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despite the mounting evidence for the existence of dark matter ( dm ) in galaxies , clusters of galaxies and the universe at large scale , the nature and properties of the dark matter particle are still largely unconstrained by observations . in fact , viable dark matter models have been constructed with masses ranging between @xmath0ev and @xmath1 gev , and interaction cross sections ranging between @xmath2 pb and @xmath3 pb ( for a review , see @xcite ) . in this vast parameter space of dark matter models , weakly interacting massive particles ( wimps ) still stand as one of the most promising dark matter candidates , since for reasonable values of the model parameters , the freeze - out of dark matter wimps from the thermal plasma left a relic population with an abundance which reproduces qualitatively well the measured value of the dark matter density @xmath4 @xcite . there are presently three different approaches pursued in order to detect the non - gravitational effects of wimps with ordinary matter : direct detection , indirect detection and collider experiments . this decade is being especially prolific in experimental results in the three search strategies . indeed , various experiments currently in operation are setting strong limits on the wimp parameter space and ruling out regions where a dark matter signal could be expected , notably xenon100  @xcite and lux  @xcite in direct searches , fermi - lat  @xcite , ams-02  @xcite , h.e.s.s . @xcite , magic  @xcite , icecube  @xcite in indirect searches and the lhc in collider searches ( see e.g. @xcite ) . moreover , in the near future the @xmath5tev run of lhc , the xenon1 t  @xcite and lz  @xcite experiments , and the cerenkov telescope array  @xcite will significantly improve the reach of collider , direct and indirect dark matter searches , respectively . these three different approaches constrain the parameter space of dark matter models in a complementary way , however , the synergy of the various search strategies is very model dependent . in this paper we focus on a simple scenario where the dark matter particle is a majorana fermion that couples to light quarks and a coloured scalar via a yukawa coupling . this scenario , despite its simplicity , offers a very rich phenomenology in direct detection @xcite , indirect detection @xcite and collider experiments @xcite . in particular , when the mediator mass is comparable to the dark matter mass , this model predicts a sharp and relatively intense gamma - ray spectral feature which , if observed , would constitute an unambiguous signal for dark matter annihilations @xcite . additionally , the collider phenomenology is distinct from the widely - used effective operator approach ( see e.g. @xcite ) , because the mediator can be directly produced in proton proton collisions . similar models , but with leptonic mediators , were studied in @xcite .    in this paper we revisit the collider limits in this scenario . most analyses include only the production of coloured scalars via strong interactions , nevertheless , in this scenario the yukawa coupling can be sizeable and the production of coloured scalars via the exchange of a dark matter particle in the t - channel can become important or even dominant . this possibility has been discussed in @xcite . here we go beyond these analyses by performing a dedicated re - interpretation of collider searches which includes also jet matching , that is important when considering the quasi - degenerate mass spectrum . a similar analysis for the case of dirac dark matter has been recently presented in @xcite . we analyse the limits on the yukawa coupling from the atlas search for jets and missing transverse energy @xcite and investigate the complementarity of the collider limits with those from direct and indirect dark matter searches . furthermore we discuss various sources of experimental and theoretical uncertainties of collider limits and assess their impact on the exclusion power . finally , we consider an extension of the model by two coloured scalars coupling to the up - type quarks and we study the impact of extending the scalar sector on the dark matter searches in view of the stringent limits from flavour violation . the paper is organized as follows . in section [ sec : model ] , we introduce the simplified model and discuss its properties with respect to indirect , direct and collider searches . section [ sec : lhc ] explains some details of our collider analysis . our results are discussed and compared to direct and indirect detection constraints in section [ sec : results ] , and we conclude in section [ sec : conclusions ] . the appendix contains a brief discussion of flavour constraints . we assume the dark matter particle @xmath6 to be a majorana fermion which couples to the light quarks via a yukawa interaction with coloured scalars @xmath7 . the lagrangian of the model can be written as @xmath8 where @xmath9 denotes the standard model ( sm ) lagrangian while @xmath10 and @xmath11 are given by @xmath12 where @xmath13 denotes the covariant derivative . on the other hand , @xmath14 contains the interactions between the sm quarks and the dark sector , @xmath15 where @xmath16 is a yukawa coupling matrix , @xmath17 denote the right - handed quark fields and summation over flavours @xmath18 , @xmath19 is implied . this lagrangian generically leads to too large flavour changing neutral currents , hence some requirements must be imposed on the yukawa couplings to fulfil the stringent constraints from flavour observables . in the following we consider two scenarios :    1 . we consider a single scalar @xmath20 that couples exclusively to the right - handed up quarks , with coupling strength @xmath21 . this scenario corresponds to an alignment type set - up of the squark sector in the mssm and can be realized by appropriate flavour symmetries at a high scale  @xcite . we consider a pair of mass degenerate scalars @xmath22 and @xmath23 which couple to right - handed up and charm quarks with a universal coupling @xmath24 . such a scenario is motivated by the paradigm of minimal flavour violation  @xcite which requires flavour universality among quarks with the same gauge quantum numbers while allowing a separation of particles belonging to different multiplets . we show explicitly in appendix [ app : flavour ] that within these two scenarios the constraints from flavour observables are easily satisfied . one may also consider a coupling to down - type quarks , which is completely analogous and qualitatively very similar . in the following we concentrate on the above two scenarios for definiteness . the model is thus completely described by the two masses @xmath25 and @xmath26 of the dark matter and the mediator(s ) , respectively , and by the yukawa coupling @xmath21 . with this framework it is possible to calculate various dark matter observables , e.g. the relic density , the annihilation cross section , the dark matter - nucleon scattering cross section or event rates at the lhc , and compare their relative exclusion power . an interesting particularity of the model analyzed here is that the strongest experimental constraints can not be derived from a small set of effective operators , but require to consider higher order effects . concretely , for indirect detection the two - to - three and loop - induced annihilation channels play an important role , firstly because the leading order two - to - two channel is helicity and velocity suppressed , and second because the hard gamma - ray spectrum from @xmath27 and the loop induced processes @xmath28 generate a very distinct spectral signature @xcite . for direct detection , the lowest order operators mediating spin - independent interactions are suppressed for majorana dark matter with chiral interactions , such that higher order contributions and the spin - dependent scattering have to be also considered @xcite . lastly , the production at the lhc is governed not only by the strong processes , but also by processes mediated by the yukawa interaction with the dark matter particle  @xcite .    in the following , we summarize the relevant features of the model concerning the relic density , as well as the direct and indirect detection , and then discuss in detail the signatures at the lhc .      probably the most compelling argument for wimp dark matter is that this class of particles is produced quite naturally in the early universe and can generate , after thermal freeze - out , the correct relic density @xmath4 @xcite as measured by the planck satellite . the lagrangian ( [ eq : l ] ) allows for tree level annihilations @xmath29 and in most of the parameter space the relic abundance is set by this process . however , for @xmath30 the scalar @xmath20 does not freeze - out before the dark matter particle @xmath6 and modifies the relic density @xcite . this process , which is known as coannihilation , can be approximately taken into account by first defining an effective cross section @xmath31 where @xmath32 corresponds to the freeze - out temperature while @xmath33 and @xmath34 correspond to the thermally averaged annihilation cross - section of a @xmath35 or an @xmath36 pair respectively , and then replacing the thermally averaged cross section by this effective cross section in the well - known solution to the boltzmann equation neglecting coannihilations . in our analysis , we use micromegas2.4 @xcite to calculate the relic density in a full numerical approach ( see also @xcite for a recent discussion of sommerfeld enhancement in a similar context ) .      [ cols="^,^ " , ]     the upper limits on the coupling @xmath21 can be translated into limits on the spin independent and spin dependent scattering cross section . the corresponding constraints are shown in fig.[fig : dd ] , together with upper limits from xenon100 @xcite and lux @xcite . for small mass splitting @xmath37 , the direct detection cross sections are resonantly enhanced , while the collider limits are weakened as discussed above . on the other hand , for @xmath38 , the collider search is very effective , while the direct detection cross section is suppressed for majorana dark matter with chiral couplings , as discussed in sec.[sec : dd ] . consequently , when converted into the direct detection cross section , the atlas limits can be stronger by one to several orders of magnitude than current bounds from direct detection experiments for masses in the range @xmath39gev . for masses around @xmath40gev and @xmath38 , the atlas constraint is strong enough to exclude even the qcd contribution to the production cross section at lhc . this translates into the dip in the constraint visible in the middle row of fig.[fig : dd ] . note , however , that while in general collider uncertainties only have a moderate impact , the upper limit is considerably affected in this range ( see blue dotted lines in fig.[fig : dd ] ) . for comparison , the atlas constraint for @xmath41 mediators is also shown by the blue dashed lines in fig.[fig : dd ] . the cross section expected for a thermal relic is also shown as black solid ( dashed ) line for @xmath42 ( @xmath41 ) mediators . comparison of constraints on the annihilation cross section obtained from searches for spectral features by the fermi - lat @xcite and h.e.s.s . @xcite ( _ cf_. @xcite ) , with constraints inferred from collider searches for jets and missing energy by atlas @xcite , as well as direct detection limits from xenon100 @xcite and lux @xcite . the black line corresponds to a thermal wimp , and the dotted lines indicate the uncertainty of the collider constraint , as discussed before . note that the results for @xmath41 mediator are very similar , and are therefore not shown . , title="fig:",scaledwidth=70.0% ] +   comparison of constraints on the annihilation cross section obtained from searches for spectral features by the fermi - lat @xcite and h.e.s.s . @xcite ( _ cf_. @xcite ) , with constraints inferred from collider searches for jets and missing energy by atlas @xcite , as well as direct detection limits from xenon100 @xcite and lux @xcite . the black line corresponds to a thermal wimp , and the dotted lines indicate the uncertainty of the collider constraint , as discussed before . note that the results for @xmath41 mediator are very similar , and are therefore not shown . , title="fig:",scaledwidth=70.0% ]     constraints on thermally produced wimp dark matter with a coloured mediator particle @xmath20 . the green region is excluded at @xmath43c.l . by the atlas search @xcite for jets and missing transverse energy . for comparison , the red shaded area is excluded by direct searches . the blue lines indicate the regions excluded by the search for an internal bremsstrahlung feature in the gamma - ray spectrum from the central galactic halo measured by h.e.s.s . @xcite , assuming a boost factor @xmath44 or @xmath40 , respectively @xcite . within the grey shaded region in the lower left corner , thermal production can not make up for the whole dark matter abundance due to efficient coannihilations . within the upper right corner , non - perturbatively large values of @xmath45 would be required . below the upper(lower ) gray line @xmath46 . the gray dashed line indicates the masses for which the coupling of the mediator equals the one of a squark.,scaledwidth=95.0% ]    one of the most interesting features of the dark matter model discussed here is the presence of a sharp spectral feature in the dark matter annihilation spectrum . it arises mainly from internal bremsstrahlung @xmath27 for @xmath47 , while for @xmath48 , also the gamma - ray line resulting from the loop - induced process @xmath49 gives a significant contribution . in fig.[fig : mdmvssigv ] , we compare constraints on @xmath50 from gamma - ray observations of the central galactic halo by fermi - lat @xcite and h.e.s.s . @xcite ( blue shaded regions ) with those inferred from direct detection @xcite and from the atlas search @xcite considered here . as expected , for small mass splitting , the region excluded by the lhc search ( green region ) is less constraining than xenon100 and lux ( red region ) . however , for mass splitting of order one , the atlas search severely constrains the possibility to observe a spectral feature arising from dark matter with a coloured mediator below @xmath51tev energies .      by requiring that thermal freeze - out yields a relic abundance that coincides with the value measured by planck  @xcite , it is possible to fix the coupling @xmath52 between dark matter @xmath6 , the mediator @xmath20 and the sm quarks for each set of masses . under this assumption , the model has only two free parameters , which we take to be the dark matter mass @xmath25 and the mass splitting @xmath53 . the collider limits considered here can be translated into an exclusion region , which we show in fig . [ fig : mdmvssplitting_lhc_thermalcoupling ] ( green region ) . for mass splitting @xmath54 , it reaches up to @xmath55tev . however , for smaller or larger mass splitting , much lighter masses remain allowed . on the one hand , for much larger splitting , the mediator @xmath20 becomes too heavy to be produced effectively . for much smaller splitting , on the other hand , two effects play a role : first , the collider search becomes less effective in this regime . second , the coupling @xmath56 gets very small due to efficient coannihilations . the combination of these effects also leads to the relatively large uncertainties in the exclusion region ( green dotted lines ) , in particular as the thermal cross section and the lhc exclusion happen to exhibit a fairly similar dependence on the mass splitting in certain regions of parameter space , see e.g. fig . [ fig : splittingvscrosssection ] . for comparison , direct detection mostly probes a region with smaller mass splitting , due to the resonant enhancement of the nucleon scattering cross section for @xmath57 ( red regions ; note that for lux only limits on spin independent scattering are available at present ) . the limits from indirect detection are currently not sensitive to the flux expected for a thermal relic , if the standard einasto profile from @xcite is adopted . however , if the flux is enhanced by a boost factor of order @xmath58 , they probe the multi - tev region ( blue contour lines ) . for comparison , we also show a constraint inferred from mono - jet searches for nearly degenerate particle spectra @xcite , which is sensitive to very small splittings for low dark matter masses . the large hadron collider offers a unique environment to search for dark matter particles with masses below @xmath59 tev through their possible production in partonic collisions . to optimize the search it is convenient to identify simplified models that characterize the signals of a larger class of dark matter models . in this paper we have focused on a model with majorana dark matter particles that couple to the up - type quarks via one or several coloured mediators and which produces a signal consisting in two or more jets plus missing transverse energy , through the production and subsequent decay of the coloured scalar particles . we have carefully analysed the production of coloured scalar particles at the lhc , considering not only the production via the strong gauge interaction , but also via the exchange of a dark matter particle in the t - channel . the latter production channel can be relevant and even dominant in some regions of the parameter space leading to the observed dark matter abundance via the thermal freeze - out of dark matter particles in the early universe . more specifically , we have emphasized the importance of the partonic subprocess @xmath60 mediated by a majorana dark matter particle in the t - channel . due to the enhancement of the rate by the square of the dark matter mass and due to the unsuppressed parton distribution function of up - quarks inside the proton , this process is the dominant production channel in large regions of the parameter space . concretely , for large dark matter masses and a coloured scalar with comparable mass , we have found that the total production cross section of coloured scalars can be enhanced by more than two orders of magnitude compared to the production channels mediated by the strong interactions . we have then derived limits on the parameters of the model employing the atlas search @xcite for jets and missing transverse energy , based on @xmath61fb@xmath62 of data collected at a center of mass energy of @xmath63tev . to re - interpret the analysis for the model considered here , we have computed the appropriate efficiencies for the relevant production channels , taking jet matching with two additional hard jets into account , for all signal regions containing two to four jets . next , we have investigated the complementarity of the collider limits with those from direct detection and indirect detection experiments . we have found that , for some regions of the parameter space of the model , the atlas searches imposes the strongest limits and rules out choices of parameters leading to the observed dark matter abundance via thermal production . for small mass splitting between the dark matter and the mediator , the collider limits are comparable to bounds from direct detection . however , if the mass splitting is of the same order as the dark matter mass , the atlas limits are considerably stronger than the latest bounds from xenon100 and lux , reaching down to @xmath64@xmath65 for @xmath66gev@xmath67tev and @xmath68 . this is due to a relative suppression of the spin - independent scattering cross section for majorana dark matter with chiral couplings , and the enhancement of the production at lhc described above . searches for sharp spectral features at gamma - ray telescopes are fully complementary in the multi - tev region . however , for @xmath69tev direct detection and collider constraints in some cases even preclude the possibility of observing sharp spectral features at future gamma - ray telescopes for the standard choices of the astrophysical parameters . it is important to stress that these limits do not suffer from astrophysical uncertainties and are therefore very robust . we have estimated uncertainties arising from the determination of efficiencies and from higher - order contributions to the production cross section , which are typically @xmath70 but can be larger in particular cases . lastly , we have also considered an extension of the model by extra coloured scalars , inspired by the particle content of the minimal supersymmetric standard model . we have found that our main conclusions still remain for the scenarios in agreement with the flavour physics experiments . we are grateful to miguel pato for earlier collaborations on which part of this work was based , and to andreas weiler for helpful discussions and for cross - checking efficiencies . this work has been partially supported by the dfg cluster of excellence `` origin and structure of the universe '' and by the dfg collaborative research center 676 `` particles , strings and the early universe '' . s.v .  also acknowledges support from the dfg graduiertenkolleg `` particle physics at the energy frontier of new phenomena '' . the interaction term of the dark matter particle and the coloured scalars with the right - handed quarks in general violates the @xmath71 flavour symmetry . therefore , it is necessary to check whether the stringent constraints arising from flavour physics are satisfied . in this appendix we discuss how two well - known possibilities to suppress flavour - changing neutral currents , namely degeneracy or alignment , can be realized within the toy - model considered in this work . consider first the possibility of a single coloured scalar @xmath20 , but allowing for arbitrary couplings @xmath73 to all right - handed quarks , @xmath74 where @xmath75 corresponds to @xmath76 . in this case the box diagram shown in fig . [ fig : ddbar ] gives a contribution to @xmath72 mixing , which is strongly constrained by the measured value of the @xmath77-meson mass splitting @xmath78 ( note that there is no contribution to cp violation in presence of a single species @xmath20 , such that constraints from @xmath79 do not apply ) . the box diagram gives a contribution to the operator @xmath80 given by @xmath81 where @xmath82 ( with @xmath83 ) . the functions @xmath84 and @xmath85 are given e.g. in @xcite . on the other hand , the experimental constraint inferred from measurements of @xmath78 is @xmath86 @xcite . for @xmath87 , this translates into an upper bound @xmath88 since thermal production requires typically @xmath89 , this means that @xmath20 has to couple nearly exclusively to the up - quark , with very suppressed coupling to charm ( or vice - versa ) . a possible exception are regions in parameter space with strong coannihilation for which @xmath90 . for a generic @xmath89 , the flavour - vector @xmath73 should be aligned with the mass eigenbasis of the quarks . this can be realized e.g. in the presence of a @xmath91 flavour symmetry under which @xmath92 and @xmath20 transform with equal charge , while all other states are uncharged . this symmetry is then broken only by the ckm mixing in the left - handed quark sector , and thus this breaking should lead to a misalignment suppressed by the quark masses as well as ckm mixing angles . more precisely , one may consider a situation where @xmath93 at some high scale @xmath94 . due to renormalization group running , the quark mass matrices @xmath95 and @xmath96 are scale - dependent . this leads to a running of the diagonalization matrices @xmath97 , with a similar expression for the down - type quarks . the left - handed rotations lead to the well - known running of the ckm matrix @xmath98 , while the right - handed rotations are unobservable in the standard model @xcite . however , in the present case they lead to a flavour - dependent running of the dark matter couplings , @xmath99 where we neglect flavour - insensitive contributions to the running and assume that @xmath100 . using the one - loop rges for the quark mass matrices from @xcite , one finds for the off - diagonal entry corresponding to @xmath101 and @xmath102 @xmath103 where @xmath104 etc . denotes the ckm matrix elements . thus , even for perfect alignment @xmath105 at the high scale , the coupling to the second generation induced by the running is approximately @xmath106 which is safely below the upper bound required from @xmath72 mixing .    alternatively , one may consider a situation where three additional scalars @xmath7 are introduced , which are taken to transform under the @xmath71 flavour symmetry . then the allowed coupling is of the form @xmath107 and the @xmath7 are all mass - degenerate . one may consider a breaking of the symmetry in the scalar mass matrix , which induces non - degenerate mass eigenvalues of the @xmath7 , and singles out a preferred basis , namely the mass eigenbasis ( similar to the right - handed squarks in the mssm ) . after rotating into this basis ( as well as the mass basis for the quarks ) the interaction term has the generic form @xmath108 where @xmath109 is a unitary matrix , which can have large off - diagonal entries . the resulting contribution to the box diagram will be proportional to @xcite @xmath110 where @xmath111 is a function of the masses . in the limit of degenerate masses this expression goes to zero by virtue of the unitarity condition @xmath112 . lets assume for concreteness that the mixing with the third generation is negligible , similar as in the ckm matrix . in this case the box diagram gives a contribution @xmath113 with @xmath114 and @xmath115 . thus , the strong requirement of precise alignment @xmath116 found above can be considerably relaxed provided the masses are quasi - degenerate . for order one mixing , the upper bound on @xmath117 required from @xmath72 mixing then translates into an upper bound on the mass splitting @xmath118 thus , in both cases discussed above , the flavour constraints can be fulfilled in presence of an ( approximate ) flavour symmetry .
we investigate the signatures at the large hadron collider of a minimal model where the dark matter particle is a majorana fermion that couples to the standard model via one or several coloured mediators . 
 we emphasize the importance of the production channel of coloured scalars through the exchange of a dark matter particle in the t - channel , and perform a dedicated analysis of searches for jets and missing energy for this model . 
 we find that the collider constraints are highly competitive compared to direct detection , and can even be considerably stronger over a wide range of parameters . 
 we also discuss the complementarity with searches for spectral features at gamma - ray telescopes and comment on the possibility of several coloured mediators , which is further constrained by flavour observables .