Effective Theory for Electroweak Doublet Dark Matter

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1 Effective Theory for Electroweak Doublet Dark Matter University of Ioannina, Greece 3/9/2016 In collaboration with Athanasios Dedes and Vassilis Spanos ArXiv: [submitted to PhysRevD]

2 Why dark matter There is extra matter in the universe! Relic abundance 1 Ωh P. Ade et al. Astron. Astrophys. 571, A16 (2014) [arxiv: ].

3 WIMPs WIMP=Weakly Interacting Massive Particle. Lifetime much larger than the age of the universe. Electrically neutral (because it s dark). Interacts weakly. Massive (cold dark matter).

4 Freeze-out of WIMPs Three stages: Everything is in equilibrium. T M DM. WIMP production stops. T M DM. WIMP annihilation stops (becomes much smaller than the expansion rate of the universe). T = T FO M DM 20.

5 EFT Content A pair of Weyl fermion SU(2) L doublets with opposite hypercharges (anomaly free). Z 2 parity (stable lightest particle). Non-renormalizable dim=5 operators in the Lagrangian Yukawa interactions, mass splitting and dipole operators. A symmetry which limits the number of free parameters.

6 Motivation Dark Matter around the Electroweak scale possible detection at LHC. Non-zero dipole moments indirect detection via gamma-ray lines. Custodial symmetry in the Yukawa sector helps avoiding direct detection without fine tuning (small number of relevant parameters). Since it is an Effective Theory, it shows that there is a family of models with similar features. Fermionic bi-doublets in many models like MSSM, doublet-singlet, doublet-triplet, SO(10) GUTs and subgroups (left-right symmetric model).

7 Yukawa interactions L mass+yukawa y 1 2 Λ UV (H T ɛd 1 ) ( H T ɛd 1 ) + y 2 2Λ UV (H D 2 ) (H D 2 ) + y 12 Λ UV (H T ɛd 1 ) (H D 2 ) + ξ 12 Λ UV ( D T 1 ɛd 2 )(H H) + M D D T 1 ɛd 2 + H.c. The Yukawa parameters are assumed to be real numbers. M D can be redefined (through redefinition of the doublets) to be a real positive number.

8 Symmetries I: Custodial Symmetry Representing H and D 1,2 as 2 ( H 0 H H = + H H 0 ) and D = ( D 0 1 D + 2 D 1 D 0 2 The Yukawa sector is invariant under and SU(2) R (custodial) with ) for y 1 = y 2 = y, y 12 = ±y H U L HU R D U L DU R L y1, y 2, y 12 y Λ UV [ Tr(H D)] 2 + H.c. 2 Similar to P. Sikivie, L. Susskind, M. B. Voloshin, and V. I. Zakharov, Isospin Breaking in Technicolor Models, Nucl.Phys. B173 (1980) 189.

9 Dipole operators L dipoles d γ Λ UV D T 1 σ µν ɛd 2 B µν + d W Λ UV ( D T 1 σ µν ɛ τ D 2 ) Wµν + i e γ Λ UV D T 1 σ µν ɛd 2 Bµν + i e W Λ UV ( D T 1 σ µν ɛ τ D 2 ) H.c., A W µν + where d γ and d W are real numbers and, since we are not concerned about CP violation, e γ = e W = 0.

10 Symmetries II: Charge Conjugation For y 1 = y 2 = y, the dark sector is invariant under a Charge Conjugation, which exchanges D 1 and D 2.

11 Symmetries II: Charge Conjugation For y 1 = y 2 = y, the dark sector is invariant under a Charge Conjugation, which exchanges D 1 and D 2. Benchmark points: y 12 = y, 0. Finally, the free parameters are: Λ UV, M D, y, ξ 12, d W, d γ

12 Physical states: particles and masses After diagonalization of the mass matrix: χ 0 1 = 1 2 (D D 0 2), χ 0 2 = i 2 (D 0 1 D 0 2), χ + = i D + 2, χ = i D 1. m χ ± = M D + ξ 12 ω, m χ 0 1 = m χ ± + ω (y y 12 ), ω v 2 Λ UV, m χ 0 2 = m χ ± ω (y + y 12 ).

13 Spectrum

14 Physical states: fermion fermion Higgs interaction L dim=5 χ χ h = Y hχ χ + h χ χ Y hχ0 i χ0 j h χ 0 i χ 0 j, Y hχ χ + = 2 ξ 12 ω v, Y hχ0 1 χ0 1 2 ω = v Y hχ0 2 χ0 2 2 ω = v Y hχ0 1 χ0 2 = 0. (ξ 12 + y y 12 ), (ξ 12 y y 12 ), Notice that the custodial fixes Y hχ0 1 χ0 1 ξ12 + y y 12, so current Direct Detection can be avoided easily. There is at least one model 3 where, under the same custodial, Y hχ0 1 χ0 1 = 0 (at tree level). 3 Doublet-Triplet Fermionic Dark Matter. A.Dedes and D.Karamitros PhysRevD [arxiv: ].

15 Physical states: neutral Gauge boson interactions L dim=4 neutral 3 point = (+e) (χ+ ) σ µ χ + A µ ( e) (χ ) σ µ χ A µ + g O L (χ + ) σ µ χ + Z µ g O R (χ ) σ µ χ Z µ + c W c W g O ij L (χ 0 i ) σ µ χ 0 j Z µ, c W Lneutral dim=5 3 point = ω v 2 (d γ s W + d W c W ) O ij L χ 0 i σ µν χ 0 j F µν Z ω v 2 (d γ s W d W c W ) χ σ µν χ + F µν Z + ω v 2 (d γ c W d W s W ) O ij L χ 0 i σ µν χ 0 j F γ µν + ω v 2 (d γ c W + d W s W ) χ σ µν χ + F γ µν + H.c. O L = O R = 1 2 (1 2s2 W ) and O L = i ( )

16 Physical states: charged Gauge boson interactions L dim=4 charged 3 point =g OL i (χ 0 i ) σ µ χ + W µ g O R i (χ ) σ µ χ 0 i W µ + g O L i (χ + ) σ µ χ 0 i W + µ g O R i (χ 0 i ) σ µ χ W + µ, L dim=5 charged 3 point = 2 ω v 2 d W O R i χ σ µν χ 0 i F µν W + + O L i = ω v 2 d W Oi L χ + σ µν χ 0 i F µν W ) ) ( i 1, O R i = 1 2 ( i 1. + H.c.

17 Earth Constraints Direct Detection experiments (LUX 4 ) limit ξ 12 + y y 12. LEP 5 m χ ± = ξ 12 v 2 Λ UV + M D 100 GeV. CMS and ATLAS 6 h γγ limits ξ 12 v 2 m χ ±Λ UV. Result: M D 90GeV (mainly from LEP). ξ 12 (2)y ± 0.16 (from LUX). small values of ξ 12 (from LHC: BR h γγ ). 4 D. S. Akerib et al. Phys. Rev. Lett. 116 (2016) no.16, [arxiv: ]. 5 P. Achard et al. Phys. Lett. B 517, 75 (2001) [hep-ex/ ]. 6 G. Aad et al. Phys. Rev. Lett. 114 (2015) [arxiv: ].

18 Earth Constraints 1.5 UV 1 TeV, M D 300 GeV 1.0 y12 0 y 12 y Ξ y

19 The role of dipoles The dipoles minimize the total annihilation cross section.

20 Astrophysical Constraints (Relic Density)

21 Astrophysical Constraints (Relic Density)

22 Astrophysical Constraints (Relic Density)

23 Astrophysical Constraints (Relic Density)

24 Astrophysical Constraints (Continuous Gamma-rays) Fermi-LAT 7 bound from dwarf Spheroidal galaxies: < σ DMDM WW, ZZ v > cm 3 s 1 (for Dark Matter mass above 200 GeV, assuming BR = 100%) 7 M. Ackermann et al. Phys. Rev. Lett. 115 (2015) no.23, [arxiv: ].

25 Astrophysical Constraints (Gamma-ray lines) Fermi-LAT 8 bounds on the annihilation of Dark Matter particles to monochromatic gamma rays at the center of our galaxy. There are two relevant channels in this model, since the coupling to the Higgs is suppressed from Direct Detection. χ 0 1 χ0 1 γ γ, with energy E γ = m χ 0. 1 Cross section cm 3 s 1 for photon energies GeV. ) χ 0 1 χ0 1 γ Z, with energy E γ = m χ 0 (1 m2 Z 1 4m 2 χ 0 1 Cross section cm 3 s 1 for photon energies GeV. 8 M. Ackermann et al. Phys. Rev. D 91 (2015) no.12, [arxiv: ].

26 Astrophysical Constraints (Gamma-ray lines)

27 The parameter space after the gamma-ray constraints 0.4 y y dγ d w

28 LHC Run I LHC Run I at s = 8 TeV and Ldt 20fb 1 Missing energy channels 9 : pp χ 0 1 χ0 1 + γ. Cross section 0.22 fb. Extremely suppressed in our case due to Fermi-LAT (cross section below 10 5 fb). pp χ 0 1 χ0 1 + (Z l + l ), l = e, µ. Cross section 0.27 fb pp χ 0 1 χ0 1 + (W µν µ). Cross section 0.54 fb pp χ 0 1 χ0 1 pp χ 0 1 χ0 1 pp χ 0 1 χ0 1 + (W /Z hadrons). Cross section 2.2 fb + 2 jets. Cross section 4.8 fb + ν ν + jet. Cross section 6.1 fb 9 These channels are studied (for dim = 7 operators) in A. Crivellin, U. Haisch and A. Hibbs, Phys. Rev. D 91 (2015) [arxiv: ].

29 Mono-Z/W at 8 TeV

30 Hadronically decaying W /Z at 8 TeV

31 Dijet at 8 TeV

32 Monojet at 8 TeV

33 Future LHC LHC at s = 13 TeV and Ldt fb 1 The most promising for our case is the mono-jet signal pp /E T + jet

34 Monojet at 13 TeV

35 Summing up... Dark Matter with mass around the Electroweak scale, while avoids current bounds from different experiments. Possible indirect detection in the future (gamma-ray lines). Can produce some events at the next runs of LHC (/E T signal). Possible direct detection detection in the future direct detection experiments.

36 Open questions... Classification of UV complete models? Other possible detection channels for LHC?

37 Thank You!

38 More figures!

39 Astrophysical Constraints (Relic Density)

40 Astrophysical Constraints (Relic Density)

41 Astrophysical Constraints (Continuous Gamma-rays) Fermi-LAT bound from dwarf Spheroidal galaxies: < σ DMDM WW, ZZ v > cm 3 s 1 (for Dark Matter mass above 200 GeV, assuming BR = 100%)

42 Astrophysical Constraints (Gamma-ray lines)

43 Feynman Diagrams for LHC: Mono-Z

44 Feynman Diagrams for LHC: Mono-W

45 Mono-Z/W at 8 TeV

46 Feynman Diagrams for LHC: Hadronically decaying W/Z

47 Hadronically decaying W /Z at 8 TeV

48 Feynman Diagrams for LHC: Dijet

49 Dijet at 8 TeV

50 Feynman Diagrams for LHC: Monojet

51 Monojet at 8 TeV

52 Monojet dσ dm inv dσ dm Χ1 0 Χ2 0 pb GeV M 1 2 GeV