Collider Constraints On Low Mass WIMP Haipeng An, University of Maryland Shanghai Jiao Tong University In collaboration with Xiangdong Ji, Lian-Tao Wang 中国科学院理论物理研究所冬季研讨会 -- 暗物质与重子物质起源

Outlines Experiments; Possible Interactions Between WIMP and SM particles; Tevatron Constraints on the parameter space; Tevatron Constraints on direct detection cross section; Relic abundance; Flavor changing neutral currents.

Direct Detection Experiments CoGeNT Observed excess could be explained by WIMP signal with mass in the range of 6~11 GeV. Cross section ~ cm 2. CRESST-II CaWO 4 32 events cannot be explained by known background. Can be explained by WIMP with mass around smaller than 15 GeV. And the cross section is about a few times cm 2. XENON100 Poisson smearing, null-result. New XENON100 result with a detecting power ten times larger will be published soon.

Direct Detection Experiments 15 GeV 5 GeV

Relic abundance Thermal freezing-out Thermal freezing-in (Multi-components) SuperWIMP Asymmetric dark matter Using relic abundance as a lower bound

Tevatron Constraints Leading jet E T > 80 GeV; p T of second jet < 30 GeV; Vetoing any third jet with E T > 20 GeV; Missing E T > 80 GeV. 1 fb -1 of data from Tevatron, 8449 events observed. SM background 8663±332; Hard process is good enough. Goodman, Ibe, Rajaraman, Shepherd, Tait, Yu ( , ); Bai, Fox, Harnik ( ). Aaltonen et al. [CDF Collaboration], PRL 101, , Study the properties of large extra dimension models

Contact Operator In the work by Irvine group, effective four particle interaction is used to study the Tevatron constraint and LHC prediction. However, in Tevatron the center-of-mass energy of the proton-anti- proton pair is 1.96 TeV, therefore if the mass of the intermediate particle is around a few hundred GeV, the interaction cannot be considered as a contact interaction. Furthermore, if the result of CoGeNT is induced by elastic SI, MI collision between dark matter and nuclei, the effective coupling can be written as

Z-boson mediator M DM << M Z. Coupling between M Z and DM should be smaller than Relic abundance is too large.

Standard Model Higgs If dark matter is a fermion, since the Yukawa couplings to light quarks are small. The relic abundance is too large. However, if dark matter is a scalar, the relic abundance constraint can be avoided. (Xiao-gang’s talk)

Possible Interactions SM Higgs + Scalar dark matter is still possible. Dark matter: Complex Scalar (Φ), Dirac Fermion (χ). Mediator: Scalar (H’), Vector (Z’). T-channel annihilation, colored particle. (Will be study elsewhere). More complicated cases …

Vector Mediator with Fermion WIMP M*M* g D =0.5, 1, 2, 3, 5 M Z’ = 5 GeV

Vector Mediator with Fermion WIMP g D =0.5, 1, 2, 3, GeV 450 GeV 480 GeV 500 GeV Contact operator case Tevatron constraint Cannot saturate Tevatron bound in perturbative region

Vector mediator fermion dark matter Scalar mediator fermion dark matter Vector mediator Scalar dark matter Vector Mediator with Fermion WIMP 5 GeV 15 GeV

Dipole Interaction Perturbatively Non-perturbatively

Dipole Interaction

Direct detection cross section Hadronic matrix elements Electric Dipole coupling Belanger, Boudjema, Pukhov, Semenov “MicrOMEGAs2.2” ( ). Fan, Reece, Wang ( ). Quark EDM (QCD sum rules) Pospelov, Ritz PRD 63,

Power counting Direct detection cross section SI: Spin-independent ~ O(1) SD: Spin-dependent ~ O(10 -3 ~10 -4 ) MI: Momentum-indenpent ~ O(1) MD: Momentum-dependent ~ O(10 -6 )

Magnetic Interaction

Tevatron Constraints on Direct Detection Cross Section g D =1 g D =0.5 M Z’ < M * constraint on g Z’ does not depend on g D. σ ∝ g D - 2

Tevatron Constraints on Direct Detection Cross Section M DM =5 GeV M DM =15 GeV

Relic Abundance Ωh 2 ≈ 0.1pb / σ. We choose g D =1 as a benchmark scenario to study the relic abundance. During the thermal annihilation M DM /T ≈ 20, during this era, dark matter particles are non-relativistic. For some operators the annihilation cross section are suppressed by v 2. J PC Group state of spin-1/2 fermion anti-fermion pair can only be 0 -+ and 1 --

Tevatron Constraints on Relic Abundance (M Z’ >80 GeV) 5 GeV, 7 GeV, 10 GeV, 12 GeV, 15 GeV

Tevatron Constraints on Relic Abundance (M Z’ >80 GeV) NR suppression Factor of 10 σ ∝ M DM 2

Dipole coupling (M Z’ >80 GeV) Factor of 10 2 σ ∝ M DM 4

Scalar Mediator with Fermion DM

Vector Mediator and Scalar DM

Scalar Mediator with Scalar Dark Matter (M Z’ >80 GeV)

Different Energy Scales Collider: In the case of M mediator < M *, the mediator is produced on-shell and then decay to DM-anti-DM pair, the energy flowing into the DM anti- DM pair is just M mediator. Thermal annihilation: The energy flowing into Z’ is 2M DM. Therefore, if the coupling is dimensional -1, like the dipole interaction case, the collider constraint on the thermal annihilation cross section is enhanced by a factor of (M DM /M Z’ ) 2. Whereas, if the coupling is dimension 1, like the scalar mediator with scalar dark matter case, the constraint on thermal annihilation cross section is weakened by a factor of (M DM /M H’ ) 2.

LEP II constraints on Z’ coupling to leptons If the MZ’ > 209 GeV, in the case of B-xL model, the constraint on x is that M Z’ /g Z’ > 6.2x TeV. If M Z’ < 209 GeV, the coupling between Z’ and leptons should be smaller than In the case of g D =1, M Z’ =80 GeV, M D =15 GeV, g e =g mu =g tau =0.01, the relic abundance is Ωh 2 = 0.58, which is about 5 times larger than the observed one. Since Ωh 2 ~ 0.1pb / σ, the contribution of the annihilation cross section from hadronic sector needs to be at least 5 time larger than from the lepton sector. If g D gets larger, the constraint from thermal relic abundance is weakened.

Possible Interactions at g D =1, M mediator >80 GeV Other interactions are either suppressed by velocity or suppressed by M D / M Z’. Except for the case of scalar mediator and scalar DM, the allowed cases are also stringently constrained.

Flavor Changing Neutral Current Quark rotation matrices can induce tree-level FCNC. In the case of new scalar mediator. If the vector mediator is non-universally coupled to quarks, it also suffers from tree-level FCNC constraints.

Summary We consider elastic, single component, dark matter, specifically, complex scalar and Dirac fermion. The mediator we can considered are vector and real scalar. In our study, the interaction is conducting by a propagating particle instead of a contact operator. Collider constraints on the direct detection and relic abundance is studied especially for heavy mediator cases (M>80 GeV, g D =1).