Capture and Decay of Electroweak WIMPonium

Transcription

1 Captue and Decay of Electoweak WIMPonium Patick Fitzpatick based on JCAP 1702 (2017) 005 with Pouya Asadi, Matthew Baumgat Emmett Kupczak, Tacy Slatye Rutges MIT

2 WIMPs WIMPs exchange ladde of electoweak gauge bosons in NR limit (v ~ 10^(-3)) gives ise to non-local, instantaneous potential leads to Sommefeld enhancement in DM annihilations: v = (0) 2 WIMP spectum possesses bound states when WIMP mass sufficiently lage elative to mass of electoweak gauge bosons > WIMPonium altenative annihilation channel fo DM significant effect on adiative signals?

3 SU(2) L tiplet Majoana femion wino L = i a µ@ µ ac + ig µw b µt b ac a, zeo hypechage, mass M c 1 2 M ( a a + h.c.) in mass eigenbasis: { 1, 2, 3 }! { 0, ± } mass splitting: M M ± M 0 = 165MeV inteactions with electoweak gauge bosons: pai states, stating with a pai of neutal winos:

4 wino pai states = Schödinge eqtn. N ( 0 0 ) C ( + ) in NR limit evolve in the Schödinge eqtn: i@ t = H 0 = apple 2 X 4M 2 M + V () unde the potential: V L+S even () = 0 p e 2 W p 2 W e m W m W 2 M W c 2 W e m Z! V L+S odd () = M W c 2 W e m Z initial (neutal) positive-enegy scatteing state Z d 3 i E CM = M v2 el i,p () i,p 0 () = 3 p p 0 4 H 0 L+S even i = M v2 el 4 adiative tansition L = ±1 to puely chagino negative-enegy bound state f E n. O W 2 M Z d 3 f () 2 =1 HL+S 0 2S+1 odd f L J = 2S+1 En f L J i V L+S even V L+S odd

5 SU(2) L -symmetic limit high-mass limit in which SU(2) L symmety appoximately unboken: M W,M Z M M! 0 Coulombic limit: V ()! W diagonalize the Schödinge eqtn: 1 W 2µ 2 V = V ( p 2 2µ E n () = X i i i () V i = i i Wino: V L+Seven () = V L+Sodd () = W W p p =2! E n = M (2 W ) 2 2 = 1 4n 2 =1! E n = M 2 W 4n 2

6 bound state spectum spin singlet spin tiplet blue, ed, geen: s, p, d wave. solid, dashed, dotted anking n fom lowest E n = (2 W ) 2 M 4n 2 even L+S E n = 2 W M 4n 2 odd L+S high-mass limit

7 WIMPonium fomation initial population of fee neutalinos, bound states fom via adiative captue electic dipole captue diagam hee ( v el ) s=1,l=1! 3 S 1,n=1 / 2 W M 2 v el e 4n i/ f = 2 W M 2 v el e 8 ( v el ) s=0,l=0! 1 P 1,n=2, P m / 2 W M 2 v el e 16 captue into s=1 (spin-tiplet) l=0 n=1 bound state (aising fom p-wave pat of initial state) dominates captue to 2p states due mostly to suppession e 4n i/ f = e 8n bound states subsequently decay to lowe-enegy states o annihilate to SM paticles. note: detecting photon lines fom captue and/o tansitions extemely challenging: NFW DM pofile (8.5kpc) = 0.4GeV/cm 3 cap = cm 3 /s! O 10 3 photons/m 2 /y

8 captue vs. diect annihilation leading-ode s-wave annihilation into all channels given by diagams: ( v el ) da / 2 W M 2 W v el ( v el ) cap ( v el ) da / W e 4 i/ f = W e 8 dak oange: tee-level inclusive annihilation > WW, ɣz, ɣɣ. blue: p-wave > 3 S 1 + ɣ, (lowest) n=1. puple: d-wave > 1 P 1 + ɣ (n = 2). maoon: s-wave > 1 P 1 + ɣ, n = 2 diect annihilation dominates the adiative captue fo the wino, due to facto in contast to positonium / e 4n e 8n

9 conclusions due to spin statistics, states with odd vs. even L+S expeience diffeent effective potentials and fom distinct towes of bound states > bound spectum, unsuppessed decay channels diffeent fom hydogen-like atoms. wino bound state captue ate subdominant to diect annihilation > pevious calculations of detectability of e.g. high-enegy gamma-ay lines fom wino DM should not equie significant modification. detection of low-enegy photon lines fom adiative captue and tansitions between bound states seem vey challenging fo wino. factos which suppess wino-onium coss section not geneic depend sensitively on ep. of DM unde the gauge goup, and elative masses of DM and foce caies > fomation of bound states cannot be safely ignoed in models with non-tivial dak sectos. >See e.g. Cielli et al JCAP 1705 (2017) 036 : DM chaged unde dak U(1) > fomation and decay of DM bound states have significant effect on adiative signals in indiect detection. >See e.g. Mitidate et al. 2017: DM femionic 5plet of SU(2)L with zeo hypechage. bound states educe the DM themal abundance by about 30%, inceasing the DM mass that epoduces the cosmological abundance to about 11.5TeV. significant bound-state coections to DM indiect detection, chaacteistic spectum of mono-chomatic lines aound E (10 80) GeV, with ates of expeimental inteest.

10 WIMPonium fomation, tansitions, annihilation initial population of fee neutalinos, bound states fom via adiative captue subsequently decay to lowe-enegy states o annihilate to SM paticles continuum-bound and bound-bound tansitions in time-odeed petubation theoy. H = H 0 + V ad. V ad. = + X e n M A(x n) p n + X n n i p 2 e W A(0) ˆ e m W P NC e 2 n 2m n A(x n ) 2! P CC S i, f =2 i M v 2 /4 E n k P 2 BS/(4M ) X i p 2 e W f 2S+1 L J n e n M (k) e m W A(0) ˆ i,n i 2S+1 f L J! (k) A(x n ) p n i,c i (d )v el d =(2 ) 2 µ f k M 2 i, f d k µ f = ke BS /(k + E BS ) k whee k = E n + M vel/4 2 fo captue k = E n1 E n2 fo decay

11 annihilation fom bound state bound states also decay though annihilation to SM final states. Z 1 i = 2µ Z 1 4µ M(B! f) = = 1 2M B Z d 3 p (p) p, (2 ) 3 pi (distinguishable paticles) d 3 p (p) p, (2 ) 3 pi (identical paticles), 1 2µ Z d 3 p (2 ) 3 d n M(B! f) 2 apple 1 p2 N (p)m( 0 (p) 0 ( p)! f)+ C (p)m( + (p) ( p)! f)

12 decays fo lowest-enegy bound states: WIMPonium decays blue > 1-3s; yellow > 3d; ed > W+W- SU(2)-symmetic limit: dominant captue into spin-tiplet 1s dec / 4 W M dominate L>0 annih / 5+2L W M spin-singlet 2p: annihilation decay ate suppessed elative to ED tansitions to lowe s and d.

13 detectability photons adiated upon captue/tansitions could allow study of the QM numbes of DM constitute a detectable signal? assuming: NFW DM pofile (8.5kpc) = 0.4GeV/cm 3 R s = 20kpc cap = cm 3 /s O 10 3 photons/m 2 /y at Eath fom the Milky Way halo fom egion within 1 degee of Galactic cente, ate is instead: few 10 5 photons/m 2 /y ate is pohibitively small fo easonable space-based telescope. gound-based gamma-ay telescope with effective aeas m 2 howeve, cuent and nea-futue gound based telescopes have lowenegy thesholds 10 20GeV need to be loweed by an ode of magnitude to obseve captue and tansition photons fom DM O (10) TeV! E n 1GeV deepest bound states