Jhep01(2015)037

JHEP01(2015)037 c,d Springer October 6, 2014 , the DM and January 9, 2015 q : : g December 15, 2014 November 11, 2014 : : , and Received DM 10.1007/JHEP01(2015)037 5 GeV). For axial-vector Published Revised Accepted , g . doi: and Christopher McCabe med a ,M DM Published for SISSA by m Sarah A. Malik [email protected] b , . Matthew J. Dolan, 3 a [email protected] , 1407.8257 The Authors. Exotics, Beyond Standard Model, Hadron-Hadron Scattering, Particle and c

We introduce a Minimal Simplified Dark Matter (MSDM) framework to quan- , oliver.buchmueller@cern.ch South Road, Durham, DH1 3LE,GRAPPA, U.K. University of Amsterdam, Science Park 904, 1098 XHE-mail: Amsterdam, Netherlands [email protected] High Energy Physics Group,Prince Blackett Consort Laboratory, Imperial Road, College, London, SW7Theory 2AZ, Group, U.K. SLAC National AcceleratorMenlo Laboratory, Park, California 94025,Institute U.S.A. for Particle Physics Phenomenology, Durham University, b c d a Open Access Article funded by SCOAP detection searches. Keywords: resonance production ArXiv ePrint: parameter space. Wereach explore of the the LHC projectedcomplementarity of and limits the multi-ton of searches xenonthe these remains. MSDM direct searches and detection effective Finally, from field experiments, weEFT the theory framework, provide and (EFT) ultimate particularly frameworks a find when to comparison that highlight exploring of the the the deficiencies limits complementarity of of in the mono-jet and direct models accurately capture theand couplings full can event be kinematics,this systematically framework and can studied. the be used dependence Theexperiments. to interpretation on establish For of all an theories mono-jet equal-footing with masses sensitivity comparison searches a than with in direct vector direct detection mediator, detection searchesmediators, LHC for LHC mono-jet light and DM searches direct masses possess detection ( better searches generally probe orthogonal directions in the Abstract: titatively characterise dark matter (DM) searches atwhere the the LHC. DM We study is two MSDM aThe models Dirac models fermion are which characterised interactsmediator by with masses, four a and parameters: vector the and mediator axial-vector couplings mediator. to DM and quarks respectively. The MSDM Characterising dark matter searches atdirect colliders detection and experiments: vector mediators Oliver Buchmueller, JHEP01(2015)037 ], and 19 – 13 , 11 , 8 7 ], including signatures with 11 4 – 1 3 5 19 – 1 – 17 16 12 8 5 ]. While this is in principle a model-independent way of interpreting 1 23 11 – 5 ] by some of the present authors, the EFT ansatz is only valid for a heavy mediator 12 In the past, searches for DM production at colliders [ 4.1 Limits from4.2 current searches Low dark4.3 matter mass region Projection for future searches 3.1 LHC simulation3.2 details Optimising mono-jet3.3 searches in the Facets MSDM of framework direct detection for which the mediator widthof is the larger mediator than its doubtful.provides mass, constraints making which Furthermore, a are for particle-like eitherenhanced) interpretation lighter or over-conservative (because mediator too the masses aggressive process (becausework the is the discussing EFT missing resonantly inadequacies approach energy of distribution is the too EFT soft). approach Further can be found in [ field theory (EFT). Invarious this higher case, dimensional bounds operatorsModel are describing the placed fields interaction on [ of thethese DM contact with searches, interaction the the scale Standard EFT Λan approach of inappropriate fails framework to severely interpretpaper in DM [ a searches at number colliders. of As circumstances shown making in it a previous experiments have become aand focal astroparticle point communities. for both the experimental and theoreticalmissing particle transverse energy (MET) such ascompared mono-jets with and results monophotons, from were quantitatively direct detection experiments in the framework of an effective 1 Introduction Since the start-up ofcle the dark Large matter Hadron (DM) Collider production (LHC) at in 2010, colliders searches and for their direct comparison parti- with direct detection 5 Comparing EFT and MSDM6 limits Conclusions 4 Landscape of collider and direct detection searches 3 Experimental details and validation Contents 1 Introduction 2 Minimal Simplified Dark Matter models JHEP01(2015)037 ] ], ], 34 med 13 32 M repre- ]). This DM 24 g , where and DM q g g , and ] or di-jet searches [ q g 31 ]. , 30 – DM ], we consider vector and axial- m 27 12 , we define our Minimal Simplified med 2 M ] will also possess significant sensitivity in 33 – 2 – ]. 22 , 21 ] (a similar approach was also advocated in [ 23 ). 1 contains technical details related to the CMS mono-jet search (including ] and mono-Higgs [ 3 20 ], a more appropriate approach to characterise DM searches at colliders is ] and is by now the standard by which MET searches are compared in that 12 are the masses of the mediator and the DM particle, while 26 , DM 25 m This paper is structured as follows: in section We focus on the development of a consistent and state-of-the-art framework within In this paper we suggest a minimal set of simplified models that can be used to charac- Similarly, the advantage of the simplified model approach in the context of DM searches As in [ that we leave for follow-up work. Dark Matter (MSDM) frameworkdiators. in the Section context ofa s-channel discussion vector and on axial-vector the me- optimal MET cut in the MSDM interpretation) and direct detection as well as DMconstraining indirect the detection DM searchesinclusion parameter [ of space these other defined searchesthe by in subject our of our framework future simplified is work.t-channel relatively In model mediators, straightforward addition, and and it approach. will is DM also be particlesinteractions possible The with and to a mediators extend scalar our or with approach pseudoscalar different to mediator spin. include requires additional Describing technical DM details [ experiment. The mediator isat produced LUX (see in figure the s-channel at the LHCwhich and collider in the limits t-channel general and way. direct detection Other collider limits searches, can such be as interpreted jets and plus compared MET in [ a and sent the coupling of thethe SM DM. particles We to use the thismono-jet mediator and minimal direct and set detection the of searches. couplingvector parameters Continuing of mediators from to the [ to elucidate mediator study the to the true reach of complementarity the of LHC and direct detection search from the LUX possible within the EFT approachof where the the relevant collider parameter limits space. were not valid in a largeterise DM region searches both at collidersspace as of well these as direct models detection is experiments. defined The by parameter four variables: is that the fullThis event allows kinematics for comprehensive over studies theoptimisation of whole of individual parameter the DM space production experimentalthe topologies is searches interpretation and accurately of over for captured. collider all the equal-footing searches of comparison in the with this parameter the framework space. results can of also In direct be addition, detection used experiments. to establish This an was not context. Today, almost everyof ATLAS and their CMS results MET in analysisprobed one provides or by an even the interpretation severalory, simplified search. valid models, constraints which Although on characterise simplified moresimplified the model topologies models complete approach models usually is such do used as with not the appropriate represent MSSM care can a [ be full inferred the- if the mono-leptons [ the use of simplifiedframework has models proven [ to beLHC very [ successful in searches for supersymmetry (SUSY) at the these arguments also extend to searches for other mono-objects such as mono-photons [ JHEP01(2015)037 (2.1) (2.2) , the mass , our MSDM 0 DM Z m and χ , and the coupling of which is exchanged in q is equal for all quarks. 0 g χ q Z 5 g . γ µ 6 χ µ ¯ χγ 0 µ ¯ χγ Z 0 µ and xenon direct detection experi- Z DM 1 g we present a comparison of the limits − DM ) from future scenarios, including limits 5 − g q − 5 , the model is completely characterised by 4.3 q γ 1 µ µ ¯ ¯ qγ qγ – 3 – 0 0 µ µ Z Z and 3000 fb q q . This set of parameters is sufficient to characterise g g 1 − q q DM X X g ⊃ − ⊃ − , 300 fb 1 − axial ) of the low mass region where direct detection experiments lose vector L , the coupling of quarks to the mediator, ] for a comprehensive list), including both s-channel and t-channel contains our main results: we show the current complementarity of L 9 mediator in the context of collider and direct detection searches have 4.2 4 0 med Z M and assume that the quark-mediator coupling ]. χ 41 – 35 In general a vector mediator can have vector or axial-vector couplings with quarks and In this paper we focus on the example of a vector mediator In this paper we introduce a Minimal Simplified Dark Matter (MSDM) framework, for vector and axial-vector couplingsModels of respectively, a where vector the sum extends over all quarks. mono-jet production and direct detection scattering rate. the dark matter. In additionmodel to with the a usual vector mass mediator and is kinetic defined terms for by the interaction terms the s-channel in mono-jetDirac production. fermion WeIn consider this the case, case as whenthe shown the schematically four in dark parameters figure matter discussed is above. a These parameters are sufficient to determine the of the mediator, the mediator to thethe dark interactions matter, of a varietywith of each different UV other) completions of (whichjet the we searches effective assume (see do operators e.g. not previouslymediators [ interact considered [ in the context of mono- for characterising searches in a well-defined, simple, and consistentwhich manner. extends the SM matter(a content minimum by of) two new fourwhile fields parameters. the whose four properties The basic are parameters two specified are fields by the are mass the of dark the matter dark and matter particle, the mediator The use of simplified modelsstandard to procedure characterise new in physics both searches the atof experimental the simplified and LHC theoretical has models become communities. isparameters, a The that advantage such they as aredirectly masses, related fully couplings to described experimental and/or by observables, cross-sections. making a this small approach All number an these effective of framework parameters fundamental are ments with multiple ton-year exposures.obtained In in section the MSDMof and the EFT EFT frameworks, framework. which We serves present to our highlight conclusions in the2 section inadequacies Minimal Simplified Dark Matter models mono-jet and direct detection searches fordimensional vector projections and of axial-vector the mediators four-dimensional indiscussion parameter various two- space. (in We section also havesensitivity a and dedicated show projected limitsfrom (in section the LHC after 30 fb experiments. Section JHEP01(2015)037 , q ' g ) (2.4) DM DM and v m ( plays an χ ) DM ) (2.3) med med , g q M m ( DM 2 ] (where ′ Z − 56 , m 2 DM 2 med q DM g m med g M med 4 ]. Although the collider ], this does not have to M M − 55 60 1 – )Θ ( s 42 ¯ qq , ) qq → 32 DM , 2 DM 0 2 med m ], the mediator width Γ m Z ( M 16 2 , χ Γ( ]. While setting the mediator couplings 32 , 11 q , 59 1 + , X 12 8 , 58 11 ) ) ) + med – 4 – DM DM π DM M m m 12 ( ( m ¯ 2 g χ χ 2 DM g so that the total width is − = med med M vector ) DM ) )Θ ( g ¯ χχ med ¯ χχ ]. If leptonic mediator couplings are introduced, di-lepton resonance → M 0 ( 64 → ′ – Z 0 Z Z Γ( 61 q , Γ( ]. A treatment of the loop-induced contribution is beyond the scope of this g 44 ≡ 57 . The left diagram shows a contributing diagram for mono-jet production with an (axial) med Γ ) so the loop-level spin-independent contribution, which is not velocity suppressed, c As has been discussed in the literature [ As both hadron collider and direct detection searches for dark matter primarily probe 3 ¯ q q − where the individual contributions for the vector and axial-vector cases are important role in mono-jetthe searches. four In free our parametersinvisible in MSDM decays the models, contribute simplified we to model. calculate Γ the We assume width that from no additional visible or to zero; the leptonhadron collider couplings and play direct no detection searchesto role [ leptons (at to tree-level) zero inbe often the the introduces case phenomenology [ anomalies insearches into either will the provide theory further [ constraints on the space of MSDM models. 10 dominates [ work so we do not consider the case ofthe mixed interactions vector of and dark axial-vector matter couplings with further. quarks, we set the mediator interactions with leptons gives a spin-independent interaction that iswhile coherently enhanced the by axial-vector the number interaction of givesis nucleons, a also spin-dependent possible signal which tohave is vector have not. couplings mixed while In vector the generalmixed and dark it interaction axial-vector matter is has couplings axial-vector spin-dependent (so couplings). and that At e.g. velocity-squared tree-level, suppressed the the quarks [ direct detection, which is characterised by the same four parameters. also been discussed elsewhere inphenomenology the of literature [ theexperiments vector they and are axial-vector very mediators different. is similar, In at the direct non-relativistic limit detection the vector interaction Figure 1 vector mediator at awhich hadron are collider. the mediatorquarks The and respectively. process dark matter is The masses, characterised right and by diagram the mediator shows couplings the to corresponding dark scattering matter process and relevant for JHEP01(2015)037 . DM but DM (2.5) (2.6) (2.7) g , g med DM to be equal, , m q g med M 2 q 2 med m 4 M − . 2 1 / 2 3 / s 3 ! ! 2 DM 2 q 2 q 2 med 2 2 med med m m m ) cut used by the mono-jet analysis, M 4 2 4 M M ], including NLO corrections results in T / − E 65 − 1 1 + 1

med – 5 – med med π π π M M M 12 12 12 2 2 q q is neither unreasonable nor unexpected: for instance, 2 g g DM ]. This allows us to generate the process where DM q 3 3 g g 68 – = = = 65 and axial axial ) ) vector DM ) g ¯ qq ¯ χχ ¯ qq → → → 0 0 0 Z Z Z Γ( Γ( Γ( quark doublet and the right-handed electrons. L , the parameters of interest for our MSDM models. q g We end this section by again emphasising that our motivation here is to flesh out the Finally, while in this article we fix the mediator couplings to all quarks POWHEG BOX described inparticles [ are pair producedin in a mono-jet association signature. withgeneration a of The the parton implementation signal to of from next-to-leading-order thisconsistently (NLO) the with accuracy process initial and a in for state, parton this POWHEG to shower. resulting allows be As for matched shown the in [ sections, on whichand the direct detection community quote limits,3.1 and LHC simulation details We generate LHC events for both the EFT and the MSDM using an extension of the This section describes our technicaldetection implementation searches. of the Our CMSbetter limits mono-jet for agree and LUX both with direct the theuse-case. mono-jet respective search collaboration’s In and limits addition, thewhich to we LUX was 10% check optimised results, or assuming that which the the isframework. EFT fully MET framework, sufficient ( is We for also also our appropriate within provide the the MSDM prescription for translating between scattering cross- other spins for theadditional mediator experimental constraints. and dark matter particle, different coupling3 structures and Experimental details and validation experiments can be accuratelyto characterised. infer qualitative These and minimalcomparison quantitative simplified of properties models collider of and enable more direct us assumptions complete detection which DM experiments on models we equal have and footing.map made allow out Variations a in of the this the MSDM paper landscape; should the be approach should explored be in extended the to future include, to for fully instance, Having different values for in the Standard Model thereof is the a factor SU(2) of six difference between the hypercharge couplings framework of MSDM models so that the search results from collider and direct detection It is straightforward to incorporatewe additional do visible or not invisible consider contributions that to here. Γ we do not enforce that this must be equal to the mediator couplings to dark matter JHEP01(2015)037 ] ], 69 73 ] for (3.3) (3.2) (3.1) , 71 72 [ 30 GeV and 8.180 [ > T ] algorithm with p Delphes3 jet has transverse 74 [ T t Pythia p k 500 and 550 GeV. The , 450 , χ , 5 400 1 denotes the transverse momentum γ , µ 1 T,j χ p µ ¯ 350 χγ T,j , p + q ¯ χγ 5 1 γ q 300 µ µ 2 T,j , p ¯ ¯ qγ qγ 2 2 + 1 1 250 – 6 – threshold by benchmarking it against exclusion Λ Λ ¯ , we have verified that this threshold is also a χ 2 χ T 4. Another jet is allowed if it has > . q q m ] PDFs. / E 2 X X 3.2 T ], this choice of scale leads to NLO corrections that q 70 / < E ⊃ ⊃ 65 . For all cases except the validation of the CMS EFT | = 1 j µ η DM EFT axial | EFT vector m L L . As noted in [ 1 ] are applied: jets are reconstructed using the anti- ], events for the EFT process are generated at LO to enable a direct j 4 4 ] (dashed lines) on the contact interaction scale Λ. The contact interaction shows a comparison of our 90% CL limits (solid lines) and the CMS 90% CL 4 is the invariant mass of the DM pair and 2 ¯ χ χ 5, but an event is vetoed if there are any additional jets satisfying this requirement. , is greater than 2.5. Seven signal regions are defined, with increasing thresholds . m 2 4 ,j Figure The parton level process produced by POWHEG is matched to We set the renormalisation and factorisation scales to 1 j < φ | η higher dimensional operators reasonable choice for placingpaper in limits our in mono-jet the analysis. MSDM models solimits from we [ use itscale throughout Λ is this the mass scale that gives the correct dimension to the vector and axial-vector ∆ for the missing transverseCMS energy: mono-jet analysis optimisedsensitivity the in the EFTwas interpretation 400 framework. GeV. They As found discussed that in the section optimal threshold a distance parameter ofmomentum 0.5. above 110 GeV Events and are| selected where the highest Thus, the mono-jet signature comprises ofin either the one event, or it two-jet is events. further If vetoed there if are the two angular jets separation in azimuth between the two jets, limits, we use the MSTW2008NLO [ showering and hadronisation and put through awith detector parameters simulation using that are tunedcuts to described the in CMS [ detector. Subsequently, the mono-jet selection where of the leading jet are relatively independent of comparison with the limitsthis provided by process CMS. in This the is(where the POWHEG another mediator BOX advantage is of integrated since out) implementing taken it and into the is account). MSDM case For capable this (where of the validationparton process, mediator distribution simulating is we functions both correctly follow (PDFs). CMS the and EFT use the case CTEQ6L1 [ importantly, it also leads torenormalisation a and substantial factorisation reduction scales in and theprediction. hence dependence the on theoretical Generating uncertainty the the on choice signal thebounds. of signal to the For NLO the accuracy purposesmono-jet should of search therefore validating [ lead our to framework more against robust the results from the CMS a small enhancement of the cross-section compared to leading-order (LO). However, more JHEP01(2015)037 T 4 / E 10 limit limit limit 400 GeV is Our CMS CL > Vector % ; our limits and T D 90 / E med 400 GeV cut which GeV 3 @ 10 > med T M 3 / ê E p . Our limits and the CMS 8 GeV ê med GeV 50 M med med = = 50 M = = DM med cut is the most important cut of m G DM med

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In figure L GeV couplings are fixed to MSDM model is is optimal in theis EFT rather framework. modest However, and the thusstill 50 GeV we reasonable. increase conclude that in the the use exclusion of contour the default cut of can use the information providedcut by on CMS the to limits brieflythis set examine analysis the in to effects our separate of MSDM varying background framework. the from The a potential signal. provided by CMS for different values of 3.2 Optimising mono-jet searches inFully the exploiting MSDM the framework adoptionand interpretation of of simplified mono-jet searches modelssearch requires cuts, as a which re-optimisation a are ofcarrying framework based current out experimental for on a signal the complete samples presentation re-optimisation generated of in all the cuts EFT is framework. beyond the While scope of this paper, we shows the results for thelimits vector agree operator within for 5% two (10%)able choices in to of the reproduce Γ left the (right) CMSour panel. mono-jet use-case. We, analysis therefore, to conclude 10% that or we better, are which is fully sufficient for the results for thethe vector CMS interaction limits with agree two to choices better of than the 10%. mediator width Γ where the sum extends(green and over black all lines) and quarks. axial-vector (red The and blue left lines) panel operators while shows the the right panel results for the vector Figure 2 lines) on the contact interactionvector scale operators; Λ. our The limits left and panel the shows CMS the limits results for agree the to vector better and than axial- 5%. The right panel shows JHEP01(2015)037 – 78 2 PMT (3.4) nσ , ). There- R c 3 and dR dE − ] and we use n )) 10 plane for various ], XENON [ 81 R ' = 1. The optimum E 77 ( – med ν ; DM M DM 75 - v n 1200 , g 3 DM . 6 GeV. Two-phase xenon [GeV] ) P( m ], S1 ranges from 2 PE to & med = 0 81 q M PMT 1000 g DM nσ m 400 GeV cut used in the CMS (and √ > n, 800 T )) is a Poisson distribution with mean / E R 450 GeV exclusion contour is modest so the E ( )N(S1; > ν 600 R ; T E n – 8 – > 250 GeV > 300 GeV > 350 GeV > 400 GeV > 450 GeV > 500 GeV > 550 GeV / ( E T T T T T T T ]. E E E E E E E S2 = 1.0 85 DM ], P( 400 ] 84 (S1) 83 , S1 = 0.3, g 37 [ q . 82 Vector: 90% CL limits 90% CL Vector: g 0 =1 200 ∞ X n ≈ ) are the S1 and S2 efficiencies [ R R ) is a Normal distribution with mean and variance ), where the numerical pre-factor is quoted in [ 50 threshold. The couplings are fixed to 450 400 350 300 250 200 150 100 E R dE

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DM E PMT m [GeV] / ( PMT S2 E σ ∞ eff 3 keV nσ Z L ] programs and is scalable to the much larger target masses required to 450 GeV, slightly larger than the √ ) R 81 > n, E DM 8 T . m / 8 E ( (S1) and ξ . Exclusion limits at 90% CL for the vector mediator in the S1 ) from NEST (at 181 kV/cm) [ ≡ = R 400 GeV cut is a reasonable choice. ) E LUX has published the limit for SI interactions but not for SD interactions. We now cut is R ( > S1 dR ] and LUX [ E d T T eff ( / / where 30 PE, N(S1; respectively, where ν L describe our procedurelimits for will calculating be both providedrate directly limits per by and kg-day the assume at collaboration. LUX that We with in model [ the the differential future, scattering both detector technology has a proven80 track record through theprobe ZEPLIN [ very small scatteringthat they cross-sections. are sensitive Xenon to experiments both SI also and have SD the interactions. advantage Dark matter interactions with nuclei lead(SD) to scattering either in spin-independent the (SI) non-relativistic or limit spin-dependent fore, (recall limits that in on the the galaxy case. cross-section In to this scatter paper offsets we a the primarily nucleon use strongest are the published limits presented limit from separately on the for SI LUX each interactions experiment, for which currently E our) analysis.E The 50 GeV increase in the 3.3 Facets of direct detection Figure 3 different values of the JHEP01(2015)037 E 3 to v , for 3 10 5 at , (3.5) . | −

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D @ Spin ) is the local dark matter velocity distribution in the galactic frame, . The left panel shows a comparison of our 90% CL limits (solid lines) and published v ( 46 48 50 42 44 40 ) gives the DM mass-dependent fraction of events that fall below this mean. We ------f = 200 GeV and remaining constant at 0.5 for higher masses.

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2 0 DM m ( values for the astrophysicalUncertainties parameters in that these are parameters usednucleon lead in scattering to cross-section the limit an direct [ uncertainty detection of community. around 50% ondistribution) the enters 90% through CL where is the Earth’s velocity relativespeed to required the for galactic a rest nucleus frame to [ recoil with energy scatter on a nucleus with mass consider events that fallξ below the mean ofcalculate the it nuclear by recoil simulatingfor band; the different the values distribution efficiency of ofm factor DM events in the log reach of LZ withneutrino a background from 10 [ ton-year exposure, and the discovery reach accounting for the irreducible Figure 4 90% CL limits (dashedpanel shows lines) our on limits for spin-independentwhich the no direct corresponding published spin-dependent detection results direct cross-sections are detection available cross-sections to compare with. Also shown in both plots is the expected JHEP01(2015)037 , ) is R 0 SD E σ (3.7) 0 SD ( is the σ F ]. This are the J 80 is a factor ], 0 SD σ 93 0 SD σ is the fractional and i f 0 SI . . This enhancement σ 0 SI 2 respectively. In order σ A 0 SD ] is for SI only, therefore σ , 91 ) R and E (finding good agreement over ( 0 SI i 4 σ S ], which is stronger than LUX’s for 95 + 1 i f i ) (3.6) J R 2 131 is the atomic number of xenon, E limit (solid lines) with the published ones ( i ≈ 2 X 0 SI F ) is the spin structure function [ A σ 2 ) comes from the factor R 0 0 SI SD v – 10 – 2 E σ σ v 3.7 ( 2 nχ stronger than the corresponding SD limits, which 2 N S µ show the limits on 2 nχ 4 A 2 m 4 µ ], N 2 π 3 from SuperCDMS [ 4 m 92 ) and ( 0 SI = = agrees with the published LUX limit to better than 10% σ 3.6 discovery of dark matter, taking into account the background R . We make the same assumptions in our calculation as those R SI 0 SI SD σ is significantly weaker than the limit on σ 4 dσ dE dE dσ 0 SD σ isotope with non-zero spin. The cross-sections th i ], and the discovery reach when coherent neutrino scattering is taken into 96 ]. For the LZ limit we assume that the efficiencies and background event rate ]. Namely, we assume that the low mass reach is from a xenon experiment with is the DM-nucleon reduced mass, 91 ). 91 6 GeV, the projected limits from LZ (the successor to LUX) assuming an exposure nχ ] and the limit on 4 µ . 94 Also shown is the limit on The left and right panels of figure 5 stronger than the published XENON100 SD limit to scatter off a neutron [ . 2 DM in the right panelused of in figure [ an exposure of 200 kg-yearsfrom and a an xenon experiment energy with thresholdneutrino a of events 4 3 are eV, keV while energy expected. threshold the and high Furthermore, the the mass exposure reach magnitude, is is distribution such and that 500 uncertainty account [ remain the same as atof experiments LUX. can The make discovery a reach 3 contribution indicates from the coherent cross-section neutrino at scattering.we which 90% reproduce The result that in resultthe [ here whole mass in range) the and left extend panel the of calculation figure to calculate the limit for SD scattering is the same relativeexpected, improvement the as limit found on in the SI limitsm of LUX and XENON100.of 10 As ton-years [ in [ over the whole mass range.for which Based no on published thisapproximation limits observation of we from the assume the performance that of LUX∼ our the Collaboration limits experiment. are for The available, limit are we also find a for good plays an importantsection role when comparing the LUX resultto with validate the our mono-jet procedure(dashed search we lines). compare (in Our our LUX limits (red) are calculated with the ‘pmax’ method, introduced function is suppressed byfunction for over xenon an isotopes orderthe therefore cross-section of to we magnitude scatter ignore off relative its aand neutron. to SD contribution. cross-sections Note the This that in the neutron eqs. meansensures dominant ( structure that difference that between the the SI SI limits are over 10 where is the Helm nuclearnucleus form spin, factor the sum [ abundance extends over of all the isotopesSI with and non-zero SD spin cross-sections and toand scatter are off the a quantities nucleon on (in which the the limit experimental of limits zero-momentum are transfer) quoted. The proton structure For SI and SD scattering, this is given by JHEP01(2015)037 at are (3.8) (3.9) s (3.10) (3.11) DM enters m 100 MeV. 100 MeV. DM and ∆ ∼ < m d , med . , ∆ 2 2 u M ). As a result (and nχ 3.5 nχ . Finally, we note that µ µ 1 GeV 1 GeV 10 GeV, since 4.3 (10%). We assume that the , the dark matter mass only 4 4 & O scale in proportion to DM and DM m 0 SD med med σ 4.2 m M 1 TeV M ) are valid when the mediator mass is 1 TeV ]. Other values for ∆ ] and we assume that the experimental and . We discuss the vector and axial-vector 2 2 2 nχ 99 3.10 2 91 0 SI µ region where direct detection searches start q σ q 2 g ) g 08 [ s . ]) and differ by 1 1 0 DM to constraints on the parameters of interest in DM DM – 11 – ) and ( − m g g 102 + ∆ 0 SD – = 3.8 d σ · · s 4 med 2 2 100 . For large values of + ∆ and cm cm ). We conclude this section with projections for future nχ πM u µ 0 2 nχ SI ) the limits on 41 39 σ µ (∆ − 4.2 4 − 2 q ) essentially vanishes for 2 q 4 85 and ∆ g med g . 10 10 × 3.10 × 2 DM 2 πM DM = 0 6 g 1 g ). . . d 3 4 9 1 4.3 = ≈ = ≈ ) and ( 0 SI 42, ∆ 0 SD . ]) but we do not discuss that further here. σ σ 0 3.8 − 98 is equal for all quarks in both of these results. Note that the dependence on , . Finally, we note that eqs. ( ) before zooming in on the low = q 97 g u DM 4.1 in eqs. ( m To explore the complementarity of collider and direct detection searches we map out Translating the limits on DM to lose sensitivity (insearches section (in section the four-dimensional parameter space ofparameters. the The MSDM following models two-dimensional by planes showing are projections considered: in two 4 Landscape of colliderIn and this direct detection section searches searches we for present the MSDM our modelscases defined 90% in in exclusion section parallel, limits showingsection from first the the LHC current constraints mono-jet on and the LUX whole parameter space (in as can be verifiedlarge from figure greater than the typical momentum transferTherefore in in the the scattering following, process, we which do is not consider direct detection limits for also used in thecoupling literature (see e.g. [ m only through the reducedenters mass the scattering rate through its explicit dependence in eq. ( where ∆ In the axial-vector model, thecross-section scattering to interaction scatter is off SD a and point the analogous like result neutron for is the our MSDM models is now straightforward.is SI For the and vector the model, cross-section the to scattering interaction scatter off a point-like nucleon in the non-relativistic limit is efficiencies and energy resolution ison perfect, electrons. and we We ignore the makethe effect use discovery of of neutrinos reach these scattering may results(see be e.g. in improved [ sections with new experimental and theoretical techniques of the neutrino fluxes are the same as those in [ JHEP01(2015)037 , q )) )). g = 3.7 is not 3.10 5 case . . DM med g = 0 DM g ) and ( ) and ( q g DM 3.6 3.8 g √ . For axial-vector ) enhancement of 2 = q 4.2 131 g 45, when the mediator . 1 ' (cf. eqs. ( , both for the case where 2 ≈ A q 4 med DM g 5 GeV) where direct detection g ) for a vector mediator exceed = . /M 5) respectively. The region to the . DM is proportional to 0 and 2 DM = 1 example provides the strongest DM m DM , g g q 5 we compare the LHC mono-jet search 2 q . m g ), we find that for the case g . med . . 5 DM g M 2.7 med DM med = m M q M g ) to ( 1) and (0 plane for the vector (left panel) and axial-vector , – 12 – and . In figure 3 . 2.4 . For a few plots we slightly extend beyond this 2 t med DM m 2 M m , the limit on 1), (0 , > vs (for a given value of DM m . DM med med ) = (1 m M . From eqs. ( DM M g ), for fixed values of DM ), for fixed values of , the direct detection experiments extend the reach to large values med 6= , g DM q DM q M g g , for fixed values of couplings g g med = = M med q q g and , for fixed values of g M q g vs ( DM vs vs ( g vs = med DM DM . DM q g M m g m DM For the different coupling scenarios the We begin by making some general comments which hold for all of the figures in this We limit the parameter space by the requirement that the mediator width Γ • • • • m limits for bothpossesses mono-jet the and weakest direct sensitivity. detectionforward The to searches, behaviour understand: of while the the cross-section the and direct scales thus, detection like for limits a is given straight- value of only exception is at smallerexperiments values lose of sensitivity. the We DM discuss massmediators, this ( the region mono-jet and further direct in detectionorthogonal section searches directions show in good the complementarity, probing parameterto space. large values While of theof mono-jet search is more sensitive the axial-vector limits bythe almost LUX two limits orders isthe of explained SI by magnitude. cross-section the in The atomicscattering the number significant cross-section case is squared difference of SD, ( a in doesFor vector the not mediator. vector exhibit mediator, the The this LUX enhancement axial-vector limits (cf. case, are eqs. significantly for stronger ( which than the the LHC limits. The coupling scenarios: ( left of the lines is excluded. section. While the collidercases, limits the are LUX similar limits in on sensitivity for the vector and axial-vector 4.1 Limits from currentWe first searches present our 90%for exclusion the limits MSDM from models the defined in 8with TeV section mono-jet the and LUX LUX result in 2013(right the searches panel) MSDM models. The solid, dashed and dot-dashed lines show three different coupling value to better visualiseof the limits. the LHC For all and figuresfigures LUX which have show searches, log a the scales. direct axial-vector comparison Thisdetection figures is sensitivities. have to linear better scales display while the the different features vector of collider and direct larger than its mass this confines the maximal valuecouples of to the all two couplings quarks and JHEP01(2015)037 . ]. + DM med 2 tr med 13 , m Q 1200 ( M . Here 1 1 - 12 = limits fb = 1 and ) so that 2 DM = 1 limit med DM 1 0.5 CL g = = m 1000 , M 19.5 med % 4 DM DM DM 2013 DM Γ g g 0.3 g 90 g − . = = = : q q q D LHC8 LUX g g g 4 = 2 800 2 tr med = q Q M q 1) case is enhanced GeV g ( @ vector g , q / 3 . 600 as discussed in [ . The limits on med 2 DM Axial M g 2 q med med g 400 ) = (0 M the width of the mediator Γ DM , g 200 and at large values of

med D @ g 700 GeV is the s-channel momentum M DM 0 ' . However, unlike for direct detection, 0 m tr 800 600 400 200

2 DM

1000

Q DM g m GeV 2 q is smallest for this case. This enhancement 5) respectively. While the LHC limits are similar g . 0 5 , med – 13 – 5 . 10 in the axial-vector case compared to the vector case . Although this approximation ignores the PDFs, we 1) mono-jet limit is closer to the 4 4 , / med 3 1 10 1) and (0 . − med , ). The axial-vector mediator is more strongly phase-space M 3 Γ 5 limit as in the case of the direct detection limits. . D . This implies that the ( . 2.7 respectively, where plane for the vector (left panel) and axial-vector (right panel) medi- 3 2 DM 2 DM ) = (0 / GeV = 0 g 1 g @ 1 10 3 1), (0 - q ) = , med g fb + ) to ( DM limits DM DM 0.5 1 ) we see that at large values of med M √ 2 q g 2 DM g = = , g g , M 2.4 19.5 CL q 2 vs ∝ DM DM m 2.7 2013 g ) = (1 = g 0.3 g % 4 10 = = = q q q q 90 − g DM DM LHC8 LUX g g g : med 2 tr 5 limits at small ) to ( , g m . q

M Q

g 1 D @ ]. It should be noted that these phase space factors also appear in the width 2.4 Vector . Note that these phase-space suppression factors also account for the diﬀerence = 0 10 18 . The 90% CL limits from current mono-jet (blue lines) and direct detection (red lines) 5 3 2 1 4 DM ) and (

10 10 10 10

DM Second, consider the collider limits for fixed values of The behaviour of the collider limits is more complex and can be understood as follows. GeV m DM 2 = m q between the vector and axial-vector EFT limits in the left panel of figure transfer [ calculation cf. eqs. ( suppressed, which accounts forg the greater suppressionin between figure the are constrained by theproduced energy in of the the finalsection colliding for state. vector partons and axial-vector since The mediators two are2 phase-space typically DM of suppression the particles form factors must that be enter the cross- From eqs. ( is proportional to 18 with respect to theexplains other why cases the because ( Γ rather than the we again expect thewe cross-section must to also take scale into as account theIn effect this of case the mediator the width partonic Γ the cross-section limit scales approximately on as find numerically that it gives a good rule of thumb for the scaling at large values of in both panels, thethe LUX vector limits case are has significantly log more scales constraining for for both vector mediators. axes while Note the that axial-vector case has linear scales. First, consider the collider limits for fixed values of Figure 5 searches in the ators. The region tolines are the for left ( of the various curves is excluded. The solid, dashed and dot-dashed JHEP01(2015)037 med 1.4 . M 4 for the 2 1.2 = 100 GeV . The solid, DM limits 6 1.0 m = 100 GeV and CL % DM DM 0.8 90 1 = 10 GeV) and both g - : , m q fb GeV GeV DM g GeV DM g 0.6 = 19.5 q m 10 100 200 2013 g = = = 100 and 200 GeV. We again : -axis has a log (linear) scale in DM DM DM , 0.4 100 and 200 GeV respectively. LHC8 LUX m m m , med vector = 400 GeV). For values of = 10 GeV is solid, M

= 10 0.2

rise in proportion to the coupling

D @ = 10 DM / plane, shown in ﬁgure Axial E DM m med 0.0 0 . The left and right panels show the limits m DM DM M 800 600 400 200

can again be understood by the diﬀerent

1400 1200 1000 DM

med , g GeV M g q (where g = med 2 T q vs M g / – 14 – E 1 - 1.4 + fb GeV GeV med GeV 2 for light mediators (when M 19.5 2 DM 10 100 200 1.2 . 2013 = = = 0 m DM DM DM 4 ' LHC8 LUX m m m ). In comparison to the collider limits where the limits are 1.0 & DM limits 3.10 g DM 2 0.8 med , the direct detection limit is strongest at CL g = in this figure and the region to the right of the lines is excluded. , M % q q DM g g 90 ) plane; we have fixed 0.6 DM : m ) and ( g DM DM = 200 GeV is dot-dashed. Note that the g g = 10 GeV. This can be easily understood with reference to figure 3.8 = = 0.4 q q = DM g g DM : q m again demonstrates the good complementarity between the mono-jet and g

0.2 D @ 6 vs ( Vector . The 90% CL limits from the LHC mono-jet (blue lines) and LUX (red lines) searches in 2 3 4 0.0 med

10 10 10

med Figure The direct detection limit curves instead show a rather simple behaviour as there are In this plane the mono-jet limits are similar for axial-vector and vector mediators: Further insights into the dependence on the chosen coupling scenarios can be gained GeV M M the MSDM parameter space. The direct detection experiments are better at probing small strength cf. eqs. ( stronger for smaller weakest for direct detection searches for axial-vector mediators since they probe different regions in there is more of anote difference that between this the behaviour is limitssame also at reason. found in the EFT limits in the leftno panel of resonance figure effects in this case. The limits on show a characteristic turning pointresonance owing occurs to the when resonance ofbelow the this, s-channel the mediator. limits The an on the off-shell couplings mediator. becomevector weaker limits The because at small the large production differencephase-space couplings is in suppression and through behaviour large factors. between The the axial-vector vector phase-space and suppression axial- is stronger so by looking at thedashed projection and in dot-dashed the lines showWe the have limits fixed for both exclude down to excluded. We show threeis different dashed dark and matter masses: the left (right) panel. Figure 6 the for vector and axial-vector mediators respectively. The region to the right of the various curves is JHEP01(2015)037 2 DM DM and g g 2 q 1.4 g med and M q 1.2 g 1.0 ) plane. The solid DM 1 0.8 g - , GeV DM DM fb GeV q g g g = q 0.6 = g 1000 500 19.5 limits : = = 2013 . As discussed previously, q g med med CL 5 . 0.4 LHC8 LUX M M % vector = 1000 GeV is dashed. Note that vs ( 90 med .

0.2 D @ M Axial med DM med plane, where we ﬁx both M ∝ m q M 0.0 0 g region. The LUX and LHC limits show

DM 300 200 100 600 500 400

DM GeV m g vs q DM g ). Therefore in the event of a DM discovery m √ DM g = 500 and 1000 GeV respectively. The region to – 15 – med 1 M - GeV 1.00 med fb GeV DM g M = 500 1000 19.5 limits q = = 2013 0.50 g : CL med med = 500 GeV is solid and LHC8 LUX M M % 90 Vector 0.20 med DM the LUX limit on g M , ) plane for the vector (left) and axial-vector (right) mediators. We have q ). However, the mono-jet search is able to break this degeneracy 0.10 g DM at large values of DM m g 3.10 = 2 DM 0.05 g q shows that the direct detection limits are fully symmetric in this plane. g we compare the two searches in the + . The parameter space to the right of the various curves is excluded. We show two 8

2 q

) and ( vs ( D @ g 0.02 DM g 18 3.8 . The 90% CL limits from mono-jet (blue lines) and direct detection (red lines) searches -axis scales are diﬀerent for each panel. DM = 1 2 4 3 ∝ 0.01 m q

, which are not yet accessible to the collider searches as the mediator is very oﬀ-shell,

. Figure g

10 10 10 10

DM Finally, we consider the limits in the In figure GeV m m med med DM because it is also(Γ sensitive to the mediatorat width, colliders which and is direct notdijet detection, symmetric or the in jets mono-jet plus analysis,the MET or coupling searches, other structure. could collider add searches important like information the in order to disentangle for a given value of m This is because thecf. direct eqs. detection ( cross-section is sensitive only to the product is similar to thatlimit shown for vector already. mediators, The exceptgood in LUX complementarity the in limit low the is axial-vectorspace. case significantly as stronger The they than probe scalings different theand of regions LHC phase-space the of parameter scalings collider discussed limits in can connection be with understood figure with reference to the width while the LHC is a better probe at larger values of and dashed lines show thethe limits right for of the curves is excluded in both panels. The behaviour of the limits in this figure different mediator masses: the M Figure 7 in the fixed JHEP01(2015)037 1) , 3 . 1.5 10 GeV 5 GeV is GeV . 1), (0 GeV GeV , ' ], CRESST- 1000 500 800 DM = = = 107 limits DM m – 1.0 )= (1 vector med med med m CL M M M , , , q 1 104 % DM - g Axial 500) GeV is dashed and fb 90 , g GeV GeV GeV , q g 19.5 100 200 200 2013 = = = 0.5 plane (right panel). In the DM DM DM LHC8 LUX m m m = 1 TeV as this approximates q g med vs ] for a recent review), and from a M 103 . DM 0.0 g

] reported signal-like excesses in recent

1.0 0.5 0.0 1.5

DM g 3.3 . Further details about the SuperCDMS 110 ] for additional non-DM explanations of the 1000) GeV is solid, (200 , DM m 117 – 16 – – GeV 1.00 GeV GeV ): (100 115 800 1000 500 med = = = 0.50 region of the vector mediator parameter space. This 5 and 6 GeV. We ﬁx med med med . ,M M M M ] and [ , , , 1 DM - DM = 3 fb 114 m 0.20 GeV GeV GeV m limits – q DM g 19.5 100 200 200 CL 2013 = = = 111 ] and DAMA/LIBRA [ m plane (left panel) and the 0.10 % DM DM DM 90 LHC8 LUX m m m 109 : med 0.05 M Vector we show the limits from the LHC mono-jet, SuperCDMS and LUX searches vs 9 0.02 5). SuperCDMS and LUX exclude the region above the green and red lines, . plane for a vector (left panel) and axial-vector (right panel) mediator. The parameter 0 DM . The current LHC mono-jet (blue lines) and LUX (red lines) 90% CL limits in the , q g 5 m ], CDMS-Si [ . 0.01 800) GeV is dot-dashed. Note that the left (right) panel has log (linear) axes.

In ﬁgure 0.02 0.01 0.20 0.10 0.05 1.00 0.50 ,

DM 108 g DM in the left panel we showand again (0 the three differentwhile coupling the scenarios: LHC ( limitswe exclude show the the limits region for to the left of the blue lines. In the right panel CoGeNT, CRESST-II and DAMA/LIBRALUX excesses. result with the In recentdetection this result experiments section from to we SuperCDMS complement as lowerresult it and the values how extends of it the is sensitivity used of are direct provided in section also an interestingpredicted region in both many from modelsphenomenological of a perspective, asymmetric theoretical since DM it perspective, (seeII[ is [ since the region whereyears. CoGeNT However, in [ 2013 boththese LUX and signals. SuperCDMS See reported also results which [ naively exclude We now focusis on of the particular low interestbecause as the momentum direct transfer detectionexperimental becomes thresholds. searches small lose This and sensitivity isto the not for nuclear understand an recoil how issue energy for collider falls collider searches below searches can and help so it to is constrain interesting this parameter space. It is matter and mediator masses(200 ( 4.2 Low dark matter mass region Figure 8 g space above and to the right of the various lines is excluded. We show three different sets of dark JHEP01(2015)037 1) , med 3 . 1.4 M vs 1.2 GeV GeV GeV GeV 6 6 6 DM = = 3.5 & m = DM DM 1.0 3.5 DM m m = : : 1) is solid, (0 m limits , : DM GeV q 0.8 m 2013 CL : g = 1 TeV and show two 1 % - 1000 ) = (1 fb LUX 90 = 0.6 : med SuperCDMS = 6 GeV. In the right panel, DM med SuperCDMS 19.5 M M , g ) but a lower mediator mass q DM 0.4 Vector g 5 m LHC8 = 1). This is in contrast to LUX 0.2 values while there is no LUX limit for DM 0.0 plane we fix g DM

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

m 5 GeV and DM g . = DM q g - g = 3 ]). q g – 17 – DM 118 2000 m 1 1 1 - limits = = region. The left and right panels show the 0.5 fb = 2013 DM DM CL g g DM Vector 5 GeV, so mono-jet searches may have an important role = , DM % g 1500 q 19.5 LUX = g m q 0.3 ' 90 D 1100 GeV (for g SuperCDMS = q g LHC8 ' region. This mass region is highly motivated in asymmetric DM GeV DM @ m 1000 DM med , the LUX and SuperCDMS limits drop oﬀ rapidly. These examples med M m M 5) is dot-dashed. In the DM . 0 m , . The LHC bounds are only limited by on-shell mediator production and 5 . plane we show three diﬀerent set of couplings: ( 500 planes for a vector mediator. In the left panel, the region to the left and above the DM

m DM g D @ m 5 GeV. - vs . The 90% CL limits from the LHC mono-jet (blue lines), LUX (red lines) and SuperCDMS . 0 1 med = 3 DM

0.1

The left panel demonstrates that in the region of interest the LHC limits are inde-

g DM M GeV m DM 4.3 Projection forIn future this searches section wethe provide extrapolations LHC of and how directand the detection direct limits search detection and avenues communities complementarity will havethe between plans continue potential for to to mid- develop. significantly and increase long-term Both the projects the sensitivity that for collider possess DM searches. demonstrate that direct detection andmediators collider in limits the have good low complementarity formodels, vector where typically to play in testing these models (see e.g. [ pendent of currently extend to and SuperCDMS, whosetively. sensitivity This drops is off alsoof rapidly demonstrated the in below choices the for 6 GeV right panel. and 3.5 While GeV the respec- LHC limit is independent m the current sensitivity ofwould the not mono-jet significantly searches change (see ouris discussion. figure excluded. The region to the right of the various lines and lines is excluded.the In the right panel,is dashed the and region to (0 different the choices of right the andthe dark above matter mono-jet the mass: limit lines is is identical excluded. for In the two different Figure 9 (green lines) searches in the low JHEP01(2015)037 ] ] 119 123 6000 1 1 1 1 yr - - - - fb fb fb fb 2013 ton 30 300 10 19.5 3000 LUX D background LZ ] tool. Ref. [ n LHC13 LHC8 4000 LHC14 GeV LHC14 @ 123 med % M 1 90 ] should achieve a similar = 1). The region to the left of , DM vector limits 2000 g 124 = q CL g

Axial

) = (1 Projected

D @ DM , g 0 q 0 g 500

2000 1500 1000

DM m GeV plane. The left and right panels show the limits med – 18 – 5 M 10 . This is the expected reach of a high-luminosity vs 1 − DM 4 . This provides an estimate of the ultimate reach of 1 m 10 . This gauges the reach for the ﬁrst year of LHC running − D 1 − ]. The successor to XENON1T [ 3 GeV @ limits 96 10 1 CL = med % M DM 2 g ] studies and form the basis of the Collider Reach [ 90 = Vector . These limits are scaled to the diﬀerent future scenarios assuming that 10 q g 4 122 – 1

Projected 120 D @ 10 . The blue and red lines show the current and projected 90% CL limits from the LHC 2 1 4 3

sensitivity. LZ with 10 ton yearthe exposure. LZ This experiment is our [ estimated limit for the lifetime exposure of the LHC. HL-LHC 14 TeV andupgrade 3000 of fb the LHC. LHC 13 TeV and 30in fb 2015. LHC 14 TeV and 300 fb

10 10 10 10

DM For the direct detection experiments we show two different scenarios: For the LHC we provide projected limits for: GeV m • • • • the searches is supportedforward by this the assumption ATLAS as and the CMS main upgrade upgrade programmes, goal. which both put the underlying performances ofsuppression remains the unchanged. search These inand assumptions ECFA were terms [ also of used signal inalso the efficiency shows Snowmass the and [ good background tion. agreement between Furthermore, the using underlying this assumption extrapolation of and maintaining using the a present full performance simula- of The basis for thesesented extrapolations in are section the 8 TeV limits of the CMS mono-jet search pre- the various curves isgreen lines excluded. shows the The directWhile detection plot discovery LUX reach legend after has is accounting bettervector for the the mediators, sensitivity same neutrino the than background. for opposite mono-jethas both is log searches panels. true (linear) and for axes. approaches The axial-vector the mediators. short-dashed neutrino Note limit that for the left (right) panel Figure 10 mono-jet and LUX searchesfor in the vector and axial-vector mediators respectively for ( JHEP01(2015)037 (5.2) (5.1) 8 TeV for . 1 TeV and 1 . ' ] that the EFT DM 12 med m M . where the collider limit is 3 1). We see that the collider DM χ , , 5 m γ as in practice, they apply only to µ χ µ ¯ χγ ) = (1 q ¯ χγ 5 DM γ q µ µ , g q ¯ ¯ qγ qγ g 1). For larger couplings the collider can even , DM DM 2 2 med med g g – 19 – cum grano salis q q M M g g ) = (1 q q X X DM up to 2 TeV, thus complementing the collider searches by ⊃ ⊃ , g q g DM eff axial m eff vector L L parameter space, which in turn will increase the discovery potential. ]. DM 91 m up to 1 TeV. However, except at very low shows our estimates of future limits on the vector mediator (left panel) DM 10 m 350 GeV, while the ultimate reach of the LHC is expected to be around 3 TeV for up to 750 GeV. For the HL-LHC the mono-jet limit are projected to extend out to ≈ background [ The xenon discovery reach when accounting for the coherent neutrino scattering When the mediator mass is sufficiently heavy to be safely integrated out, the effective For the axial-vector mediator, the mono-jet reach is similar to the vector case. How- Figure • DM DM higher dimension operators from our vector and axial-vector MSDM models are approach. This quantitatively demonstrates thatlead a to naive application incorrect of conclusions the aboutof EFT the a limits sensitivity can well-defined of model mono-jetthe for searches underlying which and limits the is in model-independent an a EFT example more-complete limits theory. poorly approximate mediator mass of the fulllimits theory. for collider We searches have should argued be ina taken our limited previous set paper of theories. [ is important However, as to they explore are thewe widely failings directly used of compare our in the MSDM the EFT limits theoretical framework with in community those it derived more from detail. the model-independent In EFT the following, 5 Comparing EFT andThus MSDM far limits we have presentedthe results only results in from our thesesuppression MSDM models. scale simplified Λ. In models this withare When section model those we valid, independent, contrast derived the where from advantage the of suppression the scale the limit is EFT on simply approach related the is to EFT the that couplings the and limits couplings we have made here:probe ( parameter space beyond themediator xenon masses discovery of reach. 2 TeV for However, LZprobing will the be large sensitive to mediator. The LZ sensitivityexperiments even determined approaches by the the ultimate neutrino background. sensitivity of direct detection ever, in this casenearly the extends mono-jet to the reach xenon extends discovery beyond reach from the the LZ neutrino background limit for for the choice of LHC in 2015, we expectm the reach of them mono-jet search to go5 TeV up for to stronger, the LZ limit will be stronger than even the high-luminosity LHC limit for a vector These limits are based on the calculations described inand section axial-vector (right panel)limits mediators improve for for each ( of the scenarios we consider. For the first year of operation of the JHEP01(2015)037 . DM 1.4 m 2 GeV 1.00 GeV > limits MSDM EFT we show 1.2 : : 200 2013 500 CL = limits = 0.50 med 11 MSDM EFT % DM : : LHC8 LHC8 LUX 2013 med M CL 1.0 m 90 M , : % , LHC8 LHC8 LUX DM 90 0.20 ), we observe that g DM : 0.8 = GeV q g q Vector g , 3.3 g q . In figure 200 0.10 g Vector = 0.6 DM DM m m 0.05 ) and ( 0.4 3.2

and the CMS 90% CL limits on Λ, 0.2 D @ 0.02 DM g 4 3 2 0.0 0.01 q

g 10 10 10

1.00 0.50 0.20 0.10 0.05 0.02 0.01 med

GeV M DM g √ / as a function of med 2 – 20 –

DM 1200 1.4 1

2 =

DM g med

1.2

MSDM EFT = M 1000 holds. Therefore, the EFT limits can be applied to the : : q 2013 limits g : CL 1.0 D LHC8 LHC8 LUX DM 800 % g q vector DM 90 g GeV @ 0.8 g limits GeV , √ q 600 / is shown in the upper left panel. Even in the valid region, the EFT limit Axial CL g med 500 % = 0.6 M MSDM EFT med : : DM 2013 90 med : 400 M m M 0.4 , LHC8 LHC8 LUX = 2 DM vector g

200

0.2 D q @

D @ med g . Comparisons between the 90% CL mono-jet limit in our MSDM models (blue solid Axial M 0 0.0 0 0

100 500 400 300 200 200 600 800 600 400

DM GeV 1000 m

DM GeV m where the sum isthe over relation all Λ quarks. = MSDM Comparing models by with using eqs. the relationwhich ( Λ are = shown ina the left comparison panel of of the figure current MSDM mono-jet limit (blue solid line) with the naive limit This may lead todetection a searches. misleading A conclusion simple regardingThe criterion the line for relative the sensitivity validity of offails the mono-jet to EFT and accurately approach direct reproduce is the that MSDM limit for these parameters. Figure 11 line) and the EFTThe framework (green red dashed) dot-dashed in linevector the shows two-dimensional mediators the planes respectively. LUX consideredthe limit. previously. The EFT The framework MSDM left isthe and and valid. resonant right EFT panels enhancement) limits The are or EFT should for overestimate limits agree axial-vector it both and in (by underestimate the missing the off-shell domain MSDM production where limit of (by the missing mediator). JHEP01(2015)037 . DM g and is stronger q = 500 GeV g plane for an the EFT limit DM med , g med M while the MSDM q DM g M ) plane for an axial- m DM vs g DM 100 MeV. the mediator is off-shell g & DM = and DM q m q g m med g ) plane. We see that the EFT ]. M 12 vs ( DM g = DM = 1 TeV. This overstating of the limit q m g a comparison of the MSDM and EFT DM m vs ( 12 as the EFT framework does not account for med – 21 – med M M = 1. We observe that at low limit is kinematically suppressed because of off-shell plane. We see again how the EFT framework misses q shows the limits in the g DM DM g m vs 11 = q DM g = 500 GeV. In this plane, it is particularly clear that naively demonstrate, the two searches probe different orthogonal and g 300 GeV while a naive application of the EFT limit gives the 8 & med to has sometimes led to the wrong conclusion that for spin-dependent . The EFT limit is naive because we assume that it applies to the M = 200 GeV in the 5 8 DM , as discussed in our previous paper [ DM m to DM m med 5 while the higher m M DM & m = 200 GeV in the med DM m For completeness, we also show in figure The final panel in this figure is the top-right panel, which shows the limits for a vector The bottom-right panel shows the limits for a vector mediator when The bottom-left panel shows the limits in the The top-left panel of figure The first general observation that we can make is that the EFT limits consistently give the off-shell mediator production.asymptotes to This the panel MSDM limit. iswhere Γ This also occurs the at only large case couplings and where large the mediatorlimits EFT masses in limit a format which may be more familiar. Here we map the MSDM limits for the limit is asymmetric because the mediatorTherefore, width the breaks the collider degeneracy possesses between not sensitivity resolved to in the the underlying EFT coupling approach. structure, which is mediator when limit again overstates the limit at low at smaller mediator production. and important physical effects: the EFT limit is symmetric in complementary regions of the axial-vector parameter space. vector mediator with applying the EFT limit obliteratesmono-jet the results. complementarity The between MSDM the model direct reveals detection that and the collider limit on MSDM model for false impression that the limitat extends high beyond values of interactions, the mono-jet searchesright outperform panels direct of detection figures searches. However as the axial-vector mediator when is too weak.enhancement This from is on-shell because mediator theand production. EFT the At framework EFT larger fails framework to dramatically take into overstates account the the limit. resonant No limit is obtained in the a poor approximation todo the the EFT underlying limits limits excludediffers obtained different dramatically parameter in from values the those but MSDMdoes also of the model. the not shape MSDM account of Not limits. for theresonant only This limit enhancement the curve is or mediator off-shell because propagator, production the of EFT and the framework thus mediator. does not include the effects of shown in figures full parameter space of thelimit MSDM as model. the red For dot-dashed comparison,(vector) line. we mediator. also The include We left again the (right)the LUX note panels direct 2013 show that detection the the experiments limits EFT in for this and an paper, MSDM axial-vector as provide long identical as results for obtained in the EFT framework (green dashed line) for each of the four parameter planes JHEP01(2015)037 0 SI 3 σ 10 1 0.5 = = DM DM g g = = q q g g , , 2 300 GeV. This D 10 . MSDM MSDM EFT : : : GeV 2013 @ 5 case it is closer to ). The left and right . , the MSDM mono- DM DM LHC8 LHC8 LHC8 LUX m plane used by the direct m L = 0 4.1 3.10 10 5) and overestimates the . limits DM DM vector g m CL 300 GeV. The EFT limit gives a = 0 dependent = % ) and ( 5 (short dashed blue line) onto . & Axial q

g Spin 3.8 D @ L H DM g 1 = 1 case, the ratio of the mediator = 0 DM 38 39 40 41 42 43 m = ------DM DM

q 10 10 10 10 10 10

SD g - s cm neutron DM

2 0 = = q q 3 g g – 22 – 10 L through eqs. ( 5 1 Vector = 0.5 H EFT = : 2013 DM 300 GeV (for g limits DM 2 . For the = g q LUX = g LHC8 . q CL D 10 , g , % EFT σ 300 GeV. As was discussed in section 90 GeV DM @ ) independent MSDM : m MSDM & : DM med Spin m LHC8 LHC8 10 DM /M m 300 GeV and overestimates them for = 1 (solid blue line) and med ]. The MSDM and EFT scattering cross-sections are approximately related . (Γ 12 DM

≈ DM D @ . A comparison between the 90% CL mono-jet limit in our MSDM models (blue lines) relative to the EFT limit can be estimated using the ‘rules of thumb’ in ap- 1 m = 42 44 46 38 40 36 q ------0 SD g

10 10 10 10 10 10 MSDM

The size of the enhancement in the 90% CL limit of scattering cross-sections We ﬁnd that the EFT limit underestimates the MSDM collider limit by almost an

cm σ

2 0 pendix A of [ by width to the mediator1/8. mass is Accordingly about we 1/2, expectlimit while by for the a the MSDM factor 2 direct and detection 8 limit respectively in to the be regime where lower the than resonant the enhancement occurs EFT jet production cross-section isenhancement is resonantly not enhanced accounted in foris the in more the region constraining EFT than limits, the which EFT explains limit why in the this MSDM limit massand range. respectively. The red dot-dashed linesshows show the the EFT LUX limits. limits and the long dashed green line order of magnitudeMSDM for limit for cases the usual cross-section vstranslation of DM the mass MSDM planepassing limits the used mono-jet to to limits the present frompanels cross-section figure show direct the vs detection SI DM and limits. SD mass cross-sections plane appropriate The is for vector performed and axial-vector by mediators the current LUX limit.framework is The MSDM valid. andlimits For EFT for these limits choices shouldmisleading agree of representation in parameters, of the the the relative domain EFT sensitivity where of limit the mono-jet underestimates EFT and the direct detection MSDM searches. Figure 12 and the EFTdetection framework community. (green The dashed) leftappropriate in and for the right vector cross-section panels and show vs axial-vector the limits mediators on respectively. the SI The and red SD dot-dashed cross-sections line shows JHEP01(2015)037 . ]). 7 12 and . We have 11 DM ) (see e.g. [ underestimates m π 2 (2 / > med ), but this is ignored to demonstrate how M DM med DM ), we find that the EFT 11 g M > m DM m and that this relation is a good q ), meaning that a particle-like g 12 med > M are the result of a naive application of med 12 – 23 – and = 100 GeV the EFT limit on 11 DM m in the upper left panel of figure DM 300 GeV for both the vector and axial-vector cases. . Of course, in reality the EFT approach is only expected to m 2 . = 2 DM m line is valid. While we see that this criterion excludes the EFT limit med ], the limits from the EFT framework for collider searches apply only M 12 DM m = 2 med In this paper we propose a Minimal Simplified Dark Matter (MSDM) framework, In summary, important physical effects are missed in the EFT framework because The EFT limits shown in figures M are very large. Inoften particular, larger in than the the regioninterpretation mass where of the of the EFT mediator the is is mediator difficult valid, (Γ the (in the mediator context widthwhich of is is a a single more mediator). robust and accurate approach for interpreting and characterising collider In many previous studies,interpret the and effective characterise field studies theory of (EFT)framework dark is framework matter very has powerful (DM) been in productionprevious utilised its at to domain paper the of [ LHC. validity. The Unfortunately,to as EFT a we discussed limited in class our of theories in which the mediator mass is very heavy and the couplings to misleading conclusions aboutframework the is real unsuitable sensitivity fordetection of searches. quantifying collider the searches. true Thus, complementarity the of EFT collider and6 direct Conclusions because the production can beto resonantly enhanced. the underlying Furthermore, the coupling LHCthe has structure mediator sensitivity width because (which breaks thebecause the production degeneracy of between cross-section the is oversimplificationMSDM sensitive of and to EFT the limits EFT highlights framework. again how The the direct EFT comparison limits, of when the applied naively, lead the EFT limit is valid,does the not limits include are the not mediator model width, independent which strongly because affects thethe the EFT full mono-jet framework effect limits. ofin the a full s-channel model mediator may propagator be is substantially ignored. stronger than For those instance, found from the the limits EFT limit on Λ the which differs most from thelimit underlying in MSDM limit the (at valid large regionparameter space. still fails For instance, to at accuratelythe MSDM reproduce limit the by MSDM 200 GeV. limit This in highlights this a part general problem of that even in regions where criterion is to assume thatThis the is EFT a limits very are weak valid criterion onlyWhen and when does applying Λ not restrict the any of EFTcriterion the limits for EFT limits the to in validity figures a ofincluded the more-complete the EFT model, line approach a isthis to more demand restricts reasonable that the minimum domain of the EFT limit. In this case, only the dashed green line below approximation when the limits on Λbe from figure valid in ato limited designate region the of region parameter where space the and EFT various description criteria is have not been valid. proposed Perhaps the most naive i.e. at low to moderate DM masses. We see from figure JHEP01(2015)037 ]), to 127 – 125 ], we find that searches. With 12 T / E 5 GeV, where direct . . DM DM m ). The EFT limits fail to give m 12 and 11 – 24 – , and from LZ after a 10 ton year exposure (see 1 , which are the DM and mediator masses, and the we introduce MSDM models for vector and axial- q − g 2 ). For instance, the mono-jet search probes larger values and 8 to ). The only exception is when ), we map out the four-dimensional parameter space of our DM 5 8 4 , g and 3000 fb ). In contrast, the LHC and LUX limits on axial-vector mediators to 9 1 to med − 5 2 ,M DM , 300 fb m 1 ). The advantage of the MSDM models is that the full event kinematics are − 1 while direct detection searches probe larger values of ). It is interesting to note that the mono-jet reach in the axial-vector case ap- 10 med The MSDM framework is easily extendable to include scalar and pseudo-scalar inter- We further explore the validity of the EFT framework by comparing the limits from We also provide estimates for the projected limits from the LHC for 14 TeV operation After validating our implementation of the CMS mono-jet and LUX direct detection M these additions it shouldto be the possible approaches to alreadyallow perform a performed more a for quantitative definition global supersymmetry ofsearches. fit (see the complementarity to for This of a example collider will andsignal MSDM [ become direct either model, detection especially at similar important the LHC in or case at of a a direct detection discovery experiment of or a ideally, dark at both. matter mediator mass and largeconclusions couplings. regarding the complementarity The of EFT collider limits and direct may detection also searches. easily lead toactions, misleading Majorana fermionsearches and and scalar DM additional particles, collider as searches, well such as as limits di-jet from and indirect jets DM + our MSDM models with thea EFT good limits (see approximation figures to thealmost MSDM all limits of for both the vector parameterthe and values EFT axial-vector considered. limits mediators Confirming over give the a results good in representation [ of the MSDM limits only in the case of heavy proaches the neutrino noise, which,an with current irreducible technology background and for calculations,combine is direct both considered detection search experiments. approachesin in It the order therefore future. to seems have critical the to best possible coverage for discovery of after 30 fb figure left panels in figures detection experiments lose sensitivity.constraining (see In figure this DMgenerally show mass full range complementarity, probing the orthogonal(see LHC directions right limits in panels the are in parameter figures more space captured and the dependence on all couplings and masses can be systematically studied. searches (see figures MSDM models by showingthat projections generally in the two LUX parameters. limits For are vector much mediators, more we constraining find than the mono-jet limits (see vector mediators. Inparameters: its most minimal variantmediator our couplings to models DM are andcharacterise quarks characterised respectively. by DM These four production parameters free are(see at sufficient to figure colliders fully and scattering at direct detection experiments searches of dark matter. In section JHEP01(2015)037 B 04 = 8 ]. s √ (2010) ]. JHEP Phys. Lett. , SPIRE ]. , IN D 82 ][ SPIRE ]. IN Maverick dark SPIRE ]. ][ IN collisions at ]. ][ SPIRE pp IN SPIRE LHC bounds on interactions TeV with the ATLAS Phys. Rev. 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