Interplay and Characterization of Dark Matter Searches at Colliders and in Direct Detection Experiments
Sarah A. Malik, Christopher McCabe, Henrique Araujo, Alexander Belyaev, Celine Boehm, Jim Brooke, Oliver Buchmueller, Gavin Davies, Albert De Roeck, Kees de Vries, Matthew J. Dolan, John Ellis, Malcolm Fairbairn, Henning Flaecher, Loukas Gouskos, Valentin V. Khoze, Greg Landsberg, Dave Newbold, Michele Papucci, Timothy Sumner, Marc Thomas, Steven Worm
IInterplay and Characterization of Dark MatterSearches at Colliders and in Direct DetectionExperiments
Sarah A. Malik, a Christopher McCabe, b,c
Henrique Araujo, a Alexander Belyaev, d,e
C´eline Bœhm, b Jim Brooke, f Oliver Buchmueller, a Gavin Davies, a Albert De Roeck, g,h
Kees de Vries, a Matthew J. Dolan, i John Ellis, g,j
Malcolm Fairbairn, j Henning Flaecher, f Loukas Gouskos, k Valentin V. Khoze, b Greg Landsberg, l Dave Newbold, f Michele Papucci, m Timothy Sumner, a Marc Thomas d,e and Steven Worm e a High Energy Physics Group, Blackett Laboratory, Imperial College, Prince Consort Road, London,SW7 2AZ, UK b Institute for Particle Physics Phenomenology, Durham University, Durham, DH1 3LE, UK c GRAPPA, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands d School of Physics and Astronomy, University of Southampton, Highfield, Southampton, SO171BJ, UK e Particle Physics Department, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, UK f HH Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK g Physics Department, CERN, CH1211 Gen`eve 23, Switzerland h Antwerp University, B2610 Wilrijk, Belgium i Theory Group, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA j Theoretical Particle Physics and Cosmology Group, Department of Physics, King’s College Lon-don, London, WC2R 2LS, UK k University of California, Santa Barbara, Department of Physics Broida Hall, Bldg. 572, SantaBarbara, CA 93106-9530, USA l Physics Department, Brown University, Providence, Rhode Island 02912, USA m Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Abstract:
In this White Paper we present and discuss a concrete proposal for the consis-tent interpretation of Dark Matter searches at colliders and in direct detection experiments.Based on a specific implementation of simplified models of vector and axial-vector mediatorexchanges, this proposal demonstrates how the two search strategies can be compared onan equal footing.
White Paper from the Brainstorming Workshop held at Imperial College London on May29th, 2014. A link to the Workshop’s agenda is given in [1].
IPPP/14/83, DCPT/14/166, KCL-PH-TH/2014-37, LCTS/2014-36, CERN-PH-TH/2014-180 a r X i v : . [ h e p - e x ] O c t ontents Since the start-up of the LHC in 2010, collider searches for Dark Matter (DM) particleproduction, and their comparison with direct detection (DD) scattering experiments suchas XENON100 [2] and LUX [3], have become a focal point for both the experimental andtheoretical particle and astroparticle communities.Collider searches are generally characterized by their use of ‘mono-objects’, such asmono-jets or mono-photons, accompanied by missing transverse energy [4–11]. Until re-cently, these searches were mainly interpreted in the framework of specific models, suchas the ADD [12] or unparticle models [13], or else used an effective field theory (EFT) toallow for the straightforward comparison with the results of DD experiments.However, interpretations within specific models are often too narrow in scope, andseveral independent groups [8, 11, 14–19] have pointed out that the interpretation withinthe EFT framework can lead to the wrong conclusions when comparing collider resultswith the results from DD experiments. As an alternative, a simplified model descriptionof collider and DD searches has been advocated in order to avoid these pitfalls [16, 20–27].The Brainstorming Workshop contributed to the development of a consistent simplifiedframework to interpret these searches, so as to facilitate comparison of the sensitivities ofcollider and DD experiments. This is required in order to establish quantitatively thecomplementarity of these two search approaches, which is critical in our continuing questfor DM. A link to the Brainstorming Workshop’s agenda, which includes links to theindividual talks, is given in [1].In this White Paper, we propose benchmark scenarios in a particular simplified modelframework for DM models and provide examples of plots that will allow for a more mean-ingful comparison of the results from collider and DD experiments. These scenarios aresummarized in Section 4. This proposal should be considered as a first practical step inthe discussion towards a more complete analysis strategy to be developed in the future.– 1 –
Comparison of DM searches
Although the Workshop touched on several interesting aspects related to models of DMand the characterization of DM searches, its main focus was on defining a concrete proposalfor how to go beyond the problematic comparison of DM searches in the EFT framework.Therefore in this document, we focus mainly on the outline of our proposal for comparingcollider and DD searches for DM on an equal footing, so as to better understand and exploittheir complementarity. This is largely based on the results of a recent paper [28] by severalof the Workshop participants, whose work was in part inspired by the Workshop.While the EFT framework is a convenient tool for interpreting DM searches from DDexperiments, recent work by several independent groups [8, 11, 14–19] has highlighted theproblem that the EFT interpretation of collider searches suffers from several significantlimitations, which prevent a comprehensive characterization of these searches. A compar-ison of DM searches at collider and DD experiments using the EFT approach does notprovide an accurate description of the complementarity of the two search strategies.
An alternative to the EFT interpretation is the characterization of DM searches usingsimplified models [29, 30]. Simplified models are widely used to interpret missing-energysearches at colliders in the context of supersymmetry, and have become a successful wayto benchmark and compare the reaches of these collider searches. In contrast to the EFTansatz, simplified models are able to capture properly the relevant kinematic properties ofcollider searches with only a few free parameters.As pointed out in [16, 20–28], simplified models of DM also provide an appropriateframework for comparing and characterizing the results of DM searches at colliders and DDexperiments. This was demonstrated within a framework of Minimal Simplified Dark Mat-ter (MSDM) models with vector and axial-vector mediators exchanged in the s-channel [28].While the collider phenomenology of the vector and axial-vector mediators is similar, at DDexperiments they are very different. These two cases therefore demonstrate how to com-pare DD and collider results on an equal footing for two distinctive scenarios. Althoughthese two mediator cases already cover a significant variety of interesting DM models, aswe discuss below in more detail, it will be important to also consider t-channel exchangesas well as scalar and pseudo-scalar mediators in the future.The MSDM models are constructed using four parameters: the mass of the DM par-ticle, m DM , the mass of the mediator, M med , the coupling of the mediator to the DMparticles, g DM , and the coupling of the mediator to quarks, g q . For the latter, as a sim-plifying assumption, the mediator is assumed to couple to all quark flavours with equalstrength. In this White Paper we assume that the DM particle is a Dirac fermion ( χ ) and– 2 –he new Lagrangian terms for the vector ( Z (cid:48) ) and axial-vector ( Z (cid:48)(cid:48) ) MSDM models are L vector ⊃ M Z (cid:48) µ Z (cid:48) µ − g DM Z (cid:48) µ ¯ χγ µ χ − (cid:88) q g q Z (cid:48) µ ¯ qγ µ q L axial ⊃ M Z (cid:48)(cid:48) µ Z (cid:48)(cid:48) µ − g DM Z (cid:48)(cid:48) µ ¯ χγ µ γ χ − (cid:88) q g q Z (cid:48)(cid:48) µ ¯ qγ µ γ q where the sum extends over all quarks.It is important to emphasize that these four variables represent the minimum set ofparameters necessary for the comparison of collider and DD experiments. Direct detectionexperiments are sensitive only to a specific combination of these parameters that enter thenucleon-DM scattering cross section, namely σ ∼ g g q µ M , where µ is the reduced mass of the nucleon-DM system, which asymptotically becomesconstant for heavy DM particles. In comparison, all four parameters play different andimportant roles in collider searches: • m DM : collider limits depend on m DM , with the sensitivity limited by the availableenergy in the centre-of-mass frame; • M med : the interplay between M med and m DM is very important for sufficiently lightmediators, as for m DM < M med / • g DM , g q : the cross section for DM production in collider experiments is sensitive to theproduct of the two couplings squared, as is the DM-nucleon interaction cross section inDD experiments. However, in addition, collider experiments are also sensitive to thesum of these couplings squared, which determines the width of the mediator (Γ med ).If the latter is too large (Γ med (cid:38) M med ), single-mediator exchange does not provide arealistic description of either DM-nucleon scattering or collider production of a pair ofDM particles — a fact that is often overlooked in the interpretation and comparisonof the searches.To produce the collider limits in MSDM models, we generate events for the DM signalat the LHC using an extension of POWHEG BOX [31–34]. The program generates theprocess of a pair of DM particles produced in association with a parton at next-to-leadingorder (NLO). It can be matched consistently to a parton shower, which as discussed in [31],is of particular importance to simulate accurately the case where jet vetoes are applied inthe analysis. This is the case in the monojet analysis where the third jet in the event isvetoed. In our case, we match to Pythia 8.180 [35, 36] and put through Delphes [37, 38]for the detector simulation.The inclusion of NLO corrections reduces the dependence on the choice of renormali-sation and factorisation scales and thereby the theoretical uncertainty, which will become– 3 –mportant if a small excess is observed. The program has three further advantages. Firstly,it can generate events for both the EFT case and also simplified models. Secondly, in ad-dition to the vector and axial-vector mediators considered here, it can also be used forstudies of scalar mediators. Thirdly, it includes K-factors which are particularly importantin models where the scalar couples to gluons in the s-channel.As demonstrated in [39], the inclusion of higher order corrections can also be advanta-geous in probing the structure of couplings between DM and SM, which can be determinedby looking at the azimuthal difference between two jets in events where the final statecontains two jets together with missing transverse energy. For instance, for loop-mediatedinteractions with gluons where a spin-0 particle is exchanged in the s-channel, the CPnature of the latter can be tested. A comprehensive comparison of the limits from collider and DD searches in all of the four2D projections of the 4-parameter MSDM model is provided in [28]. It shows that, for theexchange of a vector mediator, only for very light DM masses ( (cid:46) σ and σ , respectively. It is thus alsouseful to provide comparisons of the MSDM limits from the mono-jet and DD searches inthe ( σ , m DM ) and ( σ , m DM ) planes. As discussed in Section 5 of our main reference [28],for fixed couplings g q and g DM , collider limits defined in the ( M med , m DM ) plane of theMSDM model can be directly translated into the ( σ , m DM ) planes. Vector and axial-vectormediators lead to spin-independent and spin-dependent interactions in DD experiments,respectively. For DD searches the cross section scales exactly like ( g q g DM ) /M , whilefor collider searches it scales approximately like ( g q g DM ) / ( M Γ med ). For small valuesof the width, as in weakly coupled scenarios, there is a resonant enhancement of the crosssection in the collider case.Figure 1 shows the MSDM limits from the CMS mono-jet search for different couplingscenarios in the ( σ , m DM ) and ( σ , m DM ) planes (left and right, respectively). TheMSDM limits for the axial-vector mediator are displayed in the spin-dependent plane,and the results from the vector mediator study are shown in the spin-independent plane.To assess the dependence of the collider limits on the choice of couplings, four differentcoupling scenarios are shown: g q = g DM = [0.25, 0.5, 1.0, 1.45] (blue lines). The twoextreme scenarios of 0.25 and 1.45 are chosen because they approximate the range overwhich the LHC mono-jet search can place meaningful limits in the MSDM models. For g q = g DM (cid:38) .
45 the width of a vector or axial-vector mediator exchanged in the s-channelbecomes larger than its mass, making a particle physics interpretation of the interaction– 4 – pin dependent H Axial L % CL limits
LHC8: g q = g DM = g q = g DM = g q = g DM = g q = g DM = - - - - - - - m DM @ GeV D s S D H D M - n e u t r o n L @ c m D Spin independent H Vector L % CL limits
LHC8: g q = g DM = g q = g DM = g q = g DM = g q = g DM = - - - - - - m DM @ GeV D s S I @ c m D Figure 1 . A comparison of the current 90% CL LUX and SuperCDMS limits (red and orangelines, respectively), the mono-jet limits in the MSDM models (blue lines) and the limits in the EFTframework (green line) in the cross section vs m DM plane used by the direct detection community.The left and right panels show the limits on the SD and SI cross sections appropriate for axial-vector and vector mediators respectively. For the MSDM models we show scenarios with couplings g q = g DM = 0 . , . , . , . problematic. For g q = g DM (cid:46) .
25 the 8 TeV CMS mono-jet search no longer has sufficientsensitivity to place a significant limit on the parameter space.Figure 1 also shows the limit obtained from an interpretation of the mono-jet search inthe framework of the EFT (green line). The EFT limits should agree with the MSDM limitin the domain where the EFT framework is valid. We see that it is only for the extremecoupling scenario g q = g DM = 1 .
45 that the EFT limit approximates the MSDM limit,and only for DM masses below around 300 GeV. For larger m DM the EFT fails to describeany of the coupling scenarios. For weaker couplings, the MSDM limits get stronger forDM masses below around 50 to 300 GeV, due to the resonant enhancement of the crosssection for a s-channel mediator that was explained above. This effect is absent withinthe EFT framework. The reach in DM mass of the MSDM limits increases with largercouplings. Overall, this comparison of the EFT and MSDM limits demonstrates againthat the EFT framework is unable to capture all of the relevant kinematic properties ofthe collider searches, which is demonstrated by the large disparity between the EFT andMSDM limits. Comparing EFT collider limits with those of DD searches gives a misleadingrepresentation of the relative sensitivity of the two search strategies, especially for weakercoupling scenarios and m DM (cid:38)
300 GeV.Finally Figure 1 also shows the LUX limits for both interactions (red lines) and thespin-independent SuperCDMS limit (orange line). Whilst the comparison of the DD searchresult with the EFT collider limit is biased, a comparison with the MSDM limits from theLHC mono-jet analysis, which properly describes the kinematic properties of the collidersearch, represents a comparison of collider and DD experiments on an equal footing, estab-– 5 –ishing quantitatively the complementarity of the two search strategies. With the exceptionof light DM masses m DM (cid:46) m DM (cid:46)
300 GeV. This is especially true for small couplings where the collider cross sec-tion is further enhanced by the small mediator width. Owing to the kinematic constraint M med ≥ m DM on s-channel mediator production at the collider, DD searches are todaythe only searches providing significant limits for either cross section for m DM (cid:38)
300 GeV.
With the DD experiments and the LHC programme gearing up for major upgrades, we alsolook at their projected sensitivity to DM particles in the future. We explore three scenariosfor the LHC: 30 fb − at 13 TeV to gauge the reach of LHC Run 2, 300 fb − at 13 TeVto provide an estimate of the reach of LHC Run 3, and 3000 fb − at 14 TeV to show theexpected reach of the high-luminosity upgrade of the LHC. For the DD experiments we showthe estimated limit for the lifetime exposure of two liquid xenon experiments: the LUX-ZEPLIN (LZ) experiment [44], with an exposure of 10 tonne years, and DARWIN [46, 47],with an exposure of 200 tonne years. We also show the discovery reach for DD experimentswhen limited by the coherent neutrino scattering background [48].Figures 2 and 3 show for the different coupling scenarios the current and projected90% CL limits for the CMS mono-jet and DD searches in the ( M med , m DM ) plane for thecases of an axial-vector mediator and a vector mediator, respectively. The conclusions arethe same for the projected limits as for the current results. We predict similar comple-mentarity between the collider and DD experiments going forward, with LUX, LZ andDARWIN retaining better sensitivity than the mono-jet LHC search for vector mediatorsfor all but the very low m DM region, whereas for the axial-vector mediator the mono-jetsearch extends the reach of the DD experiments. As expected, the overall largest reach inthe DM parameter space is obtained for the largest coupling scenario g q = g DM = 1 . g q = g DM = 1 .
45, neither collider nor DDsearches approach in any region of the M med - m DM plane the discovery reach. This changesfor the weaker coupling scenarios, where for relatively low m DM the collider limits ap-proach the DD discovery reach for g q = g DM = 1, and even go significantly beyond it for g q = g DM ≤ . σ , m DM ) and ( σ , m DM ) planes. Figure 4shows projected limits in these planes for the high-luminosity-LHC (HL-LHC14) scenarioof 3000 fb − at 14 TeV. Again the four choices of couplings are shown: g q = g DM = 0 . .
45, which approximate the extremes of couplings, and the intermediate couplingscenarios of 1.0 and 0.5. A similar exposure will also be reached by XENONnT [45]. – 6 – ����� �� % ����������� ������ � � = � �� = ���� ���� ���� �� - � ����� �� �� - � ����� ��� �� - � ����� ���� �� - � ��� ������ �� � �������� ��� � �� ν ���������� � ���� ���� ���� ���� ������������������������� � ��� [ ��� ] � � � [ � � � ] ������ �� % ����������� ������ � � = � �� = � ���� ���� �� - � ����� �� �� - � ����� ��� �� - � ����� ���� �� - � ��� ������ �� � �������� ��� � �� ν ���������� � ���� ���� ���� ������������������������ � ��� [ ��� ] � � � [ � � � ] ������ �� % ����������� ������ � � = � �� = ��� ���� ���� �� - � ����� �� �� - � ����� ��� �� - � ����� ���� �� - � ��� ������ �� � �������� ��� � �� ν ���������� � ���� ������������������������ � ��� [ ��� ] � � � [ � � � ] ������ �� % ����������� ������ � � = � �� = ���� ���� ���� �� - � ����� �� �� - � ����� ��� �� - � ����� ���� �� - � ��� ������ �� � �������� ��� � �� ν ���������� � ��� ���� ���� ���� ��������������������� � ��� [ ��� ] � � � [ � � � ] Figure 2 . Projected limits for the CMS mono-jet search (blue lines) and DD searches by LUX(red line), LZ (red dashed line) and DARWIN (purple line) in the ( M med , m DM ) plane for an axial-vector mediator with the coupling scenarios g q = g DM = 0 .
25, 0.5, 1.0, 1.45. For reference, thediscovery reach of DD experiments accounting for the coherent neutrino scattering background isalso displayed (green line). The region to the left of the various curves is excluded at 90% CL. Notethe change in scale in each panel.
Also shown are the projected limits from LZ and DARWIN assuming a 10 and 200 tonneyear exposure respectively, and the projected spin-independent limits from SuperCDMSassuming a run with 108 Ge and 36 Si detectors at SNOLAB [49]. In the case of thespin-independent interactions, the SuperCDMS projection extends the sensitivity of DDexperiments to lower values of m DM , so its inclusion provides a more complete comparisonwith the collider limits. Similar conclusions regarding the comparison between the MSDMand DD limits can be derived from projections in this plane. For spin-independent in-teractions, the MSDM model with a s-channel vector mediator adds additional sensitivity– 7 – ������ �� % ����������� ������ � � = � �� = ���� ���� ���� �� - � ����� �� �� - � ����� ��� �� - � ����� ���� �� - � ��� ������ �� � �������� ��� � �� ν ���������� �� � �� � �� � �� � �� � �� � �� � �� � �� � �� � � ��� [ ��� ] � � � [ � � � ] ������� �� % ����������� ������ � � = � �� = � ���� ���� �� - � ����� �� �� - � ����� ��� �� - � ����� ���� �� - � ��� ������ �� � �������� ��� � �� ν ���������� �� � �� � �� � �� � �� � �� � �� � �� � �� � �� � � ��� [ ��� ] � � � [ � � � ] ������� �� % ����������� ������ � � = � �� = ��� ���� ���� �� - � ����� �� �� - � ����� ��� �� - � ����� ���� �� - � ��� ������ �� � �������� ��� � �� ν ���������� �� � �� � �� � �� � �� � �� � �� � �� � �� � �� � � ��� [ ��� ] � � � [ � � � ] ������� �� % ����������� ������ � � = � �� = ���� ���� ���� �� - � ����� �� �� - � ����� ��� �� - � ����� ���� �� - � ��� ������ �� � �������� ��� � �� ν ���������� �� � �� � �� � �� � �� � �� � �� � �� � �� � �� � � ��� [ ��� ] � � � [ � � � ] Figure 3 . Projected limits for the CMS mono-jet search (blue lines) and DD searches by LUX(red line), LZ (red dashed line) and DARWIN (purple line) in the ( M med , m DM ) plane for a vectormediator with the coupling scenarios g q = g DM = 0 .
25, 0.5, 1.0, 1.45. For reference, the discov-ery reach of DD experiments accounting for the coherent neutrino scattering background is alsodisplayed (green line). The region to the left of the various curves is excluded at 90% CL. only in the very low m DM region, whereas for spin-dependent interactions the axial-vectormediator complements the LZ limits very well for DM masses below a few hundred GeV,and extends sensitivity to the cross section beyond the neutrino limit for DM mass below10 GeV in all coupling scenarios.Both the choices of planes that compare the projected sensitivities of collider and DDexperiments provide accurate comparisons of the two search strategies in the MSDM onan equal footing. Whereas the ( M med , m DM ) plane might be more familiar to the collidercommunity, the ( σ , m DM ) plane is a more traditional way of displaying this comparison– 8 – � � � � � � � ν � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���� ��������� ( ����� ) �� % �� ��������� ������ �� - ������ � � = � �� = ������ - ������ � � = � �� = ����� - ������ � � = � �� = ����� - ������ � � = � �� = ���� � �� �� � �� � �� � �� - �� �� - �� �� - �� �� - �� �� - �� �� - �� �� - �� �� - �� � �� [ ��� ] σ � � � ( � � - � � � � � � � ) [ � � � ] ���� ����������� ( ������ ) �� % �� ��������� ������ � � � � � � � � � � � � � � � � [ � � + � � ] � � � � � � � � ν � � � � � � � � � � � � � � � � � � � � � � �� - ������ � � = � �� = ������ - ������ � � = � �� = ����� - ������ � � = � �� = ����� - ������ � � = � �� = ���� � �� �� � �� � �� � �� - �� �� - �� �� - �� �� - �� �� - �� �� - �� �� - �� �� - �� �� - �� �� - �� � �� [ ��� ] σ � � � [ � � � ] Figure 4 . Projected 90% CL limits for the CMS mono-jet search (blue lines), LZ (red lines) andDARWIN (purple lines) in the cross section vs m DM plane for SI and SD interactions appropriatefor the vector and axial-vector mediators respectively. The collider limits are defined for couplingscenarios with g q = g DM = 0 .
25, 0.5, 1.0, 1.45. For comparison, the discovery reach of DD exper-iments accounting for the neutrino scattering background is also displayed (green lines). For thespin-independent interaction we also show a projection of the SuperCDMS limit (orange line). among the DD community. However, when comparing the two planes care must be takenin the interpretation of the relative sensitivities of the different scenarios. For example,whereas in the ( M med , m DM ) plane the mono-jet limits get stronger with increasing cou-pling, the same results displayed in the ( σ , m DM ) plane show that for DM masses belowa few hundred GeV more parameter space is ruled out for the weaker coupling scenarios.This is explained by the fact that the planes use different observables to benchmark theperformance of the search. In one case the mediator mass M med is the benchmark, whereasin the other case it is the nucleon-WIMP scattering cross section σ . As explained above,the cross section scales as ( g q g DM ) /M for DD experiments, and approximately like( g q g DM ) / ( M Γ med ) for the collider search. It is important to take these relations intoaccount when translating between the two planes. For the example mentioned above, thisimplies that, whereas the collider limit on M med gets stronger with increasing coupling,when taking into account the factor ( g q g DM ) , it rules out less parameter space in σ asthe coupling increases. Therefore, the results displayed in these two planes are fully consis-tent but represent different ways to benchmark the search. Depending on what observableis more relevant for the question at hand, either the ( M med , m DM ) plane or the ( σ , m DM )plane might be more appropriate to answer it.We emphasize that the results and sensitivity projections presented here are valid forsingle vector or axial-vector mediator exchange, assuming equal coupling to all quarks.Experimentally, DD experiments probe a combination of the couplings to u and d quarksfor vector exchange and to u , d and s quarks for axial-vector mediator exchange. Thisis in contrast to the mono-jet search. Although the production of the vector or axial-– 9 –ector mediator is mainly sensitive to the coupling to u and d quarks, the mono-jet searchis also very dependent on the mediator width Γ med , which depends on the couplings toall quarks into which the mediator can decay. This therefore motivates one direction inwhich the MSDM framework should be extended: scenarios with different hypotheses forthe couplings to various flavours of quarks should be considered, since DD and mono-jetsearches probe different weighted combinations of these couplings.Other avenues should also be explored to cover a more comprehensive region of DMphenomenology. These include for instance, scalar and pseudoscalar mediators, t-channelmediators and Majorana fermion or scalar DM scenarios. In addition, the collider searchesare also sensitive to the properties of the mediator itself and hence results from severaldifferent topologies, such as di-jet and multi-jet events with missing transverse energy, canbe combined to place limits on the MSDM parameter space. This is particularly relevantfor scenarios where g DM (cid:54) = g q (discussed further in Ref. [28]) since one interesting featureof these other channels is that they may probe different combinations of DM and quarkcouplings. For instance, di-jet searches should be considered as complementary to mono-jet searches since they provide additional constraints on the coupling g q alone. Otherexamples are found in Ref. [21], where it was demonstrated that orthogonal regions ofparameter space can be constrained when mono-jet, mono-photon and di-jet searches arecombined. Furthermore, multi-jet plus missing transverse energy topologies, as used tosearch for supersymmetric particle production at the LHC, will complement and may evenimprove the sensitivity of the mono-jet search by probing additional final states that arerelevant to simplified models that predict significant jet activity in the final sate. Examplesare scalar and pseudoscalar models, as discussed in [50–53].Additional searches may also allow for MSDM models with more parameters to beconstrained. While we have only considered couplings of the mediator to quarks, di-lepton,mono- Z , mono- W or invisible Higgs searches could all be employed to constrain the cou-pling of the mediator to leptons or bosons. This opens the possibility of performing aglobal fit to a MSDM model, incorporating also the constraints from the indirect detectionexperiments, which are likely to provide important constraints on these MSDM models [54].This would be akin to the fits that are performed to specific models of supersymmetry, andwould be particularly useful for characterizing any discovery of a DM signal in the director indirect detection experiments and/or the LHC. Based on the discussion presented in Section 2, we propose the following procedure andbenchmark plots for the comparison of the collider and DD searches in the study of DMparameter space coverage: • We propose that comparisons be made based on MSDM models as described inSection 2. We initially restrict the proposal to MSDM models where the DM isa Dirac fermion that interacts with a vector or axial-vector mediator, with equal-strength couplings to all active quark flavours. These models are fully described byfour independent parameters. – 10 –
We propose to map the collider data into two-dimensional planes, and compare withthe results of DD searches in both the “traditional” cross section versus m DM plane(see, e.g., Figures 1 and 4), as well as the ( M med , m DM ) plane (see, e.g., Figures 2and 3), for the four coupling scenarios g q = g DM = 0.25, 0.5, 1.0, 1.45. For couplingsbelow g q = g DM = 0.25 the present CMS mono-jet search does not provide a signifi-cant limit, while for g q = g DM = 1.45 the width of the mediator becomes larger thanits mass. Therefore, the proposed range of coupling scenarios covers the two extremescenarios (0 .
25 and 1 .
45) as well as intermediate cases (0 . . g q is not universal for all quarks and where g DM (cid:54) = g q , scenarios withscalar and pseudo-scalar mediators as well as t-channel exchanges. For example, a MSDMdescription with scalar and pseudo-scalar mediators would provide some of the simplestrealisations of a non-minimal Higgs sector where the Standard Model Higgs interacts andcan mix with the (pseudo)-scalar mediators. Therefore, such models provide a direct linkwith Higgs physics and it might even be possible that there is a common origin of theelectroweak and the DM scales in Nature as it was recently explored in e.g. [55, 56]. We have focused in this White Paper on a concrete proposal for characterizing and com-paring DM searches in collider and DD experiments, based on the framework of simplifiedmodels. The results presented here are based on recent work described in [28] and aredefined in the context of Minimal Simplified Dark Matter (MSDM) models, which havefour free parameters: the mass of the DM particle, m DM , the mass of the mediator, M med ,the coupling of the mediator to the DM, g DM , and the coupling of quarks to the media-tor, g q . We emphasize that all four parameters are important for translating the colliderlimits into equivalent DD experiment sensitivities. For the example of s-channel vectorand axial-vector mediator interactions, we show how to characterize the results of searchesfor DM particles at colliders and direct detection (DD) experiments in such a way that acomparison between the two approaches can be made on an equal footing.Using sensitivity projections from the CMS mono-jet search, LZ, DARWIN and Su-perCDMS for future running scenarios, we compare the limits of these searches in twocharacteristic planes: those for ( M med , m DM ) and ( σ , m DM ). Both planes provide a– 11 –traightforward comparison of the two search approaches and, depending on the desiredapplication, one or even both planes can be used to provide a characterization of theabsolute and relative performances of collider and DD experiments. This prompts us toformulate a proposal for a better-motivated procedure for comparisons of collider data withresults from direct dark matter search experiments.This proposal is based on a particular implementation of simplified models, which isonly one from several options for developing the comparison of DM searches at colliderand DD experiments beyond the over-simplified EFT interpretation. The extension of theMSDM beyond the assumptions made in this White Paper will be important to make thisapproach complete. For instance, coupling scenarios where g q is not universal for all quarksor where g DM (cid:54) = g q should be considered, and other mediators should be investigated, suchas scalar and pseudoscalar interactions as well as t-channel exchanges. The interpretationframework advocated here represents a potential starting point for going beyond the EFTframework, but further additions to the MSDM model, as well as the consideration ofalternative approaches, will be required to develop a general strategy for comparing colliderand DD experiments in the future. Note Added
While finalising this document, we became aware of [57], which also addresses aspects ofsimplified models in order to go beyond EFT interpretations of DM searches.
Acknowledgements
The work of S.M., O.B. and J.E. is supported in part by the London Centre for TerauniverseStudies (LCTS), using funding from the European Research Council via the AdvancedInvestigator Grant 267352. The work of J.E. and M.F. was supported also in part by theUK STFC via the research grant ST/J002798/1. The work of G.L. is partially supportedby the DOE Grant
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