of the chargino. We focus on the values of T in our
study ensuring prompt decays of the chargino.
the sneutrino sector, y dominates the decay of ~1 . As T increases past O(10 2), the
gaugino fraction plays a crucial role, which explains the rise of the partial width in the
2body leptonic decay mode. With y
10 6 prompt decay of the lightest chargino to
the sneutrino and lepton is always ensured. However, for y
10 7 prompt decay of the
chargino in the leptonic channel is not viable in the absence of adequate left admixture;
T
& O(10 2) GeV is required to ensure prompt decay in the leptonic channel. The dip
in gure 4 appears as a consequence of possible cancellation between the gaugino and the
higgsino contributions to the vertex factor (e.g. / (g2V11 sin j
y V12 cos j ), g2 is the
SU(
2
) gauge coupling). It is of our interest to study the scenario where the 2body decay
mode into l ~ competes with the 3body decay mode. Since the present work focuses on
prompt decays, we ensure small left admixture with T & O(10 2) GeV in the dominantly
rightsneutrino LSP to ensure prompt decay of ~1 in the 2body leptonic decay mode. The
mass splitting
m1 & 1 GeV has been considered to ensure a competing 3body mode.
Since we have assumed a compressed higgsino spectrum, together with a mostly
rightsneutrino LSP, the light higgsino states include ~10; ~02; ~
1 and at least one generation of
CPodd and/or CPeven sneutrino LSP as described in section 2. In gure 2 we showed that
for a xed j j, the hierarchy and the mass di erences between the higgsinolike states are
a ected signi cantly by the choice of the gaugino mass parameters M1; M2, and sign( ).
In a similar compressed scenario within the MSSM, the higgsinos ~02 and ~1 decay into soft
leptons or jets [99] and ~01, producing E= T . Scenarios with compressed higgsinos in MSSM
have been studied in the light of recent LHC data [27, 29{33]. For smaller mass di erences,
130 MeV .
m1 . 2 GeV, the e ective twobody process ~
dominate the hadronic branching fraction. Further, when ~02 is also almost degenerate with
1 !
~01 [100{102] can
HJEP06(218)4
Parameters
Values
jM1j (GeV)
(500{3000)
jM2j (GeV)
(500{3000)
j j (GeV)
300
tan
5
T (GeV )
~1 , for an even smaller mass di erence
m2, ~02 !
~01 can become signi cant [103{106].
Note that while the threebody decay modes (soft leptons/ jets and ~01) su er from phase
space suppression ( m)5 , the twobody mode ( ~01) is also suppressed by a loop factor.
In addition to the above decay channels of the compressed higgsinolike states, the
present scenario with a sneutrino LSP o ers additional decay channels to the lighter
sneutrinos. While a ~0
1 !
~ would lead to missing transverse energy (as in the case for MSSM)
without altering the signal topology if the neutralino was the LSP, ~
1 ! l ~ would have
a signi cant impact on the search strategies. For a pure rightsneutrino LSP this decay
is driven by y . In the presence of large T and therefore a large leftright mixing in the
sneutrino LSP, a gaugino fraction of & O(10 2) in the higgsinolike chargino begins to
play a prominent role as the decay is driven by a coupling proportional to g
where
represents the gaugino admixture and
represents the LR mixing in the sneutrino
sector. The presence of multiple avors of degenerate sneutrinos would lead to similar decay
probabilities into each avor and would invariably increase the branching to the twobody
leptonic mode when taken together.
In the present context, as has been emphasized, only prompt decays into the leptonic
channels such as ~
1 ! l ~ and ~
i0 ! ~1 jsjs0, where js; js0 denote softjets or softleptons
can give us a signal with one or more hard charged leptons in the
nal state. Since
the latter consists of ~
1 in the cascade, it can also lead to leptonic
nal states. These
branching fractions would be a ected by any other available decay channels and therefore
it is important to study the di erent regions of parameter space for all possible decay modes
of the light electroweakinos. As shown in
gure 2, while in most of the parameter space
~01 is the lightest higgsinolike state, and ~1 is placed in between the two neutralinos (i.e.
m ~01 < m ~
1
< m ~02 ), it is also possible to have ~1 as the lightest or the heaviest higgsinolike
state. The important competing modes for ~1 and ~02 where m ~01 < m ~
1
< m ~02 include
(a) ~1 ! ~10jsjs0=
;
(b) ~20 ! ~10jsjs= ;
(c) ~20 ! ~1 jsjs0=
where (c) is usually small. However, if ~1 is the lightest higgsinolike state, decay modes
(b) and (c), together with ~
0
1 ! ~1 jsjs0=
heaviest higgsinolike state, decay modes (a), (b) and ~
although the latter would be subdominant.
can be present. Similarly, when ~
1 is the
0
1 ! ~2jsjs0=
can be present,
In gures 5 (
> 0) and 6 (
< 0) we show the variation of branching fraction in the
0
leptonic decay channels ~1 ! l ~i and ~i ! l ~i W . The relevant parameters for the scan
can be found in table 1.
HJEP06(218)4
) 0.7
BR 0.3
0.9
0.8
1.5
0.5
(b)
2
1
bino soft mass parameter, M1 for the Higgsino mass parameter,
parameter M2 is shown in the palette.
?3
?2
?1
0
bino soft mass parameter, M1 for the Higgsino mass parameter,
=
300 GeV. The wino mass
against the
parameter M2 is indicated in the palette.
Since the sneutrino masses and mixing matrices do not change in the scan, the two
body partial decay widths ( ~1 ! l ~i) and ( ~i0 !
~j ) are only a ected by the variation
of the gauginoadmixture in the higgsinolike states. However, the choice of gaugino mass
parameters do a ect the mass splittings
m2 through mixing and can even alter
the hierarchy. These alterations in the spectrum mostly a ect the 3body decay modes
described above which has a signi cant e ect on the branching ratio.
As shown in gure 2(a), for sgn( ) = + (i.e.
= 300 GeV) and for M1 < 0,
m1 is
almost entirely . 1 GeV. With large M2 and jM1j . 2 TeV, ~
1 can become the lightest
higgsinolike state making its leptonic branching probability close to 100% as shown in
gure 5(a). However, for small jM1j, and large M2, where
m1 increases, this branching is
somewhat reduced to about 0.8 and the 3body decays start becoming relevant. For M1 > 0
region the branching ratio increases as M1 increases. This can be attributed to the
consistent decrease in
m1 ( gure 2(a)) and therefore of the threebody partial decay width.
For M1 < 0, generally the branching grows for larger
m2 ( gure 2(b)) and decreases for
smaller M2 as the mass splitting goes down. It is again worth pointing out here that for
large M2 and with jM1j . 2 TeV,
m1 < 0 and ~
1 becomes the lightest state. Thus in
this region the threebody mode into ~01 is more phasespace suppressed compared to the
decay mode into ~ .
1
4 Further, as jM1j approaches , the symmetric state, which mixes
well with the bino, acquires larger bino fraction and there can be a cancellation in the
vertex factor / g2(N22
tan W N21) for the twobody decay width into sneutrino. This
and consequently Br( ~02 ! ~1 jsjs0) is rather small.
can reduce the corresponding width and then increase again as jM1j decreases. Thus the
branching ratio for the threebody decay shows a discontinuous behavior in such regions.
For positive M1, the branching ratio shows similar pattern as
m2 variation, as expected.
Larger
m1 in this region implies that the threebody decay ( ~02 ! ~10jsjs) can be larger,
For
=
300 GeV, there are marked di erences in the decay probabilities as the ~
can become the heaviest when M1 < 0, for large regions of the parameter space in contrast
to what was observed for
> 0. Figure 6(a) shows the branching ratio of ~1 ! l ~j which
decreases as M2 increases. Although, for large M2, the gaugino fraction in ~
small, thus possibly reducing the partial width in this twobody decay mode; smaller
1 would be
in this region ensures that the competing threebody mode decreases even more. Therefore,
the branching ratio in the twobody mode is enhanced. This holds true for almost the entire
range of M1. The feature in the negative M1 region, as jM1j approaches j j, where the
branching ratio rises faster for larger M2 values, corresponds to a similar fall in
m1 (see
1
m1
gure 2(c)).
In gure 6(b) we show the variation of Br( ~02 ! ~1 jsjs0) with M1; M2. For negative
M1, this branching ratio increases with decreasing M2, since the corresponding mass
difference
m2 also increases (see gure 2). The larger M2 values are not shown for M1 < 0,
since ~1 becomes the heaviest higgsinolike state in this region. Thus,
m2 < 0 as shown
in see gure 2(d), and this decay mode does not contribute. For M1 > 0 smaller M2 values
correspond to larger branching fractions, since
m2 becomes larger, increasing the partial
width. However, for large M2 values, the partial width decreases rapidly as
m2 decreases.
Note that T
= 0:5 GeV has been used in the gure. For smaller values of T the
leptonic branching ratio of ~
1 would generally be reduced when it is not the lightest
higgsinolike state. However, the generic features described above would remain similar.
Note that, y
10 6 can lead to prompt decay even in the absence of large leftadmixture,
as induced by large T . Therefore, even for small T . O(10 2), for certain choice of the
gaugino mass parameters, the leptonic branching can be competing, and thus would be
relevant to probe such scenario at collider.
4Note that, because of mi . 1:5 GeV, decay modes involving
can dominate the hadronic
branching fractions in this region. While we have estimated the same to be signi cant using routines used in
SPhenov4 [96, 97], see also refs. [100{102], the presence of large T
typically ensures that the twobody
decay mode shares rather large branching fraction in these regions. In the plot we have only included
threebody partial widths. A similar strategy has been adopted for regions with small
m2 as well.
HJEP06(218)4
We now consider the model parameter space in light of various constraints.
We implement the following general constraints on the parameterspace:
The lightest CPeven Higgs mass mh has been constrained within the range: 122
mh (GeV)
While the experimental uncertainty is only about
0.25 GeV, the present range of
3 GeV is dominated by uncertainty in the theoretical
estimation of the Higgs mass, see e.g. [110] and references there.5
The lightest chargino satis es the LEP lower bound: m
103:5 GeV [111]. The
LHC bounds, which depend on the decay channels of the ec1hargino, will be considered
only for prompt channels in more detail in section 4.
The light sneutrino(s) (with small leftsneutrino admixture) can contribute to the
nonstandard decay channels of (invisible) Higgs and /or Z boson. The latter requires
the presence of both CPeven and CPodd sneutrinos below ' 45 GeV. Constraints
from the invisible Higgs decay (' 20%) [112] and the Z boson invisible width ('
2 MeV) [113] can impose signi cant constraints on the parameter space where these
are kinematically allowed.
We further impose Bs !
+
[114] and b ! s constraints [115].
3.1.1
Implication from neutrino mass
Recent analyses by PLANCK [116] imposes the following constraint on the neutrino masses:
P mi . 0:7 eV. In the present scenario, the neutrinos can get a treelevel mass, as is usual
in the TypeI seesaw scenario. For y
10 6, and MR
100 GeV, the active neutrino
mass is of O(0:1) eV. Further, as discussed in section 2.1, a nonzero Majorana mass term
MR, and the corresponding softsupersymmetry breaking term BM introduce a splitting
between the CPeven and CPodd mass eigenstates of rightsneutrinos. In the presence
of sizable leftright mixing, signi cant contribution to the Majorana neutrino mass can be
generated at oneloop level in such a scenario, the details depend on the gaugino mass
parameters [80, 87]. Thus, regions of large BM , in the presence of large leftright mixing
in the sneutrino sector (induced by a large T ) can be signi cantly constrained from the
above mentioned bound on (active) neutrino mass. In gure 7 we show the allowed region
in the T
as follows:
BM plane. We consider y 2 f10 6; 10 7
g while the other parameters are xed
= 300 GeV, M3 = 2 TeV, MQ3 = 1:5 TeV, Tt = 2:9 TeV, ML1=2 = 600 GeV,
ms~oft = 100 GeV and MA = 2:5 TeV. While in the former case the treelevel and radiative
contributions to the neutrino mass can be comparable (with each being O(0:1) eV), the
radiative corrections often dominate for the latter. As shown in the gure, clearly larger
T values are consistent with neutrino mass for smaller BM .
5Note that, besides the MSSM contributions, rather large T can induce additional contributions to the
Higgs mass [66]. Our numerical estimation takes this e ect into account.
2 )
4e?10
2e?10
1e?10
0
0 1 2 3 4 5 6 7 8 9 10
T? (GeV )
O(10 2). The colored palette denotes the mass of the heaviest neutrino.
mass and leftfraction. The right panel shows the allowed region respecting the direct detection
constraint from XENON1T.
3.1.2
Implications for dark matter
Within the paradigm of standard model of cosmology the relic abundance is constrained
as 0:092
h
2
0:12 [116]. Stringent constraints from direct search constraints require
the DMnucleon (neutron) interaction to be less than about 10 9 pb, which varies with the
mass of DM, see e.g. LUX [117], PANDAII [118] and Xenon1T [119].
In gure 8, with y 2 f10 6; 10 7g; tan
2 f5; 10g;
=
450 GeV; mA = 600 GeV
and all other relevant parameters are xed as before, we scan over the set of parameters
fT ; m~; BM g ( rst generation only).
We plot the leftadmixture (sin j ) in the LSP
required to obtain the thermal relic abundance and direct detection cross section against
its mass in the left and the right panel respectively. We have used micrOMEGAs3.5.5 [120]
to compute the thermal relic abundance and direct detection crosssections.
With T
& O(10 3), which is the region of interest to allow leftright mixing in the
sneutrino sector, the rightsneutrino LSP thermalizes with the (MS)SM particles via its
interaction with leftsneutrino and Higgs bosons. The important annihilation processes
involve schannel processes mediated by Higgs bosons, as well as fourpoint vertices leading
to hh; W
W ; ZZ; tt nal states. However, large leftright mixing induces large direct
detection crosssection. In
gure 8 we have only shown parameter regions with a mass
di erence of at least 1 MeV between the CPeven and the CPodd states to prevent the Z
boson exchange contribution to the direct detection [59, 121, 122].6 There are tchannel
contributions mediated by Higgs bosons, mostly from the Dterm, as well as the trilinear
term T , and is proportional to the leftright mixing (sin ) in the sneutrino sector. Note
that, we have only shown points with spinindependent direct detection crosssection less
than 10 9 pb.
As shown in the left panel of gure 8, sin
of O(0:1) is required to achieve the right
thermal relic abundance. The right relic abundance is achieved soon after the dominant
annihilation channels into the gauge bosons (and also Higgs boson) nal states are open
(i.e. mDM & 130 GeV), while at the Higgs resonances (mh = 125 GeV and mA
a lower admixture can be adequate. Further, coannihilation with the lowlying
higgsinolike states (j j
450 GeV), when the LSP mass is close to 450 GeV, can also be e ective.
As shown in the right panel of the same
gure, for mDM . 450 GeV, most parameter
space giving rise to the right thermal relic abundance is tightly constrained from direct
searches (spinindependent crosssections) from Xenon1T [119] (similar constraints also
arise from LUX [117], PANDAII [118]), the exceptions being the resonant annihilation and
coannihilation regions.
Note that for very small T and y . 10 6, the e ective interaction strength of
rightsneutrinos may be smaller than the Hubble parameter at T ' mDM. In such a scenario,
nonthermal production, especially from the decay of a thermal NLSP, can possibly generate
the relic abundance [60{63]. Further, nonthermal productions can also be important in
certain non standard cosmological scenarios, e.g. early matter domination or low reheat
temperature, see e.g. [123, 124]. In addition, large thermal relic abundance can be diluted if
substantial entropy production takes place after the freezeout of the DM. For such regions
of parameter space our rightsneutrino LSP is likely to be a nonthermal DM candidate.
4
Signatures at LHC
We now focus on the LHC signal of the higgsinolike electroweakinos in the presence of
a rightsneutrino LSP. As discussed, the various decay modes available to e1 , e02 and e1
0
in presence of a rightsneutrino LSP depend not only on the mixing among the various
sparticle components but also crucially on the mass splittings. The LHC signals would
6We have checked that with 1 MeV mass splitting and a leftadmixture of O(10 2), as is relevant for
thermal relic, the heavier of the CPeven and the CPodd state has a decay width of
into the LSP and soft leptons/quarks via o shell Z boson. This corresponds to a lifetime of . 10 3 s. Thus
it would decay well before the onset of Big Bang Nucleosynthesis (BBN) and is consistent with constraints
10 20 GeV, mostly
from the same.
then re ect upon the above dependencies on the parameter space. We therefore look at all
possible signals for di erent regions of
m1=2 and T . While there are regions of
m1=2
where the chargino decays nonpromptly to pions that lead to the chargino traveling in the
detector for some length and then decay into a soft pion and neutralino. In such cases, since
both decay products are invisible, the relevant search channel at LHC is the disappearing
tracks [32, 33, 125]. Our focus however, is primarily on the prompt decay of the chargino to
hard leptons (small
m1=2 and large T ) which would be clean signals to observe at LHC.
The following production channels are of interest to us:
0 0 + 0 0 0 0
p p ! e1 e2; e1 e1; e1 e1 ; e1 e2; e1 e1; e20 e20; el el; el el ; el e; e e
(4.1)
the pair production crosssection of 0
where the sleptons and sneutrinos are heavier than the electroweakinos here. The LSP
pair production is excluded in the above list. The processes as given in eq. (4.1) are in
decreasing order of production crosssections as obtained from Prospino [126{128]. The
followed by the chargino pair production,
0
associated chargino neutralino pair, i.e e1 +e1=2 production has the largest crosssection
e1 e10 and e2 e20 are negligible compared to the other
e1 e1 0as in gure 9. In the pure higgsino limit,
processes. Since the strong sector is kept decoupled and the compressed higgsino sector
leads to soft jets and leptons, the only source of hard jets are from initialstate radiations
(ISR). The suppressed jet multiplicity in the signal could prove to be a potent tool for
suppressing SM leptonic backgrounds coming from the strongly produced tt and single
top subprocesses which would give multiple hard jets in the nal state in association with
the charged leptons. Therefore we shall focus on the following leptonic signals with low
hadronic activity:
Dilepton + 0 jet + E= T
), and associated pair production, e1 ei0 with i = 1; 2 ( e1 ! l
The monolepton signals would come from the pair production of e1 e1 , ( e1 ! l
e
and
e2=1 ! e1 W
e
0
and ei !
) leading to missing energy. Among the dilepton signals we look into
both opposite sign leptons and same sign lepton signal with missing energy. Opposite sign
leptons arise from the pair produced e1 e1 , with the chargino decaying leptonically as
+
e1 ! l e. In regions of the parameter space where
0
process may contribute to the dilepton state via ei ! e1 W
e2=1 is heavier than e1 , e1 ei0, i = 1; 2
0
followed by e1
! l .
e
channels come from e10 e20 with e1=2 ! e1 W
0
In such cases, there could be either opposite sign dilepton signal or samesign dilepton
signal owing to the Majorana nature of the neutralinos ( ei0). A similar contribution to both
. Also there are subleading contributions
from slepton pair productions which can become relevant if light sleptons are also present
in the spectrum.
It is worth pointing out that in very particular regions of the parameter space e1
is the NLSP and therefore always decays to a hard lepton and sneutrino LSP. In such
cases, signal rates for the dilepton channel would be most interesting and dominant rates
for samesign dilepton would be a particularly clean channel which will be important to
0.1
0.01
B = e1 e10, C = e1 e20 and D = e1 e2
can be estimated by using a K factor
very e ectively. This is very particular of the parameter region
when M1 is negative and one has a sneutrino LSP.
4.1
Constraints on electroweakino sector from LHC
Before setting up our analysis on the above signals we must consider the role of existing
LHC studies that may be relevant for constraining the parameter space of our interest.
LHC has already looked for direct production of lightest
e1 , e02 and e10 in both run 1 and
prompt search results only.
run 2 searches at 7, 8 and 13 TeV respectively albeit assuming simpli ed models. Search
results have been reinterpreted both in terms of nonprompt as well as prompt decays of
the Higgsinos. Since the focus of our study is on prompt decays of e1 , we consider the
The LHC results have been reinterpreted assuming simpli ed models with and without
intermediate left and right sleptons with e10 LSP contributing to E= T (see table 3).
Assuming 100% leptonic branching of the sparticles and an uncompressed spectra,
CMS has ruled out degenerate winolike m
600 GeV from samesign dilepton, three lepteo1n and four lepton searches with at most
1 jet [129]. The limits vary slightly depending on the choice of slepton masses. For
the nearly compressed higgsino sector and assuming mass degeneracy of the lightest
chargino ( e1 ) and nexttolightest neutralino ( e02) the alternate channels probed
by LHC are soft opposite sign dileptons searches [130]. The mass limits on the
, me02 < 1:2 TeV for a binolike me01 <
compressed higgsino sector relax to
230 (170) GeV for me01
210 (162) GeV.
corresponding leptons would be soft compared to BP1 and BP2a. Therefore BP2b and
BP3 require higher luminosity 106 fb 1 and 613 fb 1 respectively for observation.
The challenge in having a multilepton signal from the production of compressed
higgsinolike electroweakinos comes from the fact that the decay products usually lead to soft nal
states. However, with a sneutrino LSP and the possibility of the decay of the chargino to
a hard lepton and the LSP leads to a healthy dilepton signal with large missing energy
+
(from e1 e1 as well as e1 e20 pair production, provided the nexttolightest neutralino
decay yields a lepton via the chargino). A subdominant contribution also arises from
e1 e20 with each of the neutralino decaying to a chargino and an o shell W boson which
0
gives soft decay products. The chargino then decays to a charged lepton and sneutrino
LSP. This happens most favorably when chargino is the lightest of the higgsinos. Owing to
the Majorana nature of ei0 we can have signals for oppositesign and samesign dilepton
nal states with large missing transverse energy. Hence we look into both the possibilities:
Opposite sign dilepton + 0 jet + E= T
Same sign dilepton + 0 jet + E= T
Opposite sign dilepton + 0 jet + E= T signal
+
Opposite sign dilepton signal arises mainly from e1 e1 production process. Subdominant
0
contributions arise from e1 e1
,
e1 e20 and e1 e20 as discussed before. The dominant SM
0
contributions to the opposite sign dilepton signal with missing energy come from tt, tW
and DrellYan production. Among the diboson processes, W +W
(W +
! l
+ ; W
!
l
), ZZ ( Z ! l+l ; Z ! jj=
) and W Z+jets (W
! jj; Z ! l+l ) also contribute
substantially to the opposite sign dilepton channel. The triple gauge boson processes may
also contribute. However, these have a small production crosssection and are expected to
be subdominant. There could also be fake contributions to missing energy from hadronic
energy mismeasurements.
In
gure 12 we show the normalized distributions for important kinematic variables
for two benchmarks BP2a and BP2b with
M = 100; 40 GeV respectively along with
the dominant SM backgrounds after selecting the opposite signdilepton state (D1). We
nd that as expected the lepton pT distribution for BP2a is much harder than the SM
backgrounds processes whereas for BP2b with a lower mass gap between the chargino
and LSP, the leptons are much softer and the distributions have substantial overlap with
the backgrounds. We further use the other kinematic variables,
E= T = j ip~Ti j and Ml2+l
= (pl1 + pl2 )2
(4.4)
(where i runs over all visible particles in the nal state) represent the transverse missing
energy and invariant masssquared of the dilepton
nal state respectively which peak at
higher values for SUSY signals over backgrounds in BP2a whereas BP2b still retains a
large overlap with the SM backgrounds. However, the largest source of background for the
HJEP06(218)4
dilepton background coming from DrellYan process can be removed safely by excluding
the Z boson mass window for Ml+l . Since the SUSY signals do not arise from a resonance
the exclusion of the Z mass window is expected to have very little e ect on the signal
events. We further note that removing btagged jets would also be helpful in removing SM
background contributions from the strongly produced top quark channels which have huge
cross sections at the LHC.
Another kinematic variable of interest to discriminate between SUSY signals and SM
backgrounds is the MT2 variable [197] constructed using the leading and subleading lepton
p~T and E=~T . For processes with genuine source of E= T there is a kinematic end point of
MT2 which terminates near the mass of the parent particle producing the leptons and the
invisible particle. In SM, channels such as tt; tW; W +W
involving a W boson nally giving
the massless invisible neutrino in the event, the endpoint would be around 80 GeV. For
SUSY events the invisible particle is not massless and therefore the visible lepton pT will
depend on the mass di erence. Thus the endpoint in the signal distribution would not have
a cuto
at the parent particle mass anymore. For BP2a which has a large
M the end
point is expected at larger values (
200) GeV. However for BP2b, where the available
phase space is small for the charged lepton due to smaller
M the MT2 distribution is not
very wide and has an endpoint at a much lower value. Thus a strong cut on this variable
is not favorable when the sneutrino LSP mass lies close to the electroweakino's mass.
Following the features of the kinematic distributions, we implement the following
optimal selection criteria as follows for both signal and backgrounds:
D1: the nal state consists of two opposite sign leptons and no photons.
D2: the leading lepton has pT > 20 GeV and the subleading lepton has pT > 10 GeV.
D3: Ml+l
> 10 GeV helps remove contributions from photon mediated processes
while the Z mass window is also removed by demanding that the oppositesign same
avor dilepton invariant mass satis es 76 < Ml+l
< 106 GeV. This helps to reduce
a large resonant contribution form the Z exchange in DrellYan process.
D4: we reject any bjet by putting a bjet veto (for pT > 40 GeV). This helps in
suppressing background events coming from top quark production.
D5: we demand a completely hadronically quiet event by choosing zero jet
multiplicity (Njet = 0) in the signal events. This is e ective in suppressing contributions
from background processes produced via strong interactions.
D6: we demand E= T > 80 GeV to suppress the large DrellYan contribution.
D7: we demand MT 2 > 90 GeV which helps reduce a majority of the other SM
backgrounds.
D8: E= T > 100 GeV is implemented to further reduce the SM backgrounds.
In table 9 we show the signal events that survive the above listed kinematic selections
(cut ow). We nd that among all benchmarks, BP2a is the most robust followed by
dN dET 1
10?1
10?2
dN dNb 1
10?1
10?2
10?3
BP2a
BP2b
Drell Yan
WW
ET (GeV)
BP2a
BP2_b
tW
ZZ
Drell Yan
WW
5
N
b
T210?1
M
d
/
N
d
/1N10?2
10?3
200 250 300 350
MT2(GeV)
BP4. Note that we avoid using the MT 2 cut on the benchmarks where the mass splitting
between the chargino and the sneutrino LSP is small as D7 cut makes the signal events
negligible. As pointed out earlier, the endpoint analysis in MT 2 is not favorable for small
M as seen in the signal and background distributions in gure 12. Thus BP2b and BP3
have cuts D1{D6. In table 10 we plot the SM background events after each kinematic
cuts. Quite clearly up to cut D6 the SM background numbers are quite large, and then
drastically reduce after the MT 2 cut (D7) is imposed.
In table 11 we give the required integrated luminosities to achieve a 3 and 5
statistical signi cance for the signal events of the benchmark points. Just like for the monolepton
ZZ
tt
Drell Yan
WW
Signal
tW
Total
BP1
BP2a
BP4
Signal
BP2b
BP3
D2
129
271
298
D2
452
2394
D3
656
5399
Preselection (D1)
130
306
209
455
2424
Preselection (D1)
Number of events after cut
D3
112
265
246
D3
351
1840
D4
109
161
241
D4
345
1805
D5
68
108
153
D5
230
1186
D7
22
76
81
D6
45
189
nal state number of events at 100 fb 1 for SUSY signals.
Note that the events have been roundedo to the nearest integer. Crosssections have been scaled
using NLO Kfactors obtained from Prospino.
nal state number of events at 100 fb 1 for Standard
Model backgrounds. Note that the events have been roundedo
to the nearest integer.
Crosssections scaled with Kfactors at NLO [178] and wherever available, NNLO [191{196] have been used.
case, BP2a requires the least integrated luminosity and is in fact gives a 3 signi cance for
much lower luminosity compared to monolepton signal. However for the rest of the
benchmarks monolepton channel is more favorable while the oppositesign dilepton can act as
a complementary channel for BP1 with higher luminosity and BP3 with the veryhigh
luminosity option of LHC. BP2b type of spectrum for the model is strongly suppressed
in the dilepton channel. The signal rates can be attributed to the fact that the leptonic
branching of the chargino is much larger for BP2a (
100%) than BP1 (
12%) and
hence the signal is much more suppressed for BP1 than in BP2a. For BP4 where the
NLSP is the chargino, the opposite sign dilepton signal is a robust channel for discovery.
Thus this channel is not a likely probe for benchmarks with a smaller phase space, like
BP2b and BP3 in which cases, as seen in the previous section, monolepton signals fare
better over dilepton signals. Whereas for spectra like BP2a and BP4, with a large phase
space available, opposite sign dilepton signals are much more sensitive than monolepton
signals. In contrast spectra like BP1 with a lower leptonic branching of the chargino,
monolepton + missing energy signal is still a better channel to look for than opposite sign
dilepton channel.
BP1
BP2a
BP2b
BP3
BP4
568
51
1035
160
1:83
104
Same sign dileptons + 0 jet + E= T signal
A more interesting and unique new physics signal at LHC in the dilepton channel is the
samesign dilepton mode. The samesign dilepton in the absence of missing transverse
energy is a clear signal for lepton number violation and forms the backbone for most
studies of models with heavy righthanded Majorana neutrinos. Even with missing energy,
the samesign dilepton is a di cult nal state to nd within the SM and therefore a signal
with very little SM background. Thus nding signal events in this channel would give very
clear hints of physics beyond the SM.
In our framework of SUSY model the samesign dilepton signal with missing
energy and few jets come from the production modes e1 e20 and=or e1 e10 where the
lepton number violating contribution comes from the decay of the Majoranalike
neutrali0
nos given by e2 !
W
e1 with e1 ! le.
grounds are rare in SM, with some small contributions coming from processes such as
We note that samesign dilepton
backp p !
W Z; ZZ; W +W +=W
W
+jets, ttW and ttZ as well as from triple gauge boson
productions such as W W W where with two of the W bosons being of same sign and the
other decaying hadronically. Other indirect backgrounds can arise from energy
mismeasurements, i.e, when jets or photons or opposite sign leptons fake a same sign dilepton signal.7
For our analysis we select the samesign dilepton events using optimal cuts for both
signal and background using the following kinematic criteria:
S1: the nal state consists of two charged leptons with samesign and the leading
lepton in pT must satisfy pT > 20 GeV with the subleading lepton having pT > 15 GeV.
Additionally we ensure that there are no isolated photon and bjets in the nal state.
S2: a minimal cut on the transverse mass constructed with the leading charged
lepton (l1), MT (l1; E=~T ) > 100 GeV is chosen to reject background contributions coming
from W boson.
S3: to suppress background from W
W jj as well as those from ttW , ttZ with
higher jet multiplicities than the SUSY signal, we keep events with only up to 2 jets.
7There may be additional contributions for samesign dilepton coming from nonprompt and conversions
which we have not considered [129].
BP1
BP2a
BP2b
BP3
BP4
Preselection (S1)
5
3
32
2
30
S2
5
W +W +jj
W
W jj
tW
ttW
tt
Total background
Preselection (S1)
3856
94
60
416
188
40
128
90
S3
5
nal state number of events at 100 fb 1 for SUSY signals.
Note that the events have been roundedo
to the nearest integer where relevant. Crosssections
have been scaled using NLO Kfactors obtained from Prospino.
nal state number of events at 100 fb 1 for SM background.
Note that the events have been roundedo
to the nearest integer where relevant. Crosssections
scaled with Kfactors at NLO [178] and wherever available, NNLO [191{196] have been used.
S4: a large missing energy cut, E= T > 100 GeV is implemented to reduce SM
backgrounds.
zero jets in the event.
S5:
nally we choose the events to be completely hadronically quiet and demand
In tables 12 and 13 we show the signal and backgrounds events after each selection
cuts are imposed. As the samesign signal is strongly constrained by existing LHC data,
our benchmarks have been chosen to comply with the existing limits. Thus we nd that
our benchmark choices do not seem too robust in terms of signal rates, especially BP3 and
BP4 which has the chargino as the NLSP. It is therefore important to point out that BP1
and BP2a like spectra is naturally not favored to give a samesign dilepton signal while
BP3 and BP4 are the most probable to give the samesign signal but have been chosen
to suppress the signal to respect existing constraints (by choosing very small branching for
the neutralinos to decay to chargino) for two di erent
values. However the spectra as
re ected by BP2b and BP4 satisfying existing constraints do present us with a signi cant
number of event rates when compared to the background after cuts.
BP2b
BP4
811
1052
2251
3845
energy at ps = 13 TeV LHC.
From the above cuts, we nd that a large MT (l1) cut coupled with a large E= T and the
requirement of jet veto removes a large fraction of the dominant W Z background as well as
other fake contributions coming from tt. Other genuine contributions to this channel from
and BP4 with BR( e02 ! e1 W
! l )
W
W
jj, ttW and W W W having a lower production crosssection and are e ciently
suppressed by cuts on E= T , MT and applying a jet veto. Amongst all benchmarks, the most
sensitive to the same sign dilepton analysis are BP2b where BR( e02 ! e1 W
! l )
3:3%
10%. Note that BP2b, with a smaller
M gives
soft leptons and is therefore slightly suppressed and requires larger integrated luminosity
810 fb 1 of data as shown in table 14. Although BP4 has a larger branching fraction,
it requires 1052 fb 1 of data at LHC for observing a 3 excess owing to a higher
value
compared to BP2b. Thus the samesign dilepton can be a complementary channel to
observe for benchmarks of BP2b and BP4. We must again point out here that for BP3like
spectra with e1 NLSP the samesign dilepton would be the most sensitive channel of
discovery, for large j j and small M2, where the neutralino decay to chargino NLSP becomes
0
large (see gures 5 and 6) because of the small SM background. In such a case both e1
and e20 will decay to the NLSP along with soft jets or leptons. Thus both e1 e20 and e1 e1
0
production channels would have contributed to the signal leading to a twofold increase of
the number of signal events and would be more sensitive to detect a sneutrino LSP scenario.
We conclude that conventional channels such as monolepton or opposite sign dilepton
channels however with low hadronic activity, i.e, with at most 1 jet or no jet would be
extremely useful channels to look for cases of a sneutrino LSP. Detecting same sign
dilepton signals at higher luminosities would further serve as a strong con rmatory channel
for a sneutrino LSP scenario over a e10 LSP scenario as in the MSSM from the compressed
higgsino sector and can exclude large portions of the regions with M1 < 0. Our analyses
also shows better signal signi cance for a given integrated luminosity, when compared to
the forecast shown in table 5. Note that our estimates do not include any systematic
uncertainties that may be present and would be dependent on the speci c analysis of
event topologies. However it is worthwhile to ascertain how our results fare in presence of
such systematic uncertainties. To highlight this we assume a conservative 10% systematic
uncertainty in each case. We nd that the required integrated luminosities follow a similar
scaling and our results for the luminosity vary by atmost 10% in most cases.
Dependence on
involving the
avor of eR LSP. LHC searches explore di erent search channels
avor of the leptons owing to their high reconstruction e ciency at the
detector, for instance, e+E= T ,
+ E= T [161, 162], ee=
=e
nal states associated with
E= T [130, 132]. As we have considered both rst and second generation sneutrinos to be
light in this study, we qualitatively analyze the prospects of the signals studied by tagging
the
avor of the leptons as well as consequences of a single light generation of sneutrino
LSP assuming the net leptonic branching to be the same in both cases.8
Hence, for a
single light sneutrino LSP, the observed events in the monolepton and dilepton signals
contribute to only a single choice of lepton
avor and vanishes for the rest. We compare
the signal and background in this case for the same luminosity as before and comment on
the results obtained for our benchmarks.
For monolepton signals with degenerate sneutrino LSP ( rst two generations), say,
we look at only an electron in the nal state. This would lead to reduction of both signal
and background in table 6 and 7 by half such that the signi cance falls by a factor of p2.
If a single generation of rightsneutrino was light, say e, then only the background would
reduce by a factor 1/2. Since the signal remains unchanged as the chargino now decays
e
factor of
completely to an electron and the lightest sneutrino the signal signi cance increases by a
p2. Consequently no signal is observed for the other avor lepton channel, in this
case , where although the background decreases by half, no signal events are present.
For the dilepton signal there are three possible channels ee;
and e
with net
branching fraction of around 1/4, 1/4 and 1/2 respectively. We consider rst the
oppositesign dilepton channel. For e
nal states, only di erent avor lepton backgrounds such
as from W W; tt or tW contribute with a BR ' 2=3. However contributions from same
avor dilepton sources such as involving Z boson fall. The total background thus reduces
to nearly 70%. Since signal in this channel also reduces to half thereby the signi cance
falls. For channels with same avor (SF) leptons, i.e, ee=
, dominant SF contributions
are from Z boson whereas subdominant contributions from top quark production channel
reduce.
Although SM background reduces so does the signal statistics and hence the
signi cance. However, in presence of a single generation of light sneutrino we
the signal signi cance improves by a factor of about p2. Note that if the LSP is ee then
the chargino decays to an electron and the LSP. Therefore ee + E= T channel signi cance
nd that
improves whereas
and e channels vanish. Similarly, for an
LSP,
+ E= T channels
improve whereas the rest vanish. Similar conclusions may be drawn for same sign
dilepton channel, where the dominant backgrounds are W Z and W
W , the signi cance is
e
expected to improve only for a single light generation of sneutrinos.
Some comments on the prospect of
avor searches and other channels. In
this context, we also explore the discovery prospects of a natural higgsino sector and a
single light e
as the LSP. LHC has looked at
nal states with tau leptons, decaying
hadronically, in the context of electroweakino searches. The electroweakino mass limits
considerably reduce for tau lepton searches owing to the reduced reconstruction e ciency
of hadronically decaying
leptons (
60%) [198] compared to that of the light leptons (e, )
95%). From searches with one or two hadronically decaying tau leptons associated with
light leptons lead to stronger limits from e1 , e02 production on m
e1
; me02 > 800 GeV for
8This may not correspond to the same parameter point since the presence of the other decay modes of
the net leptonic branching is the same in both cases.
e1 a ect the leptonic branching for the single light sneutrino LSP case. However, when e1 is the NLSP,
HJEP06(218)4
0
a binolike me01 < 200 GeV for stau mass midway between the e1 and e1
. For stau
closer to the e1 , the limit [129], m
e1
; me02
1000 GeV for me01
on electroweakino searches from three tau lepton searches exclude winolike degenerate
200 GeV. Limits
> 600 GeV for a binolike me01 < 200 GeV [129] for stau mass midway between
. Limits from opposite sign tau lepton searches [199] reinterpreted from
e1 e20 production and decaying via intermediate sleptons lead to me02 ; m
me01 < 200 GeV. From opposite sign ditau searches reinterpreted in context of chargino
pair production leads to a bound close to 650 GeV on chargino for LSP masses up to
> 760 GeV for
e1
For the current scenario of a compressed electroweakino sector in presence of a light
HJEP06(218)4
LSP, the signals from the lowlying compressed higgsino sector would be:
me02 ; m
e1
Mono jet + E= T
Di jets + E= T
For the monotau channel, both signal and background scale by the tau reconstruction
e ciency, R = 0:6 is the tau reconstruction e ciency. Further a factor of 12 comes in for
the background since the branching of W or Z boson to light leptons is roughly twice that
LSP. However, owing to the reduced tau reconstruction
p R
0:78. Similarly, for the ditau channels,
0:6. Hence, the estimated reach of the higgsino mass
LSP compared to ee= LSP.
to the tau lepton as for a ee=
e ciency, the signal signi cance falls by
the signi cance scales by R
is expected to weaken for a
Note that, the pionic decay modes of the ~
1 and ~02 can dominate among the hadronic
modes as the respective mass di erences become less than about a GeV. While we have
used form factors to estimate the pionic branching fractions, we have not considered the
possibility of late decay into pions in this work. This is because we have ensured that
in the parameter space of our interest the two body mode to the lightest sneutrino(s)
always remain prompt. Further, the potential of the loopinduced channel ~
02 ! ~
01 in
deciphering the scenario has not been explored in the present work. While the photons,
thus produced in the cascade, would be soft in the rest frame of ~02, it may be possible to
tag hard photons in the lab frame. Note that the choice of light higgsinos are motivated
by \naturalness" at the electroweak scale and we do not discuss the discovery potential for
stop squarks and gluino in the present work which we plan to do in a subsequent extension.
5
To summarize, motivated by \naturalness" criteria at the electroweak scale, we have studied
a simpli ed scenario with low
parameter in the presence of a rightsneutrino LSP. For
simplicity, we have assumed the gaugino mass parameters to be quite heavy & 1 TeV. In
such a scenario, with O(100) GeV Majorana mass parameter the neutrino Yukawa coupling
can be as large as 10 6
10 7. In contrast with the MSSM with lighthiggsinos, in the
present context, the higgsinolike states can decay to the sneutrino LSP. While the neutral
higgsinos can decay into neutrino and sneutrino, the lightest chargino can decay into a
lepton and sneutrino. We have demonstrated that the latter decay channel can lead to
various leptonic nal states with up to two leptons (i.e. monolepton, samesign dilepton
and oppositesign dilepton) and missing transverse energy at the LHC, which can be
important in searching for or constraining this scenario. We have only considered prompt
decay into leptons, which require y > 10 7 and/or small O(10 5{10 1) leftright mixing
in the sneutrino sector. For smaller values of y , contribution from the latter dominates
and the leptonic partial width on small gauginohiggsino mixing (. O(10 2)). Further, the
mass split between the three states, the lightest chargino and the two lightest neutralinos
depend on the choice of the gaugino mass parameters, as well as on oneloop contributions.
We have shown how these mass di erences signi cantly a ect the threebody partial widths,
thus a ecting the branching ratios to the sneutrino. Therefore, even assuming the
gauginolike states to be above a TeV, as in our benchmark scenarios, the viability of a low
parameter depends crucially on the choice of M1; M2. This has been emphasized in great
detail. Consequently, there are regions of the parameter space where BR(e1 ! l e)
especially in the negative M1 parameter space. Such regions of parameter space would lead
100%
to enhanced leptonic rates, thereby a large fraction of negative M1 parameter space can
be excluded from current leptonic searches at LHC. For a given j j, we check the existing
constraints by recasting our signal in CheckMATE against existing LHC analysis relevant
for our model parameters to search for a viable parameter region of the model. We then
choose some representative benchmarks and observe that monolepton signals with large
E= T and little hadronic activity could successfully probe
as low as 300 GeV at the ongoing
run of LHC with 106 fb 1 of data at 3 . Additional con rmatory channels for the
scenario are oppositesign dilepton and samesign dilepton signal which require
and
800 fb 1 for observing 3 excess at LHC. While our benchmarks assume the rst two
generations of sneutrinos to be degenerate and consider only e;
for the charged leptons
which can be detected e ciently at the LHC, the reach may be substantially reduced if only
LSP
e
50 fb 1
tausneutrino appears as the lightest avor due to the low tau reconstruction e ciency.
Acknowledgments
AC acknowledges
nancial support from the Department of Science and Technology,
Government of India through the INSPIRE Faculty Award: /2016/DST/INSPIRE/04
/2015/000110.
The work of JD and SKR is partially supported by funding available
from the Department of Atomic Energy, Government of India, for the Regional Centre for
Acceleratorbased Particle Physics (RECAPP), HarishChandra Research Institute. The
authors would like to thank W. Porod for his help in providing several clari cations on
our model implementation in SPheno and S. Choubey, S. Mondal and J. Beuria for useful
discussions. Computational work for this work was carried out at the cluster computing
facility (http://www.hri.res.in/cluster) and the RECAPP cluster in the HarishChandra
Research Institute.
Open Access.
This article is distributed under the terms of the Creative Commons
Attribution License (CCBY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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