#### Di-photon excess illuminates dark matter

HJE
Di-photon excess illuminates dark matter
Mihailo Backovic 0 1 3
Alberto Mariotti 0 1 2 3
Diego Redigolo 0 1 3
0 Pleinlaan 2 , B-1050 Brussels , Belgium
1 Universite Catholique de Louvain , Louvain-la-neuve , Belgium
2 Theoretische Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel
3 Universitee Pierre et Marie Curie , 4 place Jussieu, F-75005, Paris , France
We propose a simpli ed model of dark matter with a scalar mediator to accommodate the di-photon excess recently observed by the ATLAS and CMS collaborations. Decays of the resonance into dark matter can easily account for a relatively large width of the scalar resonance, while the magnitude of the total width combined with the constraint on dark matter relic density leads to sharp predictions on the parameters of the Dark Sector. Under the assumption of a rather large width, the model predicts a signal consistent with nels with large missing energy. This prediction is not yet severely bounded by LHC Run I searches and will be accessible at the LHC Run II in the jet plus missing energy channel with more luminosity. Our analysis also considers astro-physical constraints, pointing out that future direct detection experiments will be sensitive to this scenario.
Beyond Standard Model; Cosmology of Theories beyond the SM
1 Introduction 2 3 4
Experimental constraints
Future signatures
A Comments on UV completion
Di-photon excess in a dark matter simpli ed model
Introduction
Both ATLAS and CMS collaborations recently announced a search for reasonances in the
di-photon channel, featuring an excess of events around m
750 GeV [1, 2]. The result
sparked an enormous interest within the theoretical physic community, with no less than 35
preprints appearing by the end of the week from the LHC and ATLAS announcement [3{34].
The excess suggests a resonance structure (X) with:
(pp ! X)
BR(X !
) & 2 fb ;
mX
that the new physics models which can explain the excess contain likely either CP-even (S),
CP-odd (a) scalars, or a spin two massive object (G0 ). In both scenarios the coupling
to photons is controlled by operators of dimension
ve or higher, and hence generically
suppressed with respect to tree level couplings by at least one power of a new mass scale
and some loop factors.
While a spin 2 object can certainly be motivated in the context of extra dimensions [
37
],
in this paper we focus on the simpler possibility of a scalar resonance which we take
considerations [
38, 39
] or by dark matter physics [40{43].
It is rather di cult to satisfy the large width of (1.3) by assuming a dominant branching ratio into photons or gluons, essentially because of the dimensional suppression of the scalar couplings to photons and gluons. Moreover, increasing the width via decays into SM pairs is likely to be challenged by exclusion limits on new resonances from the LHC Run I at
The lack of observation of either new charged states with mass < mS;a=2
the possibility that the large width of the singlet resonance is a result of decays into a Dark
Sector. The singlet could then play the role of a \scalar mediator" between the Standard
Model and the Dark Sector where, say, a fermionic candidate for dark matter (DM) resides.
We will show how requiring that the fermionic DM candidate fully accommodates the
observed relic abundance of
DMh2
0:12 [44] determines completely the parameters of
the Dark Sector, namely the DM mass and its coupling strength to the singlet.
Even though we focus our discussion on the large width scenario (1.3), the same
framework can certainly accomodate the di-photon excess in the narrow width scenario. This
is the case in regions of the parameter space where the DM mass is & mS=2, as well as
in regions featuring very small couplings between the singlet and the DM, which naturally
lead to a small decay width for S. However, we nd such scenarios less motivated, since
the introduction of a DM candidate in this case does not serve a purpose of explaining any
feature of the di-photon signal.
The possibility of a new scalar resonance as the mediator between the Dark Sector and
the Standard Model (SM) is very much in the spirit of simple models of singlet DM [40{43].
In order to simplify the discussion we are going to focus on a minimally model dependent
case of a CP-even scalar S coupled to a Dirac-like fermonic dark matter.
We present a simple scenario where the di-photon excess is a manifest of the singlet
scalar DM portal with e ective couplings to SM gauge bosons (while the Higgs portal
coupling is negligible). The observed features of the di-photon excess combined with
cosmological constraints on DM lead to a sharp prediction of a dark matter candidate with
mass mDM
300 GeV . mS=2; and a coupling to the scalar of O(1).
This prediction is consistent with the existing experimental bounds from correlated
LHC-8TeV searches like
Z [
45
], di-jets [46] and j+MET [47] and from dark matter direct
and indirect detection experiments. Moreover the sizeable coupling of the singlet to dark
matter suggests that the LHC-13TeV searches for large missing energy associated with a
jet, , h or Z should observe a signal consistent with dark matter of mDM
300 GeV and
a mediator with mass mS
750 GeV in the near future. Furthermore, such signal will be
within the reach of the next generation direct detection [48] experiments.
From the point of view of the ultra-violet (UV) completions of our simpli ed model,
a challenge will be to suppress the mixing of the singlet with the SM Higgs as well as
generate sizeable couplings to photons and gluons. In appendix A we discuss a concrete
UV complete scenario in the context of supersymmetry (SUSY) where the pseudo-modulus
{ 2 {
(sgoldstino) generically associated to spontaneous SUSY-breaking can be responsible for
the DM portal [49{51] and have the right structure of the couplings. Motivated by SUSY
scenarios (where the pseudo-modulus is in general a complex scalar) we comment on how
the phenomenology will change in the presence of a CP-odd singlet a. A more
comprehensive analysis is left for future works.
The remainder of the paper is organised as follows. In section 2 we present our simpli
ed model for Dirac dark matter based on a CP-even scalar portal. We discuss its decay
channels and how the requirements on the di-photon resonance and dark matter can be
ful lled. In section 3 we discuss the experimental constraints from the LHC-8TeV and from
DM detection experiments and present a nal summary of the allowed parameter space.
discussion about the possible UV completions of the simpli ed model presented in section 2
and a brief analysis on the phenomenology of a CP-odd singlet motivated by SUSY UV
completions.
2
Di-photon excess in a dark matter simpli ed model
We consider an e ective lagrangian for a new spin zero and CP-even particle S (J p = 0+)
which couples at tree level to a massive Dirac fermion
. Both S and the fermion are
singlet under the Standard Model and a global avor symmetry under which
is charged
guarantees a stable fermionic DM candidate
+ (gDMS + M )
gW W SW
W
+
gBB SB
B
:
(2.1)
We x the UV scale to
= 104 GeV conservatively sticking to the regime of validity of the
e ective eld theory. The dimensionless couplings are taken to be order O(1), while the
missing operators allowed by the symmetries in the e ective lagrangian are assumed to be
suppressed by small couplings. Here we focus on the basic phenomenological properties of
the simpli ed model of dark matter in (2.1), taking a bottom-up approach,1 while we
postpone the justi cation of our working assumptions in considering (2.1) for the appendix A.
The total width: considering the couplings in (2.1), the singlet scalar can decay into
SM gauge bosons, or invisibly with the leading order decay rate
(S !
) =
2
gDMmS
8
1
4M 2 !3=2
m2S
:
(2.2)
In gure 1 we display the branching ratios of S decays into the various channels, for some
representative values of the couplings, as a function of the DM mass. As soon as the tree
1For our phenomenological studies, we employ FeynRules [52], MadGraph5 [53, 54], MadDM [55, 56]
and micrOMEGAs [
57
].
{ 3 {
L=10 TeV, gDM=1.5, gBB=1, gGG=1 3, gWW=1 2
1.0
0.8
0.6
0.4
0.2
0.0
100
Branching Ratios
BRHS®invL
BRHS®SML
BRHS®ΓΓL
BRHS®GGL
BRHS®WWL
BRHS®ZZL
BRHS®ZΓL
MΨ
HGeVL
400
500
the gluon decay mode is enhanced by the color factor.
indicate the ratio of the width of S over its mass, i.e. mtoSt . As we pointed out in the
introduction, the ATLAS analysis hints towards a con guration of the spectrum and the
couplings for which mS
tot
3{9%. Figure 1 clearly shows the di culties in obtaining a
percent-level width by considering dominant decay modes into SM particles, which
contribute . 0:5% to mtoSt . This feature is generic of models where the decay modes into
SM particles are generated through higher dimensional operators only, if we conservatively
stick to the regime of validity of the e ective
eld theory. In such scenarios a tree level
decay mode certainly helps to enhance the width of the resonance.
decay of the singlet into DM pairs (2.2). Indeed the requirement on a large width alone (1.3)
imposes a lower bound on the Yukawa-like coupling of the singlet to DM: gDM & 0:9. In
what follows we will show how this leads to very interesting implications for both DM
direct detection as well as collider phenomenology.
{ 4 {
production cross section at 13 TeV for a scalar singlet (pp ! S) in pb.
The di-photon signal strength: the new singlet scalar S can be produced via gluon
fusion at the LHC through the dimension
ve operator controlled by gGG. Once the UV
cut-o
is xed the production cross section is determined by gGG. Figure 2 shows that
by dialing gGG one can easily achieve (pp ! S)
O(pb).
The branching ratios into SM channels are xed by the parameters gW W ; gBB and gGG
in the dimension
ve operators in (2.1) and result in decay modes which contribute to
dijet, di-boson, di-photon and Z
nal states. In order to reduce the number of parameters
of the model we will x gW W
0 in the remaining of this paper. Note that suppressing
gW W is going to arti cially enhance the
channel with respect to ZZ and W W . However,
modifying this assumption will not a ect our main conclusion. Assuming gW W
0 the
signal cross section scales like (X !
)
2 2
gGGgBB at xed dark matter mass and gDM.
In gure 2 we also give an idea of the expected signal strength, before cuts, for a scalar
singlet S decaying into photons at LHC-13TeV as a function of the DM mass which we
take to be below m2S so that S has always a sizeable invisible width (2.2).
The regions where (S !
) > 2 fb depends on the value of the DM mass M
once
the coupling strength gDM is xed to be O(1). At xed dark matter mass, the boundary
of the viable signal strength region reproduces the expected parametric dependence on
gGGgB2B. The maximum signal strength is achieved when the DM mass approaches the
2
kinematical limit M
m2S and the invisible width controlled by (2.2) is reduced.
{ 5 {
From
gure 1 and
gure 2 we see an interesting tension between enhancing the
signal strength and the total width at the same time. A large cross section in
would
prefer a DM mass close to the kinematic threshold in order to suppress (S ! invisible).
On the other hand, a large width of order mtoSt
few% prefers a DM mass of O(100) GeV.
In the following we will see how these two constraints together with the LHC-8TeV bounds
select a speci c region of the gGG-gBB plane where also a viable DM candidate can be
accommodated.
Dark matter relic abundance: the model we discuss also aims to account for the
observed relic abundance of DM in the Universe, i.e.
h
2 ' 0:12. The annihilation cross
section of DM into SM particles is driven by higher dimensional operators, typically
resulting in annihilation rates which are too low to obtain the correct
h2 for generic values
of the dimensionless couplings and dark matter mass. The correct value for
obtained if the annihilation is kinematically enhanced, i.e. if the mass of the DM is \close"2
h2 can be
to the singlet resonance. Note that this is exactly the same region where the signal strength
in
is maximized as shown in
gure 2. In the same region the kinematical suppression
reduces the invisible width of the scalar (2.2) and hence the total width (see
gure 1).
We then expect the Dark Matter mass and coupling gDM to be fully determined by the
intersection of the relic density and resonance width constraints.
Indeed, requiring a large width in combination with relic density alone provides strong
constraints on the parameters of the Dark Sector. In order to clarify this aspect further, we
performed a Markov-chain exploration of the model parameter space in fgGG; gBB; gDM;
M g. Figure 3 shows the results, where we projected the four dimensional parameter space
onto the (gDM; M ) plane. The correct relic density and a large total width can be obtained
only in the region of dark matter mass of the order of M
300 GeV, regardless of the
values of gBB and gGG. In the following we will show that some of the model points which
satisfy both the relic density and the large width requirement (red diamonds in gure 3)
are also able to accommodate the observed di-photon signal strength.
The exact desired values of the Dark Sector will depend on the value of the total
width and somewhat on the spin of the DM particle and the chiral nature of the di-photon
resonance. However, the overall conclusion that the requirement of a total width combined
with relic density will essentially x the parameters of the Dark Sector appears to be robust
and weakly dependent on the remaining model parameters.
Benchmark points: For concreteness we selected four benchmark points which provide
a yield in
of O(1{10) fb, roughly required to explain the observed di-photon excess (1.1):
P1 :
P2 :
P3 :
P4 :
gGG = 0:25
gGG = 0:25
gGG = 0:14
gGG = 0:14
gBB = 1 ;
gBB = 2 ;
gBB = 1 ;
gBB = 2 ;
(2.3)
2While the term \close to the resonance" is often used in the context of resonant dark matter annihilation,
it is seldom pointed out that the relevant measure for correct relic density is in fact jmS 2M j= tot . O(1).
{ 6 {
No constraint
Ωh2=0.1- 0.13
Ωh2=0.1- 0.13, Γ tot / mS= 3- 9 %
250
300
350
Mψ [GeV]
the M ; gDM plane. The scan assumes a Gaussian likelihood function centered around
where the range of allowed parameters is bounded by gBB = [10 2; 2]; gGG = [10 2; 1]; gDB =
h
2 = 0:12;
[10 2; 3] and m
= [200; 375] GeV. The blue circles represent the total of 10000 points scanned
over by the Markov-chain, with no additional constraints. The green triangles represent a subset
of the sampled points which give relic density in the range of 0:1 <
h2 < 0:13. The red diamonds
assume an additional requirement of mtoSt = (3{9)% GeV. The dashed lines represent the range in
which the total width in the range of (3{9)% of mS can be explained by dominant decays into dark
matter.
where we are keeping xed the cut-o scale at
= 10 TeV. We intentionally choose O(1)
values for gBB, which opens up the parameter space leading to a sizeable
cross section.
illustrative purpose, we select a large range for the mediator width (1.3) with the ATLAS
preferred value of tot=mS = 6% as central value. The relic abundance band shows the
region of
DMh2
0:12, with black lines indicating
DMh2 = 0:12. The relic abundance
band is weakly dependent on the coupling as expected for an annihilation cross section
dominated by an s-channel resonance and xes the DM mass to be M
m2S .
The desired region is the overlap between the large width band (in purple) and the
dark matter relic abundance line (black solid). For the large values of the dark matter
mass necessary to obtain the correct relic abundance, a width in the selected range can be
achieved only with a large dark matter coupling gDM. This result is in agreement with the
expectation that the dark matter relic abundance together with the requirement on the
width of S essentially xes both gDM and M .
By inspecting gure 4, we can select representative values of the dark matter mass and
dark matter coupling gDM, where we chose the total width tot
30 GeV for illustrative
{ 7 {
HJEP03(216)57
Wh2= 0.12
25 fb
ΣΓΓ=9 fb
Wh2= 0.12
100 fb
25 fb
250
MΨ HGeVL
from the top left to the bottom right corresponds to our four benchmark choices in (2.3). The blue
band shows regions where mS
tot
(3{9)% (in blue) while the region where
h
2 < 0:12 is shown in
beige. At the boundaries of the beige region (black, solid lines) the Dirac fermion accounts for all the
DM relic abundance. We overlaid the contours of the di-photon production cross section at LHC 13
as dashed red curves, where the thick dashed curve corresponds to tot
30 GeV. The intersection
of the width band with the relic density line essentially xes the dark matter parameters, as already
observed in gure 3.
purpose. We denote the model points as p1:::4 in gure 4. Table 1 summarizes the signal
yield in the di-photon channel and the DM relic abundance for the four selected benchmark
points, where all the parameters of the model are now
xed by requiring a large mediator
width, a sizable
cross section, and the correct dark matter abundance.
Note that the
production cross section for our benchmarks ranges between 2{25 fb,
providing enough room to t the ATLAS and CMS excess while taking into account event
selection e ciency and the acceptance.
{ 8 {
benchmark
(gGG; gBB)
gDM
(0.25,1)
(0.25,2)
(0.14,1)
(0.14,2)
parameters for the four selected benchmark points.
3
Experimental constraints
The scenario we consider is bounded by several existing collider searches at p
s = 8 TeV
and by astro-particle searches that we discuss in more detail in the following sections. For
a previous study of LHC Run I constraints on DM models with mediators see e.g. [58].
LHC-8TeV constraints: the model we propose populates di erent nal state
topologies, given the rich decay pattern of the scalar mediator (see gure 1). For the benchmark
points that we selected in order to accommodate the di-photon excess as well as to obtain
the correct relic abundance the largest contribution to collider signals is in channels with
missing energy. However, the channels in which the mediator decays into SM particles,
even if suppressed by a small branching fraction, can also lead to stringent bounds.
The most relevant collider bounds from LHC searches at p
s = 8 TeV are:
Recent CMS [59] search for a di-photon resonance in the mass range 150 to 850 GeV.
For a scalar resonance with mass mS
750 GeV, their results impose an upper bound
of
Mono-jet searches provide the most stringent bounds on signals with large missing
energy. CMS [47] as well as ATLAS [61] put a bound of (MET + j) . 6 fb for signals
with MET > 500 GeV.
Recent CMS di-jet searches for resonances at p
s = 8 TeV [46] provide weak limits
for production cross section of
(jj) . 1 pb for scalar resonances which couple
dominantly to gg of mass around the TeV scale. We will adopt this limit for a scalar
resonance of mS
750 GeV as a conservative estimate.
The ATLAS search [62] provides a bound on the ZZ cross section of the order
ZZ < 12 fb for a scalar resonance of mS
section is suppressed with respect to the
750 GeV. In our scenario the ZZ cross
cross section by a factor ( scWW )4
0:1,
since we xed gW W
0. Hence the bound on ZZ is less relevant than the ones on
and Z .
{ 9 {
HJEP03(216)57
Dark matter detection constraints:
beside collider bounds, we expect that our dark
matter model can also be constrained by direct and indirect detection experiments.
Direct detection experiments can constrain the model since the lagrangian (2.1) induces the following e ective operator between the dirac dark matter and the gluons
Le
gDMgGG
m2S
G
G :
Notice that the strength of this operator is correlated with the requirement on the large
total width as shown in
gure 4. The resulting spin independent cross section for DM
scattering o nucleons is then given by (see e.g. [40])
the scale of the singlet mass. In our estimate of the direct detection constraints we are
neglecting subleading operators which will be generated by the running from the UV scale
to the typical scale of direct detection experiment (
GeV). This operators should be added
in a more precise treatment of direct detection bounds.3 The LUX experiment [63] provides
a limit on the contact interaction between scalar mediators and gluons of SI . 4
cm2 for a dark matter of mass around 300 GeV.
Concerning indirect detection, the annihilation is velocity suppressed in the case of
a real scalar mediator. We hence do not expect strong bounds on our model from
measurements of galactic gamma ray
uxes. We regardless estimate the cross section for
annihilation of galactic DM into photons in our benchmark points for completeness. Recent
measurements of galactic gamma rays from the FERMI collaboration [64] put a bound of
h vi
. 10 28 cms 3 for a DM mass of O(300) GeV that we adopt for our scenario.4
Combined constraints:
The question of how much of the parameter space which can
explain the di-photon signal strength is still allowed by the existing experimental searches
tot
mS
remains. For this purpose, we performed a scan over fgGG; gBB; gDM; M g, accepting only
points featuring a width in the range 3%
9%,
> 2 fb and non over-abundance
of dark matter. Figure 5 shows the results, where we projected the four dimensional scan
onto the (gGG; gBB) plane, marginalizing over gDM and M . Signal yield of
> 2 fb can
be obtained only in the region above and to the right of the solid blue line (as expected
since the
cross section scales like gG2GgBB for a xed total width).
2
In the same plot we display the bounds from LHC-8TeV searches as dashed/dotted
lines, where dashed lines represent the strongest limits in the marginalization and dotted
lines stand for the weakest limits. Requiring
h2 = 0:12 via thermal annihilation of
will
x the value of M
and gDM, as shown in
gure 3. The resulting limits then sit between
the dashed and dotted lines, as we will illustrate for the choice of benchmark points p1:::4.
3We thank Paolo Panci for interesting discussions on this point.
4The bound depends on the halo pro le and varies in the range (10 27{10 28) cms 3 .
P1
P3
1.5
gBB
DD
P2
P4
1.0
0.8
0.6
G
G
g
0.4
0.2
0.0
g
Zg
j+MET
Gtot <3%
0.0
0.5
1.0
2.0
2.5
3.0
ruled out by individual searches speci ed on the plot, where we use dotted lines to represent the
weakest limits in the marginalization and the dashed lines for the strongest limits. The solid blue
line and the shaded region below it corresponds to the region of parameter space which can not
account for a large width of the di-photon resonance. The points labeled as capital P1 4 represent
the benchmark model points in (gGG; gBB) of (2.3), we use as illustrations in the paper. The direct
detection bounds labeled DD assume
The direct detection limits displayed in
gure 5 assume that the local dark matter
density corresponds always to
h
2
0:12, although the relic density contribution from
thermal annihilation of
does not have to account for all of the observed relic density.
The direct detection limits could hence be weaker than the ones we present. However, note
that even in most stringent case of direct detection limits, the searches for MET+j provide
the strongest absolute constraints on gGG. Hence, direct detection results do not provide
relevant limits on gGG once MET+j constraints are taken into account. The other 8TeV
collider results are instead able to constrain the combination of gBB and gGG.
Our results show that the non-shaded portion of parameter space with gGG . 0:3, assuming gBB
O(1), is still allowed by the LHC-8TeV data as well as by dark matter
direct detection constraints. Note that this region of model parameters is also able to
accommodate the di-photon excess signal strength.
Benchmark points: table 2 shows a summary of all the experimental constraints on
our scenario for the four benchmark model points in table 1. Benchmark point 2, with
(gGG; gBB) = (0:25; 2), gives the largest yield in the di-photon signal (see table 1) and it
Benchmark
p1
p2
p3
p4
< 3:5 fb
0.86
3.6
< 6 fb
3.7
3:9 10 32
10 45cm2
experiments on the four benchmark points described in table 1. All collider cross sections are given
in fb and assume p
cut of pjT > 20 GeV; j < 2:5, while for the MET+j we impose a cut of pjT > 500 GeV.
s = 8 TeV. For the constraints on
jj we compute the cross section imposing a
is already severely constrained by the
nal state. Interestingly, requiring the correct
DM relic abundance for that choice of gGG and gBB, and hence xing gDM and M
to the
values in table 1, enhances the Z
branching ratio making the benchmark 2 also excluded
by Z
searches at LHC-8TeV.
The other benchmark points are all within the allowed experimental bounds, both from
collider and from dark matter experiments, and can provide viable scenarios to
accommodate the di-photon excess as well as to account for the correct relic density of dark matter.
Note that the benchmark points predict a direct detection cross section which is not far
from the actual experimental reach, and will likely be accessible in future experiments.
4
Future signatures
In this note we have proposed a simpli ed dark matter model with a mediator of mass
750 GeV to account for the di-photon excess recently reported by the ATLAS and CMS
collaborations. If the resonance is a scalar singlet, the requirement of a moderately large
resonance width from the ATLAS collaboration (see (1.3)) hints to the existence of extra
decay channels.. Here we have investigated the possibility that the scalar singlet has an
extra decay mode into an invisible particle which can play the role of a dark matter
candidate. This simple assumption, together with the requirement of a correct relic abundance,
provides a prediction for the mass of the dark matter, that should be around
300 GeV
for a scalar mediator of 750 GeV.
The model is indeed very predictive and we can identify the expected signatures in
other channels at LHC-13TeV and in dark matter experiments. The most distinctive LHC
signature is in MET+j which has the largest cross section and will be reachable at
LHC13TeV with more luminosity. From the model independent analysis of CMS [47] one can
estimate the luminosity needed to exclude our model at 13 TeV by assuming that the
e ciencies for the main SM backgrounds are the same as in the 8 TeV run. We focus on
the MET > 500 GeV bin, which gave the most stringent constraints at 8 TeV. A back
of the envelope estimate indicates that the benchmark point p1 (with large MET+j cross
section) should be within reach with a few fb 1 at 13 TeV. Benchmark points p3 and p4
(with small MET+j cross section) would instead need few tens of fb 1 to be excluded. We
then argue that essentially all the viable portion of parameter space in gure 5 should be
within the reach of LHC-13TeV with . 100 fb 1 of luminosity. A more detailed analysis,
which we leave for a future work, is necessary in order to extract more precise values for
luminosity needed to explore the allowed parameter space in our model.
The
nal state Z
is also a promising channel. However, note that by tuning the
couplings gBB and gW W one can generically suppress this branching ratio,5 and thus the
signal. Hence the Z
is not a generic prediction of our model, in contrast to MET+j.
Interestingly, dark matter experiments are also going to be able to probe our model.
The future direct detection experiments should reach a sensitivity of approximately
10 46 cm2 for spin independent cross section assuming a dark matter mass of around
300 GeV (see e.g. XENON1T prospects [48]), which is in the ballpark of the predictions
for our benchmark points (see table 2). In fact, future direct detection experiments should
be able to probe most of the parameter space of the model which features a large width
and is compatible with LHC-8TeV MET+j searches (i.e. the region illustrated in
gure 5
with gGG . 0:3), as the direct detection cross section is set essentially by gGG and gDM
(see eq. (3.2)).
Note that both MET+j and direct detection DM cross sections can be reduced by
decreasing the value of the coupling gGG. However, in order to maintain a signi cant yield
in the
channel, this should be accompanied by an increase of gBB, pushing the model
into a somehow less appealing region of the parameter space (especially from the point of
view of the UV completion).
We conclude that the simpli ed dark matter model we presented here provides sharp phenomenological predictions that can be further scrutinized in both LHC-13TeV and in future searches for galactic dark matter.
We leave a more complete exploration of the parameter space of this scenario and the possibility of embedding it into UV complete models beyond the Standard Model for future investigations.
Acknowledgments
We thank Brando Bellazzini, Dario Buttazzo, Adam Falkowski, Gilad Perez, Filippo Sala
and Michael Spannowsky for interesting discussions. We also thank Andreas Goudelis,
Thomas Hambye and Paolo Panci for useful comments on the draft. The work of DR
was supported by the ERC Higgs at LHC. M.B. and A.M. are supported in part by the
Belgian Federal Science Policy O ce through the Interuniversity Attraction Pole P7/37. A.M. is supported by the Strategic Research Program High Energy Physics and the Research Council of the Vrije Universiteit Brussel.
A
Comments on UV completion
In this paper we studied a simpli ed model of Dirac dark matter with a real scalar mediator
described by the e ective lagrangian
1
2
+
gW W SW
W
+
+ (gDMS + M )
Here below we comment on the assumptions associated with the structure of the
lagrangian (A.1) and the challenges related to their possible UV completions:
The dimension ve operators of the second line in (A.1) can be obtained by integrating out heavy fermionic matter in vector-like representations of the SM gauge group which couples with the singlet S as
Lint =
Nf
X(
i=1
S + M ) i i :
(A.2)
HJEP03(216)57
Identifying the cut-o with
M , we can estimate for a single family: gGG
count for the representation multiplicity in the loop, Q2a is the Casimir of the
representation of the a-th group (which is just Y 2 for U(1)Y ) and a = 4ga2 with a = 1; 2; 3
are the coupling constants of the SM gauge group.
As we have shown in section 2, having a sizeable yield into di-photons and a sizeable
width requires gBB and gDM (and possibly also gGG) to be order O(1). The couplings
in front of dimension
ve operators are loop suppressed in a weakly coupled setup.
Having them O(1) certainly requires some large charge/multiplicity for the
vectorlike matter which carries SM quantum numbers and/or sizeable couplings of the
singlet in (A.2). Both these options are likely to induce problems with perturbativity
at the UV scale making the UV completions of the e ective lagrangian (A.1) more
challenging.
We proceed to comment on other operators allowed by symmetries which we neglected in the e ective action (A.1).
We are neglecting both the cubic and the quartic
interaction between the singlet S and the SM Higgs i.e. 3SH SHyH and 4SH S2HyH.
At the level of dimension
ve, we are neglecting interactions between the SM Higgs
and the Dirac fermion (gHDM HyH
) and also the ones between the singlet and the
SM fermions, for instance gSSM SHQU . These operators are not forbidden by any
symmetry and should be present in a generic dimension ve e ective action.
The presence of singlet-Higgs interactions can modify the decay modes of the singlet
which would acquire SM-like couplings through the mixing with Higgs once EWSB
is broken. The phenomenology of such a singlet has been widely studied in the
literature (see for example [65]). In our discussion we took as a working assumption
(very much in the spirit of [66]) that the singlet Higgs interactions are zero at the
UV thresholds . In such a hypothesis we can also approximate the singlet potential
with the mass term only, since a singlet vacuum expectation value would not have
any consequence on the phenomenology besides modifying the DM mass. Once we
set the tree level couplings to zero, the UV threshold corrections coming from loops
of vector-like charged matter (A.2) will generate these couplings only at 2 loops.
Therefore the Higgs-singlet couplings would be loop suppressed with respect to the
couplings to gauge bosons once the tree level boundary condition is realized.
An attractive possibility to get a structure of the couplings at the UV boundary condition
ful lling both the challenges described above can be found in the context of supersymmetry
(SUSY). In a generic low energy SUSY-breaking model, there is a light pseudo-modulus
(i.e. the sgoldstino) which sits on the same SUSY multiplet of the spin 1/2 goldstino
associated to spontaneous SUSY-breaking [67] (see [68] for a more detailed discussion of
the sgolstino phenomenology at colliders). The structure of the couplings of our e ective
lagrangian (A.1) would describe the interactions between the CP-even component of the
sgoldstino and the SM, as well as the invisible decay to the neutral goldstino. In the limit
in which gaugino masses are heavy, the dimension ve couplings of the sgoldstino to gauge
bosons dominate over the other couplings, since they scale like
Mi=pf , where Mi are the
candidate since for low p
f it would result in very light dark matter.
gaugino masses and f is the SUSY-breaking scale. Couplings of O(1) can be obtained in
extra dimensional scenarios where the gaugino masses are generated at tree level [69, 70].
In this case, however, the supersymmetry breaking scale will be tied to the gaugino mass
and will be bounded from below from constraints on the gluino mass and from above by the
requirement of a sizable cross section, imposing some further constraints on the parameters
of the e ective lagrangian. For instance, the goldstino would not be a suitable dark matter
A possibility to include a dark matter candidate in such context is to consider models
of pseudo-moduli dark matter constructed in [49{51]. In these constructions one or more
light chiral super elds generically arise in O'Raifeartaigh models which break SUSY
spontaneously. Their scalars components are pseudo-moduli associated to approximately
at
directions in the potential while their fermionic component can be a viable dark matter
candidate. The lagrangian (A.1) describes the CP-even component of a complex
pseudomodulus, coupled to a singlet Dirac-like Dark matter whose mass is not tight to the
SUSYbreaking scale. The latter can easily arise in the context of supersymmetry as a pair of
Weyl fermions with a small supersymmetric mass which remains light once their scalar
partners have acquired a large SUSY-breaking mass.
Note that in SUSY inspired scenarios, we expect the CP even and CP odd part of
the light complex pseudo-modulus to have the same mass. Hence, as a further remark, we
would like to brie y comment on the possibility that the scalar resonance is not CP even
but CP odd. Considering the analogous of the lagrangian (A.1) but in the case of a CP odd
scalar, the decay rates to SM gauge boson would be equivalent, while the invisible decay
would present a phase space suppression di erent than eq. (2.2). The analysis of the LHC
di-photon excess could proceed very similar to our study, however the dark matter features
are signi cantly di erent. In the case of a pseudo-scalar, the annihilation cross section
relevant for indirect detection is not velocity suppressed and gives a large contribution to
h vi . As a consequence, a dark matter of mass around 250{300 GeV with O(1) coupling
to the scalar mediator would lead to a very large yield to indirect detection experiments,
typically of the order of h v
i
10 26 cms 3 , which would be in tension with the FERMI
constraint [64]. Note that such a large dark matter mass is necessary to obtain the correct
relic abundance through the resonant enhancement of the annihilation via the 750 GeV
mediator. Hence in the case of a pseudo-scalar mediator the relic abundance requirement
and the indirect detection bounds could generically be in tension. We leave to future
studies a detailed investigation of this case.
Finally, let us mention that a similar e ective theory to (A.1) could also arise in the
context of Randall-Sundrum scenarios where the light singlet is a dilation/radion of a
hidden sector where conformal symmetry is spontaneously broken. However, the couplings to
quarks in these scenarios are typically sizeable and they strongly modify the
phenomenology of the singlet (see [71] for a detailed study of the implications of this setup for dark
matter).
Open Access.
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