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IPPP/13/31, DCPT/13/62, SLAC-PUB-15893 Extended gamma-ray emission from Coy Dark Matter Céline 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 σñSD = 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. 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