Photon from the Color Glass Condensate in the pa collision

Transcription

1 Photon from the Color Glass Condensate in the pa collision Sanjin Benić (Tokyo) arxiv: Hard Probes 2016, Wuhan, China, 22 September - 27 September 2016

2 Motivation photon clean probes in pa initial state goal of this work saturation effects in photon spectrum

3 Color Glass Condensate universal form of matter at x 1, Q 2 = fixed saturation scale Q 2 s α s Qs 2 xf g (x, Q 2 s ) πr 2 1 large gluon occupation number classical color fields

4 Photon in pa valence quark bremsstrahung O(α) γ q ρ p ρ A Gelis Jalilian-Marian formula 1 πr 2 A dσ q qγ d 2 k = α π 1 k (1 z)2 dz C(l ) z l l 2 (l k /z) 2 Gelis, Jalilian-Marian, Phys. Rev. D 66 (2002) color dipole: x e il x U(0)U (x )

5 Photon in pa but: high energy (small x) gluon component of the proton wave function becomes dominant new emission processes

6 Power counting proton: gluons more abundant than quarks f q f g nucleus dense, proton dilute ρ p ρ A

7 Photon in pa annihilation O(αα s ) γ q ρ p ρ A SB, Fukushima, arxiv:

8 Photon in pa bremsstrahlung from produced qq O(αα s ) γ q ρ p ρ A SB, Fukushima, arxiv:

9 pa CGC Feynman rules light-cone gauge: n µ A µ = 0, n µ δ µ 1. background gluon field A (1) (x) ρ p ρ p V(x ) ρ A = Gelis, Mehtar-Tani, Phys. Rev. D 73 (2006) Fukushima and Hidaka, Nucl. Phys. A 813 (2008) 171

10 pa CGC Feynman rules light-cone gauge: n µ A µ = 0, n µ δ µ 2. quark propagator S (0) (x, y) U(x ) ρ A = Baltz, McLerran, Phys. Rev. C 58 (1998) 1679

11 Annihilation - amplitude M λ (k) = eg e ik x Tr [ ɛ/ λ (k)s (0) (x, y) /A (1) (y)s (0) (y, x) ] xy

12 Annihilation - amplitude M λ (k) = eg e ik x Tr [ ɛ/ λ (k)s (0) (x, y) /A (1) (y)s (0) (y, x) ] xy γ q ρ p ρ A

13 SB, Fukushima, arxiv: Annihilation - rate 1 πr 2 A S N c e ik r Nc 2 1 xx u u w ) dn d 2 k dy = α α s 16π 8 ( u v 2, u + v 2, u v 2, u + v 2 e il r ϕ p (l ) ( û û Ψ 1 Ψ 1 + Ψ 2 Ψ 2 + 2û ˆl Ψ 1 Ψ 2 l unintegrated gluon distribution g 2 ρ a p(l )ρ a p (l ) δ aa π(nc 2 1) l 2 ϕ p (l ) inelastic quadrupole S(y, z, y, z ) 1 N c Tr c [ U(y )T a F U (z ) ] Tr c [ U(z )T a F U (y ) ] )

14 Remarks photon Ward identity Furry theorem (vanishing of gg γ) UV finite (lowest order is ggg γ) collinear factorization on the proton side chiral limit SB, Fukushima, arxiv:

15 Brems from produced qq - amplitude M λ (k, q, p) = ieg xyz e ik x+iq y+ip z ū(q)(i / y m) { S (0) (y, w) /A (1) (w)s (0) (w, x)ɛ/ λ (k)s (0) (x, z) } + S (0) (y, x)ɛ/ λ (k)s (0) (x, w) /A (1) (w)s (0) (w, z) (i / z + m)v(p)

16 Brems from produced qq - amplitude M λ (k, q, p) = ieg xyz e ik x+iq y+ip z ū(q)(i / y m) { S (0) (y, w) /A (1) (w)s (0) (w, x)ɛ/ λ (k)s (0) (x, z) } + S (0) (y, x)ɛ/ λ (k)s (0) (x, w) /A (1) (w)s (0) (w, z) (i γ q q- / z + m)v(p) ρ p ρ A SB, Fukushima, Garcia-Montero, Venugopalan, in preparation

17 Brems from produced qq - amplitude M λ (k, q, p) = ieg xyz e ik x+iq y+ip z ū(q)(i / y m) { S (0) (y, w) /A (1) (w)s (0) (w, x)ɛ/ λ (k)s (0) (x, z) } + S (0) (y, x)ɛ/ λ (k)s (0) (x, w) /A (1) (w)s (0) (w, z) (i / z + m)v(p) γ q q- ρ p ρ A SB, Fukushima, Garcia-Montero, Venugopalan, in preparation

18 Brems from produced qq - amplitude M λ (k, q, p) = ieg xyz e ik x+iq y+ip z ū(q)(i / y m) { S (0) (y, w) /A (1) (w)s (0) (w, x)ɛ/ λ (k)s (0) (x, z) } + S (0) (y, x)ɛ/ λ (k)s (0) (x, w) /A (1) (w)s (0) (w, z) (i q γ q - / z + m)v(p) ρ p ρ A SB, Fukushima, Garcia-Montero, Venugopalan, in preparation

19 Brems from produced qq - rate 1 dσ αα sn c = πra 2 d 2 k dy d 2 q dy q d 2 p dy p 256π 8 (Nc 2 1) ( e i s + l P ( ) u 2 e i s + l P 2 u u w l s s ) u e i(l P ) w ϕ p(l ) l 2 ( C u v 2, u + v ) 2, u v 2, u + v 2 { [ C µ(p, l, P l )C µ (P, l, P l )Tr D (/q + m)r µν ] g (/p m)r µ gν + l i l i P + P Tr [ + D (/q + m)r iν qq (l, s )(/p m)r i qqν(l, s ) ] + l i P + Cµ(P, l, P l )Tr D [ (/q + m)r µν g (/p m)r i qqν(l, s ) ] + h. c. same Wilson line product as in qq production C(y, z, y, z ) 1 N c Trc [ U(y )T a F U (z )U(z )T a F U (y ) ] } SB, Fukushima, Garcia-Montero, Venugopalan, in preparation

20 Remarks photon Ward identity soft photon theorem collinear factorization Lorenz gauge: µ A µ = 0 leading twist matches to gg qqγ from k -factorization Garcia-Montero, Master thesis (2016) Baranov, Lipatov, Zotov, Phys. Rev. D 77 (2008) SB, Fukushima, Garcia-Montero, Venugopalan, in preparation

21 Color average O[ρp, ρ A ] = [dρ p ][dρ A ]W p [x p ; ρ p ]W A [x A ; ρ A ]O[ρ p, ρ A ] McLerran-Venugopalan model ρ a A (x )ρ b A(y ) = g 2 δ ab µ 2 Aδ (2) (x y ) Qs 2 N2 c 1 g 4 µ 2 A 4N c reasonable for x 10 2 x evolution JIMWLK

22 Annihilation - photon spectrum 10 7 Q s = 5Λ QCD 10 8 Q s = 10Λ QCD 1 πr dn 2 A πr2 p αsng d 2 k dy k /Λ QCD single flavor, chiral limit thin lines: exp ( k 2 + (0.5Q s) 2 /0.5Q s ) thick lines: (log(k /Q s )) 1.5 /k 5.6 SB, Fukushima, arxiv:

23 Annihilation - mass dependence dn dy 1 πr 2 A πr2 p αsng Λ 2 QCD m/λ QCD fit (log(m/λ QCD )) 1.8 /m 2.6 mass corrections important SB, Fukushima, arxiv:

24 Conclusions and outlook complete analytical result at O(αα s ) numerical evaluation of the annihilation diagram sensitivity to quadrupole gluon correlators phenomenological applications bremsstrahlung - numerical evaluation x evolution