Extended gamma-ray emission from Coy Dark Matter

0.58 MB·

by  Celine Boehm

IPPP/13/31, DCPT/13/62, SLAC-PUB-15893
Extended gamma-ray emission from Coy Dark Matter
C´eline Bœhm,1,2 Matthew J. Dolan,3 Christopher McCabe,1 Michael Spannowsky,1 and Chris J. Wallace1
1Institute for Particle Physics Phenomenology, Durham University,
South Road, Durham, DH1 3LE, United Kingdom
2LAPTH, U. de Savoie, CNRS, BP 110, 74941 Annecy-Le-Vieux, France
3Theory Group, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
[email protected], [email protected], [email protected],
[email protected], [email protected]
We show that it is possible for WIMP dark matter to produce a large signal in indirect dark
matter searches without producing signals elsewhere. We illustrate our point by fitting the Fermi-
LATextendedgalacticgamma-rayexcesswithasimplemodelofDiracdarkmatterthatannihilates
primarily into b quarks via a pseudoscalar. Current collider constraints are weak while the 14 TeV
4 LHCrunwillconstrainalimitedportionoftheparameterspace. Nosignalisexpectedinadditional
1 indirect searches or at future direct detection experiments. Our results emphasise the importance
0 of fully understanding potential indirect signals of dark matter as they may provide the only infor-
2
mation about the dark matter particle.

y
a
M I. INTRODUCTION matter with mass between 5-50 GeV provides a good fit
to the galactic excess. Previous particle physics oriented

8 studiesofthissignalhavefocussedonthem ≈10GeV
The precise nature and interactions of particle dark DM
region [27–41], motivated in part by the persistent signs
matter remain unknown. Of the many proposed possi-
] ofasignalinDMdirectdetectionexperimentsconsistent
h bilitiesoneparticularparadigmhasendured: theweakly
p with this mass [42–46].
interacting massive particle (WIMP). WIMPs are as-
- In this work, we instead consider the higher mass re-
p sumedtohaveweak-scaleinteractionswiththeStandard
gion m ∼30 GeV, which requires that the dominant
e Model particles offering the potential for the discovery DM
annihilationisintobquarks. Thiscaseisparticularlyrel-
h of dark matter in many channels: direct detection at
[ evanttoourdiscussionsinceitisforthismassthatdirect
underground detectors [1], production at particle collid-
detectionexperimentsaremostsensitive. Whenthedark
2 ers [2–5] or through indirect searches [6, 7]. Typically,
matter is a Dirac fermion, we show that the observed
v it is assumed that if a signal of WIMP dark matter is
annihilation cross-section is achieved if the interaction
8 found in one of these channels, then a signal will also be
5 found in another channel. Thus the strong limits from is mediated by a relatively light pseudoscalar with cou-
4 plings to Standard Model particles that are proportional
the XENON100 [8] and LUX [9] direct detection experi-
6 to the Yukawa couplings (i.e. Higgs-like). This coupling
ments,whichnowexcludescatteringcross-sectionsbelow
. structure is well motivated for pseudoscalars from min-
1 a typical weak-scale cross-section, have caused some to
0 imal flavour violation (MFV) [47] and ensures that the
be pessimistic about the WIMP paradigm.
4 dominant annihilation channel is into b quarks.
1 However, this pessimism is misguided. It is plausi- Although this scenario produces the observed weak-
: ble that WIMP dark matter is coy so that it appears at scale annihilation cross-section, we show that in much of
v
i one experiment without producing any other observable the parameter space, CDM produces no observable sig-
X signals. We demonstrate this by showing that a sim- nalatotherindirectdetection,directdetectionorcollider
r ple model of ‘Coy Dark Matter’ (CDM) can explain the experiments. Withapseudoscalarmediator, theinterac-
a
recent spatially extended gamma-ray signal of unknown tion of dark matter with nucleons is suppressed by the
origin from the galactic centre (observed in data from square of the nuclear recoil energy, which is small owing
the Fermi-LAT satellite) [10–17], without producing sig- to the non-relativistic nature of the interaction. From
nals elsewhere. Other examples of CDM include light a collider perspective, pseudoscalars in this mass range
neutralino dark matter, which can lead to a large sig- are particularly hard to constrain, since their suppressed
nalintheeffectivenumberofneutrinosNeff butnowhere couplings to massive vector bosons weaken direct search
else [18, 19]. This breakdown of the crossing symmetry constraintsfromLEPandtheTevatron. Wefindthatthe
relating indirect and direct detection along with collider greatest sensitivity is afforded by monojet plus missing
searches has also been addressed in [3, 5, 20–23]. energy (MET) searches at the LHC, which are sensitive
Intriguingly,iftheextendedgalacticgamma-rayexcess tomediatorproductionfollowedbydecaytodarkmatter
is interpreted in terms of dark matter annihilation, the and accompanied by hard QCD radiation.
annihilation cross-section of ∼ 10−26 cm3s−1 required Our paper is structured as follows: in Sec. II we dis-
to explain the signal is consistent with that required cuss the extended gamma-ray excess from the galactic
to obtain the observed relic abundance through thermal centre and find the dark matter mass and annihilation
freeze-out[24–26],afeatureoftheWIMPparadigm. De- cross-section required to explain it with dark matter an-
pendingonthespecificsoftheannihilationchannel,dark nihilation. Following that, we discuss constraints on this
2
scenario from collider searches in Sec. III and direct and
other indirect detection searches in Sec. IV.
(cid:68)
1
(cid:45)
s
II. THE EXTENDED GAMMA-RAY EXCESS 2(cid:45)
m
c 10(cid:45)7
Owing to the large dark matter number density there, V
e
one of the most promising places to look for dark mat-
G
ter annihilation products is a small (∼ 0.1 kpc) region (cid:64)
centred on the galactic centre. Evidence for a spatially EΓ syst.
extended excess of gamma-rays in this region was ini- d(cid:144) stat.
(cid:70)
tiallyfoundin[10]andsubsequentlyconfirmedbyseveral
d m (cid:61)30GeV
independent analyses [11–17]. A spectrally and morpho- 2Γ DM
E (cid:88)Σv(cid:92)(cid:61)3(cid:137)10(cid:45)26cm3s(cid:45)1
logically similar excess has also been reported at more
extended distances from the galactic plane [48, 49]. 10(cid:45)8
In addition to dark matter annihilation, it has been 0.3 1.0 3.0 10.0
suggested that interactions between cosmic rays and E (cid:64)GeV(cid:68)
Γ
gas [50–52] or an unresolved population of millisecond
pulsars [12, 14, 15, 53] can explain the excess. However,
more detailed studies have raised problems with both of FIG.1. Thedatapointsshowtheextendedgamma-rayexcess
these explanations [17, 54]. It is also possible that a new froma7◦×7◦regioncentredonthegalacticcentre(from[16]).
The red and black error bars show the systematic and sta-
mechanismnotproposedisresponsible,sincethegalactic
tistical uncertainties respectively. The blue solid line shows
centre is a complex astrophysical environment [55]. For
the photon spectrum corresponding to 30 GeV dark matter
thepurposeofthiswork,weassumethatalloftheexcess
withanannihilationcross-sectionthatgivestheobservedrelic
isaresultofdarkmatterannihilation. Weusetheresults
density. The branching ratios are determined by the Yukawa
from the analysis of [16] (listed in their Appendix A), couplings y .
f
whoconsideredalleventswithina7◦×7◦ regioncentred
on the galactic centre (the position of Sgr A∗). Galac-
tic backgrounds were modelled with the standard LAT The following simplified model gives a good fit to the
diffuse model, with isotropic residuals assumed for in- extended gamma-ray excess shown in fig. 1. We take
strumental and extragalactic sources. After background the dark matter χ to be a Dirac fermion with mass
subtraction the extended emission component that they m which interacts with a pseudoscalar a with mass
DM
findisshowninfig.1,wheretheredandblackerrorbars m through the coupling g :
a DM
correspondtosystematicandstatisticaluncertaintiesre-
spectively. L⊃−ig√DMaχ¯γ5χ−i(cid:88)√gf af¯γ5f +h.c. (2)
To proceed with the dark matter interpretation, it is 2 2
f
necessary to specify the dark matter halo profile. While
it is well determined far from the galactic centre, the The pseudoscalar couples to the Standard Model
slope is uncertain at small radii; typically there are no fermions with g , which we assume is equal to the Stan-
f
observationsbelow1kpcandtheresolutionofnumerical dard model Yukawa coupling g =y ≡m /174 GeV.
f f f
simulations is ∼0.1 kpc. The Einasto [56] and Navarro, This relation is common for pseudoscalars, motivated
Frenk and White (NFW) [57] profiles are traditionally from the minimal flavour violation (MFV) ansatz [47].
used as benchmark profiles as they provide good fits to ThephotonfluxΦatEarthfromaregion∆Ω, assum-
dark matter numerical simulations [58]. However, it is ing prompt photon emission arising from annihilation of
possible that the dark matter halo profile remains diver- Dirac dark matter, is [60]
gent close to the centre such that profiles may behave as
ρex∝amrp−lγe,wtihtehVγia>L1a(cγte=a I1IisnimthuelatNioFnWfapvrooufirlse)a. pArsofialne ddEΦ = 14r4(cid:12)π (cid:18)mρ(cid:12) (cid:19)2(cid:104)J(cid:105)∆Ω(cid:88)(cid:104)σv(cid:105)fddNEγf , (3)
γ DM γ
with γ =1.24 [59]. Given that the γ-ray emission traces f
themorphologyoftheprofile, theconsequenceofamore
where r = 8.25 kpc is the distance from the galactic
stronglypeakedprofile intermsofindirectdetection isa (cid:12)
centre to the Earth, ρ = 0.42 GeVcm−3 is the local
muchbrightergamma-rayemissionrelativetothecaseof (cid:12)
dark matter density [61, 62], (cid:104)σv(cid:105) is the annihilation
anEinastoorNFWprofile. Fortheextendedgamma-ray f
cross-sectiontof¯f anddNf/dE istheenergyspectrum
excess, it is found that a generalised NFW profile γ γ
of photons produced per annihilation to f¯f. We use the
ρ(r)=ρ (cid:18) r (cid:19)−γ(cid:20)1+(cid:18) r (cid:19)(cid:21)γ−3 . (1) tabulated values of dNγf/dEγ from [60, 63], which are
s r r generatedwithPYTHIA 8.135[64]anddisregardanycon-
s s
tribution to the flux that is not prompt i.e. we neglect
with γ =1.2 gives the best fit [16]. all photons generated by the propagation of cosmic rays.
3
6.0
LHC8TeV
10.0
(cid:68) 5.0 LHC14TeV
1
(cid:45)
s
3
cm 4.0 M (cid:61) 3 0 G e V
26 D m DM
(cid:45)0 3.0 g 1.0 Fermi(cid:72)3Σ(cid:76)
1
(cid:64)
(cid:92)
v (cid:88)Σv(cid:92) (cid:181)y2
Σ f f
2.0
(cid:88) 1Σ
2Σ
3Σ
1.0 0.1
20 25 30 35 40 45 50 0 20 40 60 80 100 120
m (cid:64)GeV(cid:68) m (cid:64)GeV(cid:68)
DM a
FIG. 2. The solid, dashed and dotted contours show the 1, 2 FIG. 3. The red shaded region shows the values of g
DM
and 3σ favoured regions in the m -(cid:104)σv(cid:105) plane, along with and m that fit the galactic excess at 3σ (marginalising over
DM a
the best fit point, shown by the dot. The branching ratios m ). The red dashed line shows the values of g and m
DM DM a
are determined by the Yukawa couplings y . The excess is that give (cid:104)σv(cid:105)=3×10−26 cm3s−1 for m =30 GeV. The
f DM
consistent with an annihilation cross-section that gives the solid blue line shows the constraint from the current 8 TeV
observed dark matter relic density. CMS monojet search, and the blue dashed line our extrapo-
lation of a similar search at 14 TeV with 40 fb−1.
The average J factor over a region of size ∆Ω is
1 (cid:90) ratiointothefinalstatef¯f isdeterminedbytheYukawa
(cid:104)J(cid:105)= cosbJ(b,l)dbdl, (4) couplings y . The black dot shows the best fit point and
f
∆Ω
the solid, dashed and dotted lines show the 1, 2 and 3 σ
regions respectively. These regions are determined by
where
minimisingaχ2 distributionasdescribedin[16]. Wesee
(cid:12)
(cid:90) ds (cid:18)ρ(r)(cid:19)2(cid:12) thatthecross-sectionisconsistentwiththatrequiredfor
J(b,l)= r ρ (cid:12)(cid:12) √ (5) a thermal relic, i.e. (cid:104)σv(cid:105) (cid:39) 3×10−26 cm3s−1, for mDM
l.o.s (cid:12) (cid:12) (cid:12)r= r(cid:12)2+s2−2r(cid:12)scosbcosl around30GeV.Inaddition, oneshouldnotdiscountthe
possibility that (cid:104)σv(cid:105) (cid:29) 3 × 10−26 cm3s−1 in the pri-
and s varies over the line of sight. We use the form of mordialUniversesinceregenerationmechanisms,suchas
ρ(r) in eq. (1) with γ = 1.2, rs = 23.1 kpc and ρs is those proposed in [65, 66], may maintain the would-be
chosen so that ρ(r(cid:12)) = ρ(cid:12). Following [16], we calculate candidate as the main dark matter component.
(cid:104)J(cid:105) in the 7◦×7◦ region by summing over pixels of size
The red shaded region in fig. 3 shows the values of
0.1◦×0.1◦.
the pseudoscalar-dark matter coupling g and mass
DM
For the simplified model in eq. (2), the s-wave annihi-
m that fit the galactic excess at 3σ. In this region
lation cross-section for χ¯χ→f¯f is a
we have marginalised over m . The red dashed line
DM
(cid:115) shows the values of gDM and ma that result in (cid:104)σv(cid:105) =
(cid:104)σv(cid:105) = NC yf2gD2Mm2DM 1− m2f (6) 3 × 10−26 cm3s−1 for mDM = 30 GeV. Typically, a
f 8π (m2 −4m2 )2+m2Γ2 m2 coupling of order one or less is required to fit the ex-
a DM a a DM
cess. Theannihilationisresonantlyenhancedwhenm ≈
a
where N = 3(1) for coloured (colour-neutral) particles 2m , explaining the ‘funnel’ that extends to small val-
C DM
and Γ is the pseudoscalar width. Among the possible ues of g . We find that the width of the pseudoscalar
a DM
final states, the dominant annihilation channel is to b varies from a few MeV to a few GeV over the parameter
quarks; the branching ratio to a particular final state is space. For m = 30 GeV and (m ,g ) = (40,0.4),
DM a DM
determined by y , for which y is the largest. the width is Γ =1.9 MeV and the largest branching ra-
f b a
An example of the resulting gamma-ray spectrum for tioisBR(a→b¯b)=89%,followedbycc¯andτ+τ− at7%
m =30 GeV, (cid:104)σv(cid:105) ≡ (cid:80) (cid:104)σv(cid:105) = 3×10−26 cm3s−1 and4%respectively. Onceitiskinematicallypossiblefor
DM f f
and the astrophysical parameter choices above is shown the pseudoscalar to decay into dark matter, this channel
by the solid blue curve in fig. 1. This gives a good fit to dominates. For instance, for the point m = 30 GeV
DM
thedata. Beingmorequantitive,fig.2showstheresultof and (m ,g ) = (90,1.0) the width is Γ = 1.3 GeV
a DM a
afitinthem -(cid:104)σv(cid:105)planeassumingthatthebranching with BR(a→χχ)=99.7% and BR(a→b¯b)=0.3%.
DM
4
III. COLLIDER SEARCHES ruled out for g larger than the bottom Yukawa. In-
DM
deed, this is what appears. The production cross-section
for the pseudoscalar plus a hard jet increases by up to a
In general, it is hard to find evidence for this model
factorofsevenat14TeVduetothelargeincreaseinthe
at a collider, particularly for a pseudoscalar that satis-
gluon PDF. For instance, for (m ,g ) = (100,1.0) we
fies m > m /2 so that constraints from h → aa de- a DM
a h
find that the monojet cross-section increases from 15 fb
cays are forbidden. We have implemented our model of
to 96 fb. The dominant background from Z(→ νν)+1j
Dirac fermion dark matter with a pseudoscalar media-
also increases, from 135 fb at parton level to 650 fb for
tor using FeynRules [67] with the UFO output [68] to
MET > 400 GeV and |η| < 2.4. We again mention
generate events in MadGraph5 [69]. We include the di- j
that this cross-section is likely an overestimate because
mension five G G˜µνa operator, which is obtained from
µν the top-quark loop is not taken fully into account [72].
integrating out the top-quark loop. To check our im-
While the monojet search is likely to start to cut into
plementation, we compare our cross-section for tt¯a and
the parameter space in the m ≥2m region, the area
the inclusive pp → a cross-section with those available a DM
below this is difficult to probe.
for pseudoscalar Higgs bosons in the literature. We find
goodagreementwiththeresultsoftheLHCHiggsCross- Since the pseudoscalar mediator interacts most
Section Working Group [70]. strongly with the top quark due to its Yukawa-like cou-
We find that the greatest sensitivity comes from the plings, searches in the tt¯a final state may also be an ef-
8 TeV CMS monojet search using 19.5 fb−1 of data [71]. fective means of constraining this model. A representa-
The 90% confidence limit we derive from that search is tive search is the ATLAS search for tt¯+ MET [74] in
shownasthesolidbluelineinfig.3. Thereisaconstraint the dilepton final state. This search requires the pT of
only at large values of the coupling g and this search the leading lepton to be greater than 25 GeV and relies
DM
doesnotcutintothepreferredFermi-LATregionofgood on the mT2 [75] variable as its main discriminant. For
fit. The relative weakness of the LHC limit is a good the main Standard Model tt¯background, this quantity
demonstration of how a naive expectation of the limit has a kinematic edge at mW. The four ATLAS search
based on crossing symmetry fails [23]. It is likely that regions therefore encompass mT2 > 90,100,110 and
including the dimension five G G˜µνa operator, rather 120GeVtosuppressthis. Wehadroniseoureventsusing
µν
PYTHIA 6[76]andpassthemthroughthePGS4[77,78]
than performing a loop calculation, overestimates the
detectorsimulatorwithanATLAS-specificdetectorcard,
productioncross-sectionwiththeresultthatourlimiton
andanalysetheresultingLHCOoutputusingamodified
g is an overestimate [72]. We also note that at such
DM
version of Parvicursor [79]. We find that the ATLAS
large values of g , the mediator width is larger than
DM
search has a relatively low acceptance for our model,
its mass, making the particle interpretation of the me-
in line with the stated ATLAS efficiencies for light top
diator questionable [73]. It is this fact that explains the
squarks in [80]. Furthermore, the cross-sections for tt¯a
shape of the exclusion contour, since once the mediator
production are known to be approximately three times
can decay to dark matter, the mediator width increases
by a factor of O(103), which suppresses the production smaller than for tt¯h production at the same mass. AT-
LAS set a limit in the m = 90 GeV channel of 2.5 fb.
cross-section. This limit assumes that m = 30 GeV T2
DM
Since this includes the leptonic top decays, this corre-
but other values of m consistent with the excess will
DM
spondstoaninclusivecross-sectionof51fb(i.e. without
give a similar result. The magnitude of the limit will re-
decaying the tops). However, the pp → tt¯a cross-section
main the same but the strongest constraint on g will
DM
for a 100 GeV pseudoscalar mediator is only 40 fb, so it
shift to m ≈2m .
a DM
isnotsurprisingthatthatthissearchisnoteffective. We
We also provide a rough estimate of how monojet re-
have cross-checked our results using the CheckMATE [81]
sults at 14 TeV will affect this scenario. To do this we
package which incorporates the results of [75, 78, 82–
assumethatCMSwillcontinueusingtheE/ =400GeV
T 84]. We have also used CheckMATE to check our scenario
bin. As the expected backgrounds (mostly from Z(→
against the [85–87] searches at 7 and 8 TeV and find no
νν)+1j)inthisbinwillincrease,weassumethatthelimit
constraint.
on the number of monojet events will increase in such a
way that S/B will remain approximately constant. The WenextconsidersearchesfromLEPandTevatron. In-
blue dashed line in fig. 3 shows the results we obtain for teractions between pure pseudoscalars and massive vec-
anintegratedluminosityof40fb−1at14TeV,representa- tor bosons are suppressed. Accordingly, the limit from
tive of about two years running. The improvement from Higgs searches at LEP and the Tevatron which rely on
the 14 TeV run looks dramatic, however it is important the vector boson fusion (VBF) and associated produc-
torealisethatthemonojetsearchisnotparticularlysen- tionmodesdonotconstrainourmodel. Instead, welook
sitivetog whenthepseudoscalarisproducedon-shell, to searches which are sensitive to gluon fusion at the
DM
as is the case when m >2m . In this case the mono- LHC.In[88]theATLASCollaborationsearchedforneu-
a DM
jet plus missing energy cross-section is approximately tral BSM Higgs bosons decaying to µ+µ− and τ+τ− at
√
σ(pp → a+j)BR(a → χχ). For g > y the branch- s = 7 TeV, presenting results for m > 100 GeV in
DM b a
ing ratio is almost 100%, and so if a particular point in order to avoid large backgrounds from the Z-boson res-
parameter space is ruled out, we would expect it to be onance. We have checked that this does not constrain
5
our model in this regime. For instance, ATLAS set a with m¯ = (1/m +1/m +1/m )−1 [96]. Since we are
u d s
limit of 20 pb on σ×BR(a→τ+τ−) for m =100 GeV. considering scattering at LZ, which has a xenon target
a
In our simplified model with g = 0.05 we obtain a nucleus, we ignore contributions from proton scattering
DM
cross-sectionof0.45pb,over40timeslowerthantheAT- becausethespinofaxenonnucleusisdominantlycarried
LAS limit. For larger values of g the invisible width by the neutron. In this case, using
DM
increases, so that the branching ratios into visible final
states decrease and this search loses efficiency. ∆u=−0.44, ∆d=0.84, ∆s=−0.03 (10)
Finally,Υresonancedecaysandsearchesfordirectpro-
and y =m /174 GeV, we obtain g ≈2.8×10−3.
duction of the mediator followed by decay to µ+µ− can q q nna
The non-relativistic limit of eq. (8) leads to a spin-
beusedtoconstrainthecouplingg forpseudoscalarme-
f
dependent interaction; for dark matter with speed v, we
diators below 10 GeV [89, 90]. While we assumed that
g = y , these searches are likely to constrain g (cid:46) y find that the differential scattering cross-section to scat-
f f f f
for m (cid:46)7 GeV and g (cid:46)0.01y for m (cid:46)5 GeV. Fur- terofanucleusofmassmN withspinJN andspinstruc-
a f f a
ture function S (q) [98] is
ther details can be found in [91]. These searches do not A
a priori rule out an interpretation to the gamma-ray ex-
dσ q4 3g2 g2 m 1
cess in terms of our simplified model since a decrease in = nna DM N S (q), (11)
dE m2 m2 8m4v2 2J +1 A
gf can be compensated by increasing gDM. In any case, R DM N a N
these constraints are completely avoided by considering
where q2 = 2m E is the momentum transfer and E
the region m >10 GeV. N R R
a is the nuclear recoil energy. The typical recoil energy
While future monojet and B physics searches may
under investigation at direct detection experiments is
constrain the parameter space with m ≥ 2m and
a DM E ∼10keVsothatq ∼100MeV. Crucially,weseethat
m (cid:46)10 GeV, we conclude that in much of the parame- R
a the factor q4/m2 m2 suppresses the cross-section by a
ter space, no signal will appear at collider experiments. DM N
factor O(10−12). Owing to this, the number of expected
events at LZ between 2 PE and 30 PE in the vicinity of
m =30 GeV is
IV. DIRECT DETECTION AND OTHER DM
INDIRECT SEARCHES (cid:16)g (cid:17)2(cid:18)250 MeV(cid:19)4(cid:18) Exp (cid:19)
N ≈1 event DM .
s 1 m 107 kg-days
The LUX experiment [9] currently has the world lead- a
(12)
ing sensitivity for spin-independent and spin-dependent
Here we have followed the standard procedure to calcu-
dark matter-neutron interactions in the mass range that
late the number of events [99, 100] and assumed that
we are interested in. For experiments planning to run in
efficiencies at LZ are the same as those at LUX.
theforeseeablefuture,LZ,whichisthesuccessortoLUX,
In addition to the result above, which takes into ac-
should provide the best sensitivity, approaching the sen-
count all of the momentum dependence in the scattering
sitivity where the irreducible background from neutrinos
process, we also provide a reference cross-section σ˜SD
dominates [92–94]. n,p
that can be compared directly with experimental limits.
The interaction between dark matter χ and a quark q
Mapping eq. (11) onto the form that is constrained by
is described by the effective operator
experiments (see e.g. [101] for details), we find that
y g
L= q DMχ¯γ5χq¯γ5q , (7) 9 q4 g2 g2 µ2
2m2a σ˜nSD = 16πm2 m2 nnamD4M n (13)
DM N a
valid because the mediator mass ma is much greater the (cid:16)g (cid:17)2(cid:18)250 MeV(cid:19)4
momentum transferred in the scattering process. In or- ≈8×10−43 cm2 DM , (14)
1 m
dertocomparetheoreticalpredictionswithexperimental a
results,itisnecessarytomatchthequark-levelmatrixel-
where µ is the dark matter-neutron reduced mass and
ement with the nucleon-level matrix element, evaluated n
wehaveassumedthatm =30GeVandq =100MeV.
in the non-relativistic limit. A clear discussion of this DM
This cross-section is similar to the projected LZ limit
procedure is given in [95–97], with the result that
σ˜SD ≤7×10−43 cm2 at m = 30 GeV that is pre-
n DM
y g sented in [94], validating the result of the more pre-
q DM(cid:104)χ |χ¯γ5χ|χ (cid:105)(cid:104)n |q¯γ5q|n (cid:105)
2m2 f i f i cise analysis above. As mentioned previously, the spin
a g g , (8) of a xenon nucleus is dominantly carried by the neu-
→ nn2am2DM(cid:104)χf|χ¯γ5χ|χi(cid:105)(cid:104)nf|n¯γ5n|ni(cid:105) tron so we ignored the contribution from the proton
a spin. In contrast, the proposed PICO250 experiment
where n represents either a proton or neutron and (a joint experiment from the COUPP and PICASSO
collaborations) is more sensitive to the dark matter-
 
proton scattering cross-section σ˜SD and they estimate
gnna = (cid:88) yq∆q −m¯  (cid:88) ∆q (cid:88) yq (9) that they will exclude scatteringpcross-sections smaller
m m m m
n q=u,d,s q q=u,d,s q q=u,...,t q than 8 × 10−43 cm2 at mDM = 30 GeV [94]. The
6
dark matter-proton cross-section takes the same form as V. CONCLUSIONS
eq. (13) except g ≈−1.1×10−2 should be used in-
ppa
stead of g . With q = 50 MeV, appropriate for scat-
nna IfdarkmatterisaWIMPwithweak-scaleinteractions
tering off flourine, we find that
withtheStandardModelparticles,thentheprospectsof
discovery at direct detection, indirect detection or col-
(cid:16)g (cid:17)2(cid:18)650 MeV(cid:19)4 lider experiments are good. In many models of WIMP
σ˜SD ≈8×10−43 cm2 DM , (15)
p 1 m dark matter, if a signal is produced in one experimental
a
channel, then a signal will also be observed in another.
However, we show that this need not be the case and
so that PICO250 will set a slightly stronger constraint
that dark matter may be coy, producing a single large
on m than LZ.
a observable signal in isolation.
Even with the large exposure collected by LZ and
We demonstrate this by considering the extended
PICO250 (a factor 103 larger than the current exposure
gamma-ray excess from the galactic centre, observed by
ofLUX),wefindthatLZandPICO250wouldonlybegin
the Fermi-LAT satellite. Although the origin of this
toobserveeventsform (cid:46)250MeVandm (cid:46)650MeV
a a excess is uncertain, one way to account for it is with
respectively. Forheaviervaluesofthepseudoscalarmass,
WIMP dark matter annihilating dominantly to b quarks
the number of events drops rapidly so that there is no
inthegalacticcentre. Weshowedthatasimplemodelof
possibility of LZ or PICO250 observing any events from
DiracdarkmatterthatiscoupledtotheStandardModel
darkmatterscatteringform (cid:38)10GeV.Asthetreelevel
a throughapseudoscalar,whichhascouplingstotheStan-
contribution is strongly suppressed, we should consider
dardModelparticlesthatareproportionaltotheYukawa
if the loop-induced spin-independent interaction gives a
couplings, can account for the excess (see fig. 1). A fit
larger contribution. The authors of [95] considered this
to the excess shows that the preferred dark matter mass
possibility and found that the spin-independent interac-
m is between ∼20-50 GeV and that the annihilation
tionissmallerthanthetreelevelcontributionconsidered DM
cross-section is consistent with (cid:104)σv(cid:105)(cid:39)3×10−26 cm3s−1
above. Therefore, we conclude that direct detection ex-
(see fig. 2), required for the dark matter to obtain its
periments cannot probe this scenario.
relic abundance through the thermal freeze-out mecha-
Finally, we consider other indirect searches for WIMP nism. This cross-section implies that the dark matter-
dark matter. Firstly, limits from the anti-proton pseudoscalar coupling g is O(1) or less over a large
DM
flux (derived from low-energy data collected by BESS- range of pseudoscalar mass m (see fig. 3).
a
PolarII[102])excludeathermalWIMPthatdominantly
Finding additional experimental evidence for this sim-
annihilates to quarks when m = 3-20 GeV [103],
DM ple model is difficult. From colliders, the greatest sensi-
which is below the mass range favoured by the gamma-
tivity comes from the CMS monojet search. Although
ray excess in fig. 2. Using the anti-proton flux calcu-
this search does not currently constrain any of the
lated with [60], we also checked that the limit derived
favoured parameter space, the projected limit from the
from the anti-proton flux at higher energy, as measured 14 TeV LHC run constrains the region m (cid:38)2m (see
a DM
by PAMELA [104], does not exclude the favoured re-
fig. 3). Owing to the suppressed dark matter-nucleus
gion, in agreement with [103, 105]. Secondly, the cosmic
interaction, future direct detection experiments have no
microwavebackground(CMB)providesconstraintsfrom sensitivitywhenm (cid:38)190MeV.Furthermore,additional
a
the energy deposition arising from dark matter annihila-
indirect searches in the anti-proton flux, the CMB, the
tion[106]. However,theseconstraintsareweakenedwhen
neutrino flux from the Sun and the photon flux from
the dominant annihilation channel is to heavy quarks or
dwarf spheroidal galaxies do not provide further con-
τ leptons,withtheresultthatcurrentandprojectedlim-
straints.
itsdonotconstrainthismodel[107,108]. Thirdly,limits
Therefore, over much of the parameter space, the ex-
from the neutrino flux from dark matter annihilation in
tended gamma-ray excess exists in isolation as the sole
the Sun are not applicable because the capture cross-
evidence for particle dark matter. For WIMPs that pro-
section from scattering on protons,
duceobservablesignalsinisolation,ourresultsemphasise
theimportanceoffullyunderstandingthatsignal. Inthe
(cid:16)g (cid:17)2(cid:18)1 GeV(cid:19)4 case of the extended gamma-ray excess, it is crucial that
σp ≈2×10−43 cm2 DM , (16)
SD 1 m additional hypothesises with an astrophysical origin are
a
fully explored so that they may excluded.
is orders of magnitude below the limit of 10−38 cm2
from Super-Kamiokande [109]. Here we assumed that
m =30 GeV and q =20 MeV, typical for a scatter- ACKNOWLEDGEMENTS
DM
ing event in the Sun. Fourthly, Fermi-LAT limits from
dwarf spheroidal galaxies are unlikely to definitively de- MJDthanksRandelCottaandAlexWijangcoforcom-
tectorrejectthedarkmatterhypothesis[17]. Therefore, paring results with him. CM thanks Alastair Currie,
weconcludethatadditionalindirectdetectionsignatures Jonathan Davis and Felix Kahlhoefer for discussions re-
do not provide further constraints. garding LUX, Takashi Toma for discussions on the ve-
7
locity dependence of annihilation cross-sections and Kai has been partially supported by the European Union
Schmidt-Hoberg for discussions on constraints from B FP7ITNINVISIBLES(MarieCurieActions,PITN-GA-
searches. CJW thanks ITP Heidelberg for hospitality 2011- 289442).
while some of this work was carried out. This work
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