Dark Photon Dark Matter: Theory and Constraints

Transcription

1 Dark Photon Dark Matter: Theory and Constraints Josef Pradler Vienna Institute of High Energy Physics, Austrian Academy of Sciences May 31, 2015 Beyond WIMPs: From Theory to Detection

2 Looking for new species CF1 Snowmass report 2

3 Looking for new species Beyond WIMPs CF1 Snowmass report 2

4 Looking for new species Way beyond WIMPs CF1 Snowmass report 2

5 Plan 1. Overview about Dark Photons 2. Primordial Abundance 2. Direct Detection of Dark Photon Dark Matter 3. Competing Astrophysical constraints based on works done in collaboration with Haipeng An, Maxim Pospelov, Adam Ritz (see references later) 3

6 Dark Photons Model parameters apple, m V, pe 1,m 1 hq SUp3q c ˆ SUp2q L ˆ Up1q Y ˆ Up1q 1 with Vector V µ } apple1 below EW 2 F µ V Y µ apple scale 2 F µ V µ L 1 4 F 2 µ 1 4 V 2 µ apple 2 F µ V µ ` ej µ ema µ Stueckelberg case Higgsed case L Å 1 2 m V V 2 µ L Å 1 2 m V V 2 µ ` e 1 m V h 1 V 2 µ ` 1 2 e12 h 12 V 2 µ hard photon mass + h self-interactions 4

7 Dark Photons Two ways to think about apple 2 F µ V µ Keep the mixing: Or diagonalize kinetic term: V e V V e applee applep 2 e e Photon-Dark Photon mixing manifest Ordinary matter has millicharge under new force 5

8 Dark Photons see, e.g. Essig et al 2013 (plot illustrations from N.Toro) 6

9 Dark Photons e- fixed target expt. (A1, APEX, HPS, ) e- beam dump experiments e+ e- colliders (BaBar, KLOE, Belle) (among other searches) 7

10 Dark Photons (g-2) explanation of the muon is now excluded from CERN SPS Kaon facility through NA48/2 collaboration 2015 (data ) 8

11 Dark Photons (Fig. from Jaeckel 2013) 9

12 Dark Photons Dark Photon becomes a dark matter candidate (Fig. from Jaeckel 2013) Decays to leptons (and hadrons) 9

13 Can we make Dark Photon Dark Matter? Checklist: is stable on cosmological timescales has the correct relic density large scale adiabatic fluctuations is preferably detectable (if nature is kind) 10

14 Decay of sub-mev Dark Photons Stability: 11

15 Decay of sub-mev Dark Photons Stability: 1. Make it light, below 2me. Prevents V Ñ e`e decay 2. Have small apple! 1, to slow down V Ñ 3 V Ñ3 17apple m 9 V m 8 e V Pospelov, Ritz, Voloshin 2008 (see also Redondo, Postma 2008) => Vectors can be have lifetime greater than the Universe 11

16 Thermal abundance Abundance, early Universe production: 1. thermal production through Compton scattering, e-pair annihilation V Y V freeze in T m e 1/T 1{T For values of the mixing angle that are not already challenged by experiment for m V Á 1 ev, such rates are sub-hubble. 12

17 Matter effects apple 2 F µ V µ ` ej µ ema µ on shell V Ñ L int applem 2 V A µ V µ ` ej µ ema µ. f A X V M iñf`vt plq applem 2 V rej em µs fi xa µ,a y T plq i Coupling of V to EM current inside a medium 13

18 Matter effects apple 2 F µ V µ ` ej µ ema µ on shell V Ñ L int applem 2 V A µ V µ ` ej µ ema µ. f A X V M iñf`vt,l applem2 V m 2 V T,L rej µ ems fi T,L µ i Coupling of V to EM current inside a medium 13

19 Matter effects apple 2 F µ V µ ` ej µ ema µ on shell V Ñ L int applem 2 V A µ V µ ` ej µ ema µ. f A X V M iñf`vt,l applem2 V m 2 V T,L rej µ ems fi T,L µ i Coupling of V to EM current inside a medium => effective mixing angle apple T,L apple ˆ m 2 V m 2 V T,L 13

20 Matter effects apple T,L apple ˆ m 2 V m 2 V T,L Re T,L 9! 2 p T 2 pt " m e q => effective mixing angle suppressed at high T => production shuts off Re T,L p!,t r,t,l q m 2 V => Resonance may appear Resonance dominates the production for light vectors at T m e but is not efficient to reach a dark matter abundance in ROI m V Á 1 ev see Redondo, Postma 2008 & Arias et al 2012 [for mv > 2 me see also Fradette, Pospelov, JP, Ritz 2014] 14

21 Dark Photon Dark Matter Abundance, early Universe production: 1. thermal production 2. resonant production 3. non-thermal production: field can e.g. be generated during inflation Quantum fluctuations yield abundance for free => Jeremy s talk Graham, Mardon, Rajendran

22 Dark Photon Dark Matter Detection: 1. Small mass ~ kev means large number density n DM DM {m DM 2. photo-ionization cross sections of ordinary photons can be huge, say, 10 7 bn Those compensating factors make up for tiny coupling apple! that renders V stable on cosmological timescale! => absorption of ~kev vectors can be looked for in electron band 16

23 Dark Photon Absorption Photon vs. Dark Photon absorption of energy! m V Photon Dark Photon ~q! ~q m V v DM Op10 3 q! => little difference for us:,v Á r e allows to expand Hamiltonian p~p e ~ q exppi~q~r e q»p~p e ~ qˆp1 ` i~q~r e `...q Using normal photon cross sections will be accurate to Op! 2 r 2 shellq Op 2 q OppZ q 2 q 17

24 Dark Photon Absorption (including medium effects) Amplitude: M iñf`vt,l eapplem 2 V m 2 V T,Lpqq xp f J µ emp0q p i y" T,L µ pqq Rate: T,L 1 ÿ 2! p2 q4 p4q pq ` p i p f qe 2 apple 2 T,L" µ" xp i J emp0q p µ f yxp f Jemp0q p i y f 18 18

25 Dark Photon Absorption (including medium effects) Amplitude: M iñf`vt,l eapplem 2 V m 2 V T,Lpqq xp f J µ emp0q p i y" T,L µ pqq Rate: T,L e2 2! ª d 4 xe iq x apple 2 T,L" µ" xp i rj µ empxq,j emp0qs p i y Effective mixing angle inside the medium apple 2 T,L apple 2 ˆ m 4 V m 2 V T,L 2 Related to the polarization tensor of the photon in the medium µ T µ ÿ T i µ T i ` L Lµ L i 1,

26 Dark Photon Absorption (including medium effects) Amplitude: M iñf`vt,l eapplem 2 V m 2 V T,Lpqq xp f J µ emp0q p i y" T,L µ pqq Rate: T,L e2 2! ª d 4 xe iq x apple 2 T,L" µ" xp i rj µ empxq,j emp0qs p i y T,L apple2 T,L Im T,L! An, Pospelov, JP, 2013 An, Pospelov, JP, Ritz 2014 Absorption rate given by the imaginary part of the polarization functions 20

27 Absorption in Xenon Compute absorption rate from refractive index (via tabulated atomic X-ray data, using Kronig-Kramers relations) T! 2 p1 n 2 refrq L p! 2 ~q 2 qp1 n 2 refrq In the non-relativistic limit: ~q!! : L T 21

28 Absorption in LXe Ionization-only S2 analyses amply suited for Dark Photon search. Drifting charges in an electric field is a powerful amplification mechanism E ion pxeq 12 ev Sensitivity to Dark Photons of m V 12 ev Xe I ` V Ñ Xe II ` e ; Absorption of, say, m V 300 ev can produce ~25 electrons. 22

29 Absorption in XENON10 Ionization-only signal S2 pushes sensitivity for sub-kev signals Despite uncertainties in electron yield, calibration, and background we can set a robust limit: 1. count all events 2. do not subtract backgrounds 3. infer limit irrespective of electron yield S2 width e [µs] S2 electrons e nuclear recoil energy E nr [kev] XENON10 collaboration,

30 Absorption in XENON100 S1 and S2 => utilize XENON100 study on axion absorption XENON100 collaboration, 2014 predicted Dark Photon scintillation signal (S1) 24

31 Direct Detection Limits ionization threshold kinetic mixing κ XENON10 XENON100 XMASS => direct detection has sensitivity to kev-scale super-wimps m V (ev)

32 Astrophysical Limits - I V Limit on diffuse galactic and extragalactic gamma ray flux from photon injection spectrum (compilation from Yuksel, Kistler 2008) Pospelov, Ritz, Voloshin

33 Astrophysical Limits - I E 2 γ dφ/de γ (kev/cm 2 /sec/sr) E γ (kev) m V =100keV κ = diffuse γ extragalactic galactic diffuse 100 gamma rays and CMB limits exclude Dark Photon Dark Matter heavier than ~ few x 100 kev kinetic mixing κ XENON10 XENON100 XMASS diffuse γ CMB m V (ev) [gamma ray limits quantitatively identical to previous estimates]

34 Astrophysical Limits II - Stars Virial theorem: (imagine, the star forms from an initially dispersed cloud) xe kin y 1 2 xe gravy 3 2 T 1 2 GM d m p R d => T OpkeVq core temperature of solar mass star => Particles with mass < OpkeVq are kinematically accessible and can be produced. E.g. axions etc. 28

35 Reaction to energy loss xe kin ` E grav y 1. Stars supported by radiation pressure (active stars): Virial theorem: xe kin y 1 2 xe gravy => Gravitational potential energy becomes more negative (tighter bound) => average kinetic energy increases, star becomes hotter, negative heat capacity 2. Stars supported by degeneracy pressure (white dwarfs, neutron stars): possess positive heat capacity, the star indeed cools by the energy loss 29

36 H He C,O Stars as laboratories Hot, blue see e.g. Raffelt s excellent book H He Asymptotic Giant Red Giant H He H C,O White Dwarfs Horizontal Branch Cold, red Main Sequence Globular Cluster color-magnitude diagram 30

37 Horizontal H He Branch stars HB helium burning core «10 4 g cm 3 T «10 8 K Energy loss leads to increased 3 Ñ 12 C and shortens the helium burning lifetime Observable: Predicted number of stars on HB vs on the RGB in Globular Clusters (which are all of the same age) agrees within 10% with observations Limit: luminosity into new states should not exceed nuclear energy generation rate L x À 0.1L 3, which is À 10 erg g 1 s 1 31

38 Stellar V-production f A X V M iñf`vt,l applem2 V m 2 V T,L rej µ ems fi T,L µ i Transverse Resonance m 2 V Re T! 2 p Longitudinal Resonance m 2 V Re L! 2 pm 2 V {! 2 ô! 2! 2 p d prod d!» 2r 2 e!{t prq 1 a!2 m 2 V B! 2 P prq{br r r res ˆ # apple 2 m 2 V!2 apple 2 m 4 V longitudinal, transverse, longitudinal: An, Pospelov, JP 2013 transverse: Redondo

39 Solar Dark Photon Limit kinetic mixing κ Coulomb e =0.01 ALPS-I ALPS-II (proj.) CAST (T) Energy loss constraint from sun: Observable: SNO, 8B flux L dark 0.1L d L d 4 ˆ Watt Astrophysical constraint stronger than laboratory probes An, Pospelov, JP 2013 m V (ev) SC: Sun (L) (T) HC: Sun 33

40 Direct Detection of solar Dark Photons atomic ionization threshold end of resonance region κ =10 12 m V =1eV longitudinal flux dominant an sub-kev => liquid scintillators flux at earth (cm 2 s 1 kev 1 ) T L again best suited ω (ev) 34

41 Direct Detection of solar Dark Photons Coulomb ALPS-I New direct detection limit superior to astrophysical bounds => See Javier s talk on how the solar constraint can be improved. kinetic mixing κ SC: Sun (L) (T) Xenon ALPS-II (proj.) m V (ev) 1 CAST (T) An, Pospelov, JP

42 Dark Photon Dark Matter Position of stellar limits understood from: Sun HB RG! P pr 0q»300 ev,! P pr 0q 2.6 kev,! P pr 0q 200 kev. Astrophysical limits are strong, but direct detection can probe unchartered territory An, Pospelov, JP, Ritz

43 Simplified Models of super-wimp absorption (in contrast to WIMP-nucleon scattering) (pseudo)scalar (pseudo)vector tensor g S S, g P P 5, g V V µ µ, g A A µ µ 5, g T T µ µ, electron Discussed the example of vector V with coupling g V eapple. 37

44 Simplified Models of super-wimp absorption (in contrast to WIMP-nucleon scattering) (pseudo)scalar (pseudo)vector tensor g S S, g P P 5, g V V µ µ, g A A µ µ 5, g T T µ µ, If the DM mass is not protected by some symmetry (like for dark photons or axions), loop corrections induce a mass shift m g i UV => g i À m 100 ev for As we have just seen, such couplings in the naturalness regime are being probed by direct detection! 38

45 Summary Light (kev and below), very weekly interacting particles ( super- WIMPs ) are probed efficiently through stellar cooling or related astrophysical processes. Dark Photons (hidden photons, A, ) can be super-wimps and they can be dark matter through non-thermally generated abundance. Liquid scintillator direct detection experiments allow to test for Dark Photon Dark Matter for vector masses > 10 ev. 39