The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

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1 The role of ElectroWeak corrections in indirect Dark Matter searches Paolo Ciafaloni INFN, sezione di Lecce Firenze, 18/12/2013 The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

2 2 Results from PAMELA ( ) -1 s sr] antiproton flux [GeV m AMS (M. Aguilar et al.) BESS-polar04 (K. Abe et al.) BESS1999 (Y. Asaoka et al.) BESS2000 (Y. Asaoka et al.) CAPRICE1998 (M. Boezio et al.) CAPRICE1994 (M. Boezio et al.) PAMELA kinetic energy [GeV] The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

3 Indirect DM search and radiative corrections + W W rad corr / decays propagation e p detectoin If Physics (L) is known, what is the spectrum of stable particles (e +, ν, p, γ) at the interaction point? Radiative EW corrections significantly alter the final answer! The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

4 Indirect DM search and radiative corrections + W W rad corr / decays propagation e p detectoin If Physics (L) is known, what is the spectrum of stable particles (e +, ν, p, γ) at the interaction point? Radiative EW corrections significantly alter the final answer! The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

5 Indirect DM search and radiative corrections + W W rad corr / decays propagation e p detectoin If Physics (L) is known, what is the spectrum of stable particles (e +, ν, p, γ) at the interaction point? Radiative EW corrections significantly alter the final answer! The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

6 Effects of radiative weak corrections P.C., D. Comelli, A. Riotto, F. Sala, A. Strumia, A. Urbano (arxiv: ) 10 1 dn dlog 10 E Figure: e + (green), p (blue), γ (red), ν = (ν e + ν µ + ν τ )/3 (black) Assumptions: SM up to M > M W, extended preserving gauge invariance. The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

7 Effects of radiative weak corrections P.C., D. Comelli, A. Riotto, F. Sala, A. Strumia, A. Urbano (arxiv: ) 10 1 dn dlog 10 E Figure: e + (green), p (blue), γ (red), ν = (ν e + ν µ + ν τ )/3 (black) Assumptions: SM up to M > M W, extended preserving gauge invariance. The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

8 Effects of radiative weak corrections Why do weak corrections have such a big effect on the spectrum? I) Weak corrections not so weak at the TeV scale II) Soft gauge bosons emission high multiplicity, soft spectrum greatly enhanced III) Weak interactions connect all SM particles The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

9 Effects of radiative weak corrections Why do weak corrections have such a big effect on the spectrum? I) Weak corrections not so weak at the TeV scale II) Soft gauge bosons emission high multiplicity, soft spectrum greatly enhanced III) Weak interactions connect all SM particles The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

10 Effects of radiative weak corrections Why do weak corrections have such a big effect on the spectrum? I) Weak corrections not so weak at the TeV scale II) Soft gauge bosons emission high multiplicity, soft spectrum greatly enhanced III) Weak interactions connect all SM particles The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

11 Effects of radiative weak corrections Why do weak corrections have such a big effect on the spectrum? I) Weak corrections not so weak at the TeV scale II) Soft gauge bosons emission high multiplicity, soft spectrum greatly enhanced III) Weak interactions connect all SM particles The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

12 EW corrections - I Σ Σ % s Figure: 1 loop EW and RGE relative corrections to σ(e + e µ + µ ) as a function of the c.m. energy in GeV. The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

13 EW corrections - I e e p 1 k p 2 Virtual e + + Real e + + d 3 k ω (p 1 p 2 ) (p 1 k)(p 2 k) dω dθ ω θ σ V + σ R σ B (1 α log 2 α log2 E λ s 2 ) (σ V + σ R ) Resum σ B exp[ α log 2 s 2 ] The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

14 EW corrections - I e e p 1 k p 2 Virtual e + + Real e + + d 3 k ω (p 1 p 2 ) (p 1 k)(p 2 k) dω dθ ω θ σ V + σ R σ B (1 α log 2 α log2 E λ s 2 ) (σ V + σ R ) Resum σ B exp[ α log 2 s 2 ] The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

15 EW corrections - I e e p 1 k p 2 Virtual e + + Real e + + d 3 k ω (p 1 p 2 ) (p 1 k)(p 2 k) dω dθ ω θ σ V + σ R σ B (1 α log 2 α log2 E λ s 2 ) (σ V + σ R ) Resum σ B exp[ α log 2 s 2 ] The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

16 EW corrections - I e Z e + + σ σ B exp[ α w log 2 s ] M 2 no need to add real emission α w log 2 s M 2 M = M Z M W 10 % at 1 TeV: Dominant contribution. Higher orders? The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

17 EW corrections - I e Z e + + σ σ B exp[ α w log 2 s ] M 2 no need to add real emission α w log 2 s M 2 M = M Z M W 10 % at 1 TeV: Dominant contribution. Higher orders? The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

18 EW corrections - I e Z e + + σ σ B exp[ α w log 2 s ] M 2 no need to add real emission α w log 2 s M 2 M = M Z M W 10 % at 1 TeV: Dominant contribution. Higher orders? The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

19 EW corrections - I Inclusive observables Include real emission "infrared safe, no large logs? The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

20 EW corrections - I Early Unification Σ Σ % E GeV Figure: QCD ( αs αs π ) and EW ( π log2 s ) corrections to e + e 2j + X MW 2 The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

21 EW corrections - I BN Violation s M 2 W σ e log 2 + σ ν log 2 s MW 2 What about IR theorems? 0 A neat example of the effects of spontaneous symmetry breaking! The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

22 EW corrections - I BN Violation s M 2 W σ e log 2 + σ ν log 2 s MW 2 What about IR theorems? 0 A neat example of the effects of spontaneous symmetry breaking! The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

23 EW corrections - I BN Violation s M 2 W σ e log 2 + σ ν log 2 s MW 2 What about IR theorems? 0 A neat example of the effects of spontaneous symmetry breaking! The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

24 EW corrections - I Where we stand Fixed order calculations (up to 2 loops) and resummations (Comelli, M.Ciafaloni, P.C, Pozzorini, Denner, Kühn, Melles, Fadin,...) Asymptotic behaviour ( s >>> MW 2 ) for fully inclusive and fully exclusive observables can be written in terms of external legs quantum numbers. Surprise! Charge violating amplitudes can grow indefinitely with energy! The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

25 EW corrections - I Where we stand Fixed order calculations (up to 2 loops) and resummations (Comelli, M.Ciafaloni, P.C, Pozzorini, Denner, Kühn, Melles, Fadin,...) Asymptotic behaviour ( s >>> MW 2 ) for fully inclusive and fully exclusive observables can be written in terms of external legs quantum numbers. Surprise! Charge violating amplitudes can grow indefinitely with energy! The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

26 EW corrections - I Where we stand Fixed order calculations (up to 2 loops) and resummations (Comelli, M.Ciafaloni, P.C, Pozzorini, Denner, Kühn, Melles, Fadin,...) Asymptotic behaviour ( s >>> MW 2 ) for fully inclusive and fully exclusive observables can be written in terms of external legs quantum numbers. Surprise! Charge violating amplitudes can grow indefinitely with energy! The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

27 EW Corrections - II High Multiplicity Factorization: σ i = σ B P i Unitarity: σ TOT = σ B (P 0 + P 1 + P ) = σ B As energy grows, P 0 0 and probability shifted towards higher i s One hard (TeV) positron becomes 1000 soft (GeV) particles The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

28 EW Corrections - II High Multiplicity Factorization: σ i = σ B P i Unitarity: σ TOT = σ B (P 0 + P 1 + P ) = σ B As energy grows, P 0 0 and probability shifted towards higher i s One hard (TeV) positron becomes 1000 soft (GeV) particles The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

29 EW Corrections - II High Multiplicity Factorization: σ i = σ B P i Unitarity: σ TOT = σ B (P 0 + P 1 + P ) = σ B As energy grows, P 0 0 and probability shifted towards higher i s One hard (TeV) positron becomes 1000 soft (GeV) particles The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

30 EW Corrections - II High Multiplicity Factorization: σ i = σ B P i Unitarity: σ TOT = σ B (P 0 + P 1 + P ) = σ B As energy grows, P 0 0 and probability shifted towards higher i s One hard (TeV) positron becomes 1000 soft (GeV) particles The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

31 EW Corrections - III Electroweak cascade DM Z p e µ + µ µ e e e + The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

32 Calculating spectra of stable particles M z M x M DM D EW D MC I I J J J f dn I f d ln x (M, x) = J 1 x dz D EW I J(z) D MC J f ( ) x z I, J = W ± T,L, e± L,R,.. f = e±, γ, p, ν The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

33 Calculating spectra of stable particles EW Evolution Equations D EW I J (z, µ2 ) ln µ 2 = α 2 2π k 1 x D EW I J(z, µ 2 = s) = δ IJ δ(1 z); EW kernels P EW feature log µ 2 terms, therefore: dy y PEW I K(y, µ 2 ) D EW K J(z/y, µ 2 ). D EW I J(z) = D 2 (z) ln 2 M M W + D 1 (z) ln M M W + D 0 (z) Generically neglect D 0, however for x 0 and x 1... The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

34 A side remark P x (1!x) E M V E x E x P coll V V (x) = [ x 1 x + 1 x x + x(1 x)] ln E2 MV 2 Improve through eikonal approximation: P V V (x = M V E, 1 M V E ) = 0 Possibly relevant also for "Effective W approximation" The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

35 A side remark P x (1!x) E M V E x E x P coll V V (x) = [ x 1 x + 1 x x + x(1 x)] ln E2 MV 2 Improve through eikonal approximation: P V V (x = M V E, 1 M V E ) = 0 Possibly relevant also for "Effective W approximation" The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

36 A side remark P x (1!x) E M V E x E x P coll V V (x) = [ x 1 x + 1 x x + x(1 x)] ln E2 MV 2 Improve through eikonal approximation: P V V (x = M V E, 1 M V E ) = 0 Possibly relevant also for "Effective W approximation" The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

37 Primary Spectra dn dlog 10 E 10 1 dn dlog 10 E Figure: Comparison between spectra with (continuous lines) and without EW corrections (dashed). The final states are: e + (green), p (blue), γ (red), ν = (ν e + ν µ + ν τ )/3 (black). The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

38 W L at M 3000 GeV dn dlog 10 E 1 dn dlog 10 E E in GeV e L at M 3000 GeV Μ L at M 3000 GeV dn dlog 10 E 10 1 dn dlog 10 E E in GeV E in GeV The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

39 Effects of propagation - an example PAMELA Positron fraction 10 3 p p PAMELA background? 1 background? p kinetic energy in GeV Figure: DM signals in the e + (left) and p (right) fraction, with (dashed) and without (dot-dashed) electroweak corrections for a W T + W T channel. The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

40 Opening forbidden channels vσ = a + bv 2 ; v 10 3 χχ f f a = 0 χχ f f V a 0 (ang. mom. cons., C arguments fail) full this work 10 LO dn d lnx p Γ Ν e The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

41 Thermal abundance d(na 3 ) a 3 dt = vσ eff (n 2 n 2 eq); vσ eff = abf r a r b (σ χ a χ b ff + σ χ a χ b ffw) r a = neq a n a δ a0 + for a = Ma χ M 0 χ M 0 χ c ND c D 10 Σ00 Σ 00 H 10 1 c ND c D 4 c ND c D The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

42 Conclusions (Summary) "One-loop Bloch-Nordsieck Theorem": [ M ] (0) + M (1) 2 dπ W M 2 IR ab f +W = 0 a,b,f ab f + ( αw IR = O 4π logn s m 2 W Large BN violating corrections: LHC, ILC: isolated initial charges. Indirect DM: not fully inclusive energy spectra. Early Universe: decoupled heavy states. ) ; n = 1, 2 The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

43 Conclusions (Summary) "One-loop Bloch-Nordsieck Theorem": [ M ] (0) + M (1) 2 dπ W M 2 IR ab f +W = 0 a,b,f ab f + ( αw IR = O 4π logn s m 2 W Large BN violating corrections: LHC, ILC: isolated initial charges. Indirect DM: not fully inclusive energy spectra. Early Universe: decoupled heavy states. ) ; n = 1, 2 The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

44 Conclusions (Summary) "One-loop Bloch-Nordsieck Theorem": [ M ] (0) + M (1) 2 dπ W M 2 IR ab f +W = 0 a,b,f ab f + ( αw IR = O 4π logn s m 2 W Large BN violating corrections: LHC, ILC: isolated initial charges. Indirect DM: not fully inclusive energy spectra. Early Universe: decoupled heavy states. ) ; n = 1, 2 The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

45 Conclusions (Summary) "One-loop Bloch-Nordsieck Theorem": [ M ] (0) + M (1) 2 dπ W M 2 IR ab f +W = 0 a,b,f ab f + ( αw IR = O 4π logn s m 2 W Large BN violating corrections: LHC, ILC: isolated initial charges. Indirect DM: not fully inclusive energy spectra. Early Universe: decoupled heavy states. ) ; n = 1, 2 The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

46 Conclusions (Summary) "One-loop Bloch-Nordsieck Theorem": [ M ] (0) + M (1) 2 dπ W M 2 IR ab f +W = 0 a,b,f ab f + ( αw IR = O 4π logn s m 2 W Large BN violating corrections: LHC, ILC: isolated initial charges. Indirect DM: not fully inclusive energy spectra. Early Universe: decoupled heavy states. ) ; n = 1, 2 The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

47 Conclusions (Summary) "One-loop Bloch-Nordsieck Theorem": [ M ] (0) + M (1) 2 dπ W M 2 IR ab f +W = 0 a,b,f ab f + ( αw IR = O 4π logn s m 2 W Large BN violating corrections: LHC, ILC: isolated initial charges. Indirect DM: not fully inclusive energy spectra. Early Universe: decoupled heavy states. ) ; n = 1, 2 The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

48 Extra slide The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26

49 QED QCD QCD EW M Figure: Equazioni di evoluzione IR. Sotto M: QED, QCD Sopra M: QCD, "symmetric" EW con 4 gauge bosons degeneri. σ = f (µ 2 ) σ H (E); = P(µ 2 ) f f log µ 2 The role of ElectroWeak corrections in indirect Dark Matter searches Firenze, 18/12/ / 26