Dark Photon: Stellar Constraints and Direct Detection

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1 Dark Photon: Stellar Constraints and Direct Detection Haipeng An Perimeter Institute In collaboration with Maxim Pospelov and Josef Pradler ,

2 Motivations Related to the dark sector Dark portal Dark matter itself (or part of dark matter) Sommerfeld enhancement Solution to muon g-2 problem Sub-keV dark photons can be produced inside the Sun and can be detected by detectors at the Earth Mimic the signal of light dark matter

3 Outline What is dark photon? Lagrangian Origin of mass Stueckelberg case and Higgsed case Stueckelberg case Solar flux and stellar constraints direct detection Higgsed case Solar flux and stellar constraints direct detection Summary

4 Outline What is dark photon? Lagrangian Origin of mass Stueckelberg case and Higgsed case Stueckelberg case Solar flux and stellar constraints direct detection Direct detection Solar flux and stellar constraints direct detection Summary

5 The Lagrangian The Standard Model Extra vector field SU(3) C SU(2) L U(1) Y G aµ W iµ B µ U(1) D V µ Below EW breaking, L = 1 4 F 2 µ 1 4 V 2 µ 1 2 apple0 B µ V µ 1 2 applef µ V µ 1 2 applef µ V µ + ea µ J em µ.

6 Origins of mass Massive U(1) gauge theory L mass = 1 2 m2 V V µ In this talk, Should there be a dark Higgs? No! (Naturalness) Stueckelberg case m V < µ a m V 2 Would-be Goldstone Yes! A Higgs at weak scale has just been found. Higgsed case L mass = 1 2 m2 V V 2 µ L mass = 1 2 m2 V V 2 µ L int = e 0 m V h 0 V 2 µ e02 h 02 V 2 µ

7 Outline What is dark photon? Lagrangian Origin of mass Stueckelberg case and Higgsed case Stueckelberg case Solar flux and stellar constraints direct detection Higgsed case Solar flux and stellar constraints direct detection Summary

8 Direct Detection Signal rate N exp = VT Z!max! min d! d T d! T v + d L d! Total absorption rate L v Br Flux from the Sun Branching ratio to the desired signal. Total absorption rate; Solar flux; Branching ratio to desired signals.

9 Total absorption rate Feynman diagram: apple 2 F µ V µ! µ V µ E.O.M J em applem 2 V A V Matrix element: M VT,L +i!f = m 2 V applem 2 V [ej em] µ fi T,L µ T,L µ = e 2 hj em,j µ emi = T Tµ i T i + L Lµ L Correlation function inside the medium

10 Total absorption rate m V scaling k µ J µ em =0 J µ em L µ m V L m 2 V Non-magnetic material T =! 2 " r L = (! 2 ~ k 2 ) " r M VT,L +i!f = m 2 V In the small m V limit, applem 2 V M T m 2 V, M L m V. " r = " r 1 Relative permittivity [ej em] µ fi T,L µ T,L

11 Total absorption rate Total absorption rate abs T,L = 1 X M VT,L +i!f 2 2! X f f hi J µ em fihf J em ii = hi J µ emj em ii Unitarity 2ImhJ µ em,j emi T =! 2 " r L = (! 2 ~ k 2 ) " r Im T, Im L

12 Total absorption rate Total absorption rate m 2 V! 2 " r apple 2! m 2 2 V! 2 Im" r " r L = apple2 m 2 V Im" r " r 2! " r / n A, Atom number density T / n 1 A L / n A

13 If transverse modes dominate T / n 1 A The effective atom number density should as small as possible. CAST experiment Unevenly distributed low density detector Dark matter detectors Signal rates depend on the gap between the shielding and the detector Daily modulation and annual modulation

14 If longitudinal mode dominates L / n A High density, large volume dark matter detectors No significant modulations

15 Longitudinal or transverse, it s a question!

16 Solar flux Total production rate m V scaling prod T / apple 2 m 4 V! p 4 prod L / apple 2 m 2 V! 2 In arxiv: (JCAP 0807,008 (2008)) L =! 2 p ~ k 2 L / m 4 V Not correct!

17 Solar flux Resonant production Transverse resonance Longitudinal resonance m 2 V =Re T =! 2 p m 2 V =Re L =! 2 pm 2 V /! 2 m 2 V =! 2 p! 2 =! 2 p

18 Solar flux Resonant production A V On shell In thermal field theory, this is equivalent to that a thermal bath of photon slowly transits into dark photons.

19 Solar flux Resonant production On shell conditions Transverse photon Dark photon! 2 ~ k 2 =! 2 p! 2 ~ k 2 = m 2 V m 2 V =! p 2 Longitudinal plasmon (collective motion of electrons)! 2 =! p 2! 2 ~ k 2 = m 2 V! 2 =! 2 p

20 Solar flux Bose-Einstein distribution for both T-photon and L- plasmon, the dark radiation powers are dp T dv d! = apple2!4 p Inside the Sun, q! 2! 2 p (m 2 (e!/t V! p ) 1) p dp L dv d! = apple2 m 2 V!2 p! 2 m 2 V (!! 4 (e!/t p ) 1) 1eV.! p. 300 ev T L mode dominates, 1eV. m V. 300 ev mode dominates, m V 1 ev

21 Stellar constraints Considering only the transverse contribution. P dark apple P luminosity Life time of the Sun The red giant stars Frieman, Dimopoulos and Turner (PRD 1987), Raffelt and Dearborn (PRD 1988), Raffelt and Starkman (PRD 1989)

22 Requirement to detectors Based on the correct analysis, the total absorption rate for the solar dark flux abs / n A High density, large volume Inside the Sun, 1eV.! p. 300 ev The detector should be able to detect ~ 100 ev energy deposition

23 XENON10 limit XENON10 Number of electrons 300 ev ~ 25 electrons Br 1 Photo-ionization dominates. E 1 12 ev

24 CoGeNT limit CoGeNT data available from 400 ev. Br 1 Photo-ionization dominates.

25 Stueckelberg case

26 Outline What is dark photon? Lagrangian Origin of mass Stueckelberg case and Higgsed case Stueckelberg case Solar flux and stellar constraints direct detection Higgsed case Solar flux and stellar constraints direct detection Summary

27 Higgsed case Direct detection Solar flux Total absorption rate Branching ratio to desired signal

28 Solar flux Processes in the Stueckelberg case are still there: m 2 V (L), m 4 V (T ) Higgs-strahlung m 2 V! 2 Goldstone equivalence theorem m 0 V

29 Solar flux Higgs-strahlung Dominant, m 2 V!2 p sub dominant, m V! p Resonance decay N L! p 3, N T T 3 T 3! 3 p, in the Sun Transverse photon decay dominates.

30 Total absorption rate Dark Higgs-strahlung process dominates in small m V region, using Goldstone equivalence theorem:

31 Total absorption rate Total absorption rate, summing over all possible final state x V A x i> J em J em i>

32 Total absorption rate Total absorption rate: x V A x T =! 2 " r L = (! 2 ~ k 2 ) " r i> J em J em i> 2ImhJ µ em,j emi Im T, Im L

33 Absorption rate Inelastic scattering of dark Higgs d d! apple2 e 02 E! 4 2 E Collinear divergence regularized by the medium effect. apple 4E(E!) log! 2 " r 1 Im" r (!) Energy injected into the medium Energy of incoming Higgs Br 1 for both XENON10 and CoGeNT

34 Total absorption rate Issue with " r Lorentz symmetry is broken by the medium to the SO(3) rotation symmetry. In general, " r = " r (!, ~ k 2 ). ~ k 2 However, the dependence on k 2 is suppressed if 1.!m e This is always true in our situation.

35 Higgsed case e = 0.1

36 Higgsed case XENON10, Sun RG

37 Summary and outlook The stellar bounds are significantly strengthened in the small m V region. Large volume, high density materials should be used to build solar dark photon detectors. For the Stueckelberg case, the XENON10 result gives the most stringent constraint on the parameter space. For the Higgsed case, we expect the next generation dark matter detector can be more sensitive to the current stellar constraint. Future detectors with low electron recoil threshold DAMIC (Alvaro s talk), Sub-MeV detectors (Essig et al), Semiconductor detectors (Graham et al).