Par$cle physics Boost Factors

Transcription

1 Par$cle physics Boost Factors Junji Hisano (ICRR, Univ. of Tokyo) TANGO in PARIS Tes$ng Astropar$cle with the New GeV/TeV Observa$ons May 4 th 6 th, 2009 Ins$tut d'astrophysique de Paris, France

2 Contents of my talk Introduc$on of par$cle physics boost factors Non thermal DM produc$on Breit Wigner resonance mechanism Sommerfeld mechanism Constraints on par$cle physics boost factors Summary

3 Introduc$on A Clash of Clusters SDSS Galaxy Map Credit: X ray (NASA/CXC/Stanford/S.Allen); Op$cal/Lensing (NASA/STScI/UC Santa Barbara/M.Bradac) Credit: M. Blanton and the Sloan Digital Sky Survey. Content of the Universe Credit: NASA / WMAP Science Team What is (cold) dark maper in the Universe? How is the dark maper produced in the early universe? 3

4 χ Thermal relic scenario DM par$cle,, is weakly interac$ng massive par$cle (WIMP), and it is in thermal equilibrium in the early universe. Boltzmann eq. for DM number density (Y n/s) as a func$on of x(= M/T ). Y (= n/s) dy dx = s σv xh (Y 2 Y 2 EQ) A[er x f 20, DM is decoupled from thermal bath. Y x f / σv When S wave process in the DM annihila$on is dominant, ( cm 3 ) /s Ω DM =0.23 σv e M/T Decoupling larger σv Y EQ x = x f x(= M/T )

5 Thermal relic scenario DM par$cle, χ, is weakly interac$ng massive par$cle (WIMP), and it is in thermal equilibrium in the early universe. Dark maper with mass 100GeV 1TeV is consistent with thermal relic scenario, σv π α2 m 2 = π (1/127)2 (300GeV) 2 = cm 3 /s From the naturalness, new physics beyond the standard model in par$cle physics is expected to appear around 100 GeV 1TeV scale. DM candidate: Neutralino in Supersymmetric standard model Kaluza Klein photon in Universal extra dimension T odd photon in LiPle Higgs model

6 Puzzle in cosmic rays physics Anomalies in e+/e fluxes measured by Pamela/ATIC might be signature of DM annihila$on in our Galaxy. σv = cm 3 /s, M = 650GeV (χχ e + e ) σv = cm 3 /s, M = 900GeV (χχ µ + µ ) However, effec$ve cross sec$on is $mes larger than expected in thermal relic scenario.

7 Boost factors Source term from DM annihila$on in cosmic rays Q(E, x) = 1 2 n2 ( x) σv dn e ± de Astrophysical boost factors: Clumpy structure in dark maper spa$al distribu$on, Par$cle Physics boost factors: Non thermal DM produc$on Velocity dependent annihila$on cross sec$on typical velocity at thermal decoupling: v 0.3c in our galaxy: v 10 3 c Breit Wigner resonance mechanism Sommerfeld mechanism n( x)

8 Non thermal DM produc$on x nt ( M/T nt ) Heavy long lived par$cles decay in the DM par$cles at, below decoupling temperature from thermal bath, x f (= M/T f ). Ω DM Ω DM (thermal) x nt x f Boost Factors 0.2 ( )( M cm 3 )( )( ) 1/2 /s 100MeV GeV σv T nt g (T nt ) Candidates: In some SUSY models, the long lived gravi$no/moduli produce efficiently Wino or Higgsino DM, whose annihila$on cross sec$on is larger as σv cm 3 /s ( ) 2 M 200(100)GeV

9 Breit Wigner resonance mechanism The non rela$vis$c DM annihila$on is enhanced due to resonance, Thermal distribu$on when M 2 R Γ2 R σv (ECM 2 M R 2 )2 + MR 2 Γ2 R MR 2 =4M 2 (1 δ) ( δ 1) E 2 CM 4M 2 + M 2 v 2 (v 2 1) If δ > 0, the thermal averaged cross sec$on σv becomes larger at lower temperature ( x x a ( 1/max[δ, γ]) ) σv (x/x a ) 2 σv T =0 (Ibe, Murayama, Yanagida) Unphysical pole δ > 0 Breit Wigner 4δ 0 smaller T larger T v 2 Here, x M/T and γ Γ R /M R.

10 Breit Wigner resonance mechanism Annihila$on is maintained even a[er decoupling ( x = x f ( 1/20) ) dy dx = s σv xh Y 2 (x f x x a ) Y (= n/s) Decreasing even a[er x=xf Resonance Ω DM Ω DM (non-res) x a x f BF max[δ, γ] 1 x f Boost Factors Non resonance e M/T Y EQ x f x a x

11 Breit Wigner resonance mechanism boost factor 1 In order to get a large boost factor (~ ), we need DM par$cle pair close to the resonance with narrow width. 1) How to produce unphysical resonance close to threshold? 2) How to suppress width? Can we suppress annihila$on a[er decoupling? MR 2 =4M 2 (1 δ) γ Γ R /M R (Ibe et al)

12 Sommerfeld mechanism Long distance aprac$ve forces modify wave func$on of the DM twobodies state, and enhances the annihila$on cross sec$on. Radial Shroedinger equa$on for S wave wave func$on 1 M ψ(r) V (r)ψ(r) = Mv2 ψ(r) S ψ( )/ψ(0) 2 Ψ(r)(= ψ(r)/r) Annihila$on cross sec$on is enhanced (suppressed) by a factor (Here, boundary condi$on is ψ ( ) =imv ψ( ) [plane wave].) When long distance force is Coulomb like ( S = Boost Factors πα/v 1 e πα/v S πα/v (v α) V = α/r ) (Mv 2 α 2 M)

13 Sommerfeld mechanism Yukawa poten$al: V (r) = α r e m φr mφ/(αm) zero energy resonance S Origin: massive par$cle exchange 1,electroweak gauge bosons 2,hidden gauge bosons 3, hidden scalar bosons 1/v enhancement v/α (Arkani hamed et al)

14 1/v enhancement Yukawa poten$al: V (r) = α r e m φr When α 2 M Mv 2 αm φ, 1/v enhancement is induced. It is saturated if v m φ /M. mφ/(αm) zero energy resonance S Pamela/ATIC anomalies are explained when m φ 1GeV α 1/30 M 1TeV 1/v enhancement since. v 10 3 (Arkani hamed et al, and also many papers) v/α (Arkani hamed et al)

15 Zero energy resonance When αm m φ, bound state(s) appear in the two body DM par$cle system, and if αm φ Mv 2, cross sec$on is enhanced by the resonance. r m 1 φ (αm) 1 E 0 When the binding energy is close to zero (zero energy resonance), the cross sec$on is further enhanced as σv 1/v 2 (JH, Matsumoto, Nojiri) V (r) = α r e m φr αm φ

16 Zero energy resonance S Pamela/ATIC anomalies are explained when m φ 100GeV α 1/30 M 1TeV mφ/(αm) zero energy resonance 1/v enhancement v/α (Arkani hamed et al)

17 Sommerfeld mechanism Annihila$on a[er decoupling is suppressed compared with Breit Wigner resonance mechanism. Thermal relic abundance of SU(2) triplet fermion DM σv v 1 σv v 2 σv v 4 (1/v enhancement) (zero energy resonance) (Breit Wigner resonance) ΩDMh 2 M(TeV) (JH, Matsumoto, Nagai, Saito, Senami)

18 Sommerfeld mechanism Enhancement comes from ladder diagrams in perturba$ve expansion. A 0 A 0 ( α v ) A 0 ( αm m φ ) A 0 ( α v A 0 ( αm m φ ) 2 A 0 ( α v ) 2 A 0 ( αm m φ ) 3 (m φ 0) ) 3 (v 0) Enhancement factor for the l th par$al wave cross sec$on is S 2π (l!) 2 ( α v ) 2l+1 (mφ 0) (Iengo)

19 ! " " 3-1 ( cm sec ) Sommerfeld mechanism by electroweak interac$on The DM par$cle is neutral so that annihila$on into two photons is one loop process. However, the cross sec$on becomes comparable to that into W boson pairs due to the Sommerfeld mechanism Annihilation cross section to Triplet Doublet -3 ( v/c = 10 ) χ χ W + W -! m = 0.1 (GeV) m = 0.1 (GeV)! m = 1 (GeV) W +! m = 1 (GeV) χ χ ± χ ± W χ 3-1 ( cm sec ) W ± Annihilation cross section to 2! Triplet Doublet γ γ -3 ( v/c = 10 ) " m = 1 (GeV) m = 0.1 (GeV) " m = 0.1 (GeV) m = 1 (GeV) m (TeV) m (TeV) (JH Matsumoto, Nojiri)

20 Constraints on par$cle physics boost factors EM/hadronic injec$ons to thermal bath/cmb are constrained from Big Bang Nucleosynthesis (BBN) and Reioniza$on. Constraints look marginal to the Pamela/ATIC anomalies. BBN constraints on χχ W + W M(GeV) Reioniza$on BBN constraints on χχ e + e (Gallia,Ioccoc, Bertone, Melchiorri) M(GeV) (JH, Kawasaki, Kohri, Moroi, Nakayama)

21 Summary of my Talk In this talk, I review par$cle physics boost factors. It may be needed to explain the recent observed anomalies in cosmic rays by DM annihila$on. The representa$ve mechanisms for par$cle physics boost factor are Non thermal DM produc$on Breit Wigner resonance mechanism Sommerfeld mechanism Now many challenges to construct realis$c models are devoted. In order to check mechanisms for par$cle physics boost factor, we have to check various consistencies among cosmic ray observa$ons, BBN, and reioniza$on history.