A brief review, focused on classes of models in which an interplay between Direct and Indirect searches of Dark Matter and searches of New Physics at the LHC can be established, is presented. Some simplified scenarios, featuring weakly as well as feebly/superweakly interacting dark matter, which can be embedded in many theoretically motivated particle physics frameworks, will be discussed

Arcadi, G.

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DOI 10.1393/ncc/i2015-15027-0Colloquia: IFAE 2014IL NUOVO CIMENTO 38 C (2015) 27Theoretical models for Dark MatterG. ArcadiInstitut fu¨r Theoretische Physik, Georg-August Universita¨t - Go¨ttingen, Germany andLaboratoire de Physique The´orique Universite´ Paris-Sud - F-91405 Orsay, Francereceived 7 January 2015Summary. — A brief review, focused on classes of models in which an interplaybetween Direct and Indirect searches of Dark Matter and searches of New Physicsat the LHC can be established, is presented. Some simplified scenarios, featuringweakly as well as feebly/superweakly interacting dark matter, which can be embed-ded in many theoretically motivated particle physics frameworks, will be discussed.PACS 12.60.-i – Models beyond the standard model.PACS 14.80.-j – Other particles (including hypothetical).1. – IntroductionThe identification of the particle nature and of the generation mechanism of the DarkMatter (DM) component of the Universe is one of the biggest puzzles of Particle Phyiscs.A very powerful tool for getting an insight on the DM properties is the correlation ofdifferent search strategies: the Indirect Detection (ID) of the products of DM annihilationor decays in cosmic rays, the Direct Detection (DD) of scatterings of DM particles flowingthrough suitable detectors, or production at the LHC, either directly or from decays ofother exotic states. In the following this kind of correlation will be illustrated in somesimple, but general, theoretical frameworks.2. – Monojet searches in effective Dark Matter modelsThe complementarity of different DM searches is particularly strong in the case ofWeakly Interacting (WIMP) DM. A very powerful tool for investigating this comple-mentarity is an effective theory description in terms of four field operators like e.g.: (fordefiniteness we consider a Dirac fermion DM) [1]:OV = qγμqχγμχΛ2, OA = qγμγ5qχγμγ5χΛ2,(1a)Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 G. ARCADI]2 [GeV/cχM1 10 210 310]2-Nucleon Cross Section [cmχ-4610-4510-4410-4310-4210-4110-4010-3910-3810-3710-3610-1 = 8 TeV, 19.5 fbsCMS,-1 = 7 TeV, 5.1 fbsCMS,XENON100COUPP 2012SIMPLE 2012CoGeNT 2011CDMS IICMS Preliminary2Λq)μγq)(χμγχ(Spin Independent, Vector Operator ]2Mediator Mass M [TeV/c-110 1 10 [GeV]Λ90% CL limit on 050010001500200025003000=M/3Γ,2=500 GeV/cχm=M/10Γ,2=500 GeV/cχmπ=M/8Γ,2=500 GeV/cχm=M/3Γ,2=50 GeV/cχm=M/10Γ,2=50 GeV/cχmπ=M/8Γ,2=50 GeV/cχmCMS Preliminary = 8 TeVs-1L dt = 19.5 fb∫2Λq)μγq)(χμγχ(Fig. 1. – Left panel: Limit from monojet searches, effective vectorial operator, by CMS [2],translated into DM scattering cross-section together limits with current limits from DD experi-ments, reported in the plot. Right panel: Monojet limit re-expressed in function of the mass ofa generic mediator for some values of the DM mass and of the width of the mediator reportedin the plot.with Λ representing the effective scale (including as well possible new couplings) of thenew Physics originating DM interactions, possibly mimicing the mass of a heavy media-tor. These operators describe pair production of DM at the LHC, which can be detectedin events with missing energy plus initial state radiation, like monojets, as well as, bycrossing symmetry, DM scattering on nucleons and annihilations into SM fermions, re-lated to the relic density and possible ID. We show in the left panel of fig. 1 the limit fromcollider searches on Λ, reexpressed in terms of the DM scattering cross-section and com-pared with the constraints from dedicated experiments. Collider limits complement theones from Direct Detection experiments since the latters are the most competitive for DMmasses above 10GeV while LHC searches can probe more efficiently the low mass region.The effective theory description is however strictly valid only if there is a clear sep-aration between the scale Λ and the one processes under study. This is not always thecase for collider processes and the limits presented should be indeed modified accordinga more refined theoretical treatment. This kind of treatment, and a set of new limitsassociated, has been presented in [3]. The effective description is also unsatisfactory inthe case in which the mediator is within the kinematical reach of LHC, since it can beproduced on-shell, with a very strong enhancement of the monojet cross-section, withrespect to the effective limit. We show indeed in fig. 1 how the limit on Λ is reformulatedin terms of the mass M of a generic mediator, for some definite values its width. Thisresult can be interpreted through this schematic expression of the monojet productioncross-section:σ (pp→ χχ + j) ≈ g2χg2qE2(q2 −M2)2 + M2Γ2 ,(2a)where E is the center-of-mass energy, q the momentum transfer and gχ and gq are thecouplings of the mediator with, respectively, DM and quarks. For M sensitively greaterthan√q2 the effective approximation is valid with Λ ≡ M/√gqgχ. For M ∼√q2 ∼1TeV the cross-section is strongly enhanced, according to Γ, and the result is interpretedas a stronger limit on Λ. For M < 2mχ only off-shell contributions are present in themonojet cross-section. This is intepreted as a very weak limit on Λ.THEORETICAL MODELS FOR DARK MATTER 3Fig. 2. – Left panel: ATLAS observed limit (dashed black line), with 1-2 σ uncertainty(green/yellow bands) on Z′ production cross-section times branching fraction into a leptonpair. Red and Blue lines are the LUX exclusion limit for the values of α and DM mass reportedon the plot. Minimum values of MZ′ obtained by combining ATLAS and LUX limit for thevalues of α =AχDVχDreported in the plot. Limits from monojet searches and from LEP have beenreported as well. Points below the lines are excluded.3. – Interplay between LHC and Direct DM searches in Z′ scenariosThe same complementarity discussed above can be enforced as well in more refinedscenarios in which specific mediators for the DM interactions with SM particles are intro-duced, possibly within the kinematical reach of LHC. In this case the relevant parametersare the DM and mediator masses and the new couplings. The possibility of direct pro-duction of the mediator allows to further signals which can complement the informationfrom Dark Matter searches. A popular benchmark for searches of new physics at LHCare Z ′ models, consisting in extensions of the SM with an extra U(1) gauge symmetry(see, e.g., [4] for a theoretical review). Current experimental strategies rely on singleZ ′ production possibly visible as resonances in, e.g., dilepton distributions [5] and verysevere limits have been already set. These limits are however relaxed in case of sizablecoupling of the Z ′ with the DM since the resonances are sensitive to its visible branchingfraction [6]. This effect can be studied by mean of the general LagrangianΔL ⊃ gDχ¯γμ(V χD −AχDγ5)χ Z ′μ + gD∑ff¯γμ(V fD −AfDγ5)f Z ′μ,(3a)which encopasses many existing Z ′ realizations in terms of five paramters: an overallgauge coupling gD and the parameters Vf,χD and Af,χD which represent the vectorial andaxial couplings of the Z ′. The parameters V χD and AχD, governing the invisible branchingfraction of the Z ′, are upper bounded by DM direct detection limits. The correlationbetween different search strategies is again crucial.In the left panel of fig. 2 we compare the LHC exclusion limit from searches of dileptonresonances (the strongest in case that the Z ′ is coupled to both leptons and quarks) withthe predictions of some realizazions of Z ′ coupled with the DM. V χD has been fixedaccording the exclusion limit of the LUX experiment for the considered values of the DMmass, namely 8 and 50GeV, corresponding, respectively, to the least and most severelimits, while we have assigned values ranging from 0 to 1000 to α = AχD/VχD . Thecombinations gDVfD(AfD) have been fixed in order to coincide with the interactions ofthe Z boson (this scenario is dubbed Sequential Standard Model (SSM)). As evident4 G. ARCADIFig. 3. – Summary plots in the plane (mψ,mΣf ) for two assignments of the pair (λ, λ′). Theblack solid lines represent the correct DM relic density while the blue bands represent a value ofthe DM lifetime within two orders of magnitude a reference value set to 1027 s. The red regionis excluded by current searches of metastable particles.LHC constraints on the mass of the Z ′ becomes weaker for configurations which allowfor sensitive couplings, and thus sizable invisible branching ratio, of the Z ′ with the DM.The complementarity between LHC and DD searches is better evidenced in the rightpanel of fig. 2, in the plane (mχ,mZ′). At high DM masses LUX limit is severe, allowingonly a tiny invisible branching fraction. Current LHC limits thus apply and then thelimit on the mass of Z ′ is independent on the DM mass. At lower DM masses the LUXlimit weakens and the higher invisible branching fraction relaxes the limit on the massof the Z ′. On the other hand strong couplings with the DM make relevant the monojetproduction cross-section setting a lower limit to the Z ′ mass.4. – LHC signals for FIMP/SuperWimp Dark MatterAn interesting alternative to conventional WIMP scenarios is constituded by fee-bly/superweakly interacting DM coupled to some exotic states, which can be pair pro-duced at the LHC and are long-lived, such that decay vertices are displaced, with respectto the production ones, or might even lie outside LHC detectors. DM evades both LHCand DD detection; it is however possible to relax the assumption of exact stability of theDM and establish a correlation between Indirect Detection of DM decays LHC detectionof the mediator. A simple realization has been illustrated in [7]. A scalar field, charged(at least partially) under the SM gauge group, features a Yukawa-type interaction withthe DM and a standard model fermion as well as two standard model fermions (quarksor leptons according the assignment of quantum numbers):Leff = λ ψfΣ†f + λ′f′fΣ†f + h.c.,(4a)where f, f ′, can be either quarks or leptons, according the assignment of the quantumnumbers of Σf . This simple setup can be encorporated in several SuperSymmetric sce-narios with Σf represented by a sfermion. The DM decays into three SM fermionswith a rate prortional to λ2λ′ 2. The already strong constraints (see, e.g., [8]) imposeλλ′ ≤ 10−(16÷22). Within this condition the conventional WIMP production is not effec-THEORETICAL MODELS FOR DARK MATTER 5tive. The DM can be nonetheless generated from the decays of Σf through a combinationof freeze-in and SuperWimp production [7] and its relic density:ΩDMh2 ≈ mψmΣfBr (Σf → fDM)[7.17× 102gΣg3/2∗τ−1ΣmΣ+ ΩΣh2](5a)is determined by the decay parameters of Σf which can be tested at the LHC. TheLHC prospects of this scenario are summarized, through two examples, in fig. 3, inthe plane (mψ,mΣf ). As already anticipated the possible signals of decay of the scalarfield are displaced vertices or metastable tracks, the latters already probed by dedicatedsearches [9]. Remarkably, constraints from DM ID have already a very strong impact; inparticular, by requiring an hypothetical next future contemportary LHC and ID signalit is possible to identify a rather definite region in the plane (mψ,mΣf ).5. – ConclusionsThe increasing experimental progress in DM searches should be accompaigned byan analogous progress of theoretical tools. Correlation between DM searches is a verypowerfull tool. It has been illustrated in some simple, but theoretically motiviated,scenarios.∗ ∗ ∗The author acknowledges support from the European Union FP7 ITN-INVISIBLES(Marie Curie Actions, PITN-GA-2011-289442) and from the ERC Advanced GrantHiggs@LHC.REFERENCES[1] Fox P. J., Harnik R., Kopp J. and Tsai Y., Phys. Rev. D, 85 (2012) 056011.[2] Tech. Rep. CERN CMS-PAS-EXO-12-048, CERN, Geneva (2013).[3] Busoni G., De Simone A., Morgante E. and Riotto A., Phys. Lett. B, 728 (2014) 412;Busoni G., De Simone A., Gramling J., Morgante E. and Riotto A., JCAP, 1406(2014) 060.[4] Langacker P., Rev. Mod. Phys., 81 (2009) 1199.[5] Aad G. et al., Phys. Rev. D, 90 (2014) 052005.[6] Arcadi G., Mambrini Y., Tytgat M. H. G. and Zaldivar B., JHEP, 1403 (2014) 134.[7] Arcadi G. and Covi L., JCAP, 1308 (2013) 005.[8] Garny M., Ibarra A. and Tran D., JCAP, 1208 (2012) 025.[9] Aad G. et al., Phys. Lett. B, 720 (2013) 277; Chatrchyan S. et al., JHEP, 1307 (2013)122.

Theoretical models for Dark Matter

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Theoretical models for Dark Matter

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