Dilepton transverse momentum in the color dipole approach

Transcription

1 Dilepton transverse momentum in the color dipole approach M. B. Gay Ducati Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil Seminar based on work with M.A. Betemps, MBGD, M.V.T. Machado and J. Raufeisen (hep-ph/ ) M.B. Gay Ducati - DIS April / St. Petersburg p.1

2 Motivations The Drell-Yan (DY) process can be studied similarly to the DIS through the dipole approach; At small-x, the dipole cross section is driven by the gluon content of the target; Investigation of the gluon content through the Drell-Yan process at high energies; The unitarity effects can be studied in the dipole cross section; In the dipole approach DY distribution is finite for small values. Reliable estimates for the recent experiments RHIC and LHC can be done; M.B. Gay Ducati - DIS April / St. Petersburg p.2

3 Color dipole approach DIS in the dipole approach, γ * 1-z γ * r z p σ γ p T,L (x, Q2 ) = p d 2 r q q lifetime >> interaction time factorization of the cross section dz Ψ q q T,L (z, r; Q2 ) 2 σ dipole (x, r). σ dipole (x, r) interaction of the dipole q q with the nucleon. coherence length (q q lifetime) l c 1 2m N x, small-x high energy M.B. Gay Ducati - DIS April / St. Petersburg p.3

4 gated for pa collisions at RHIC and LHC energies. In particula nuclear parton distributions that describes the present nuclear ea the DGLAP approach including the high density effects introduc bative Glauber-Mueller approach. Drell-Yan in the dipole approach N q(x 1 /α) γ (α) g(x 2 ) l r l + N Where is the Dipole? dσ T,L (qn qγ N) d ln α q r photon-quark transverse separation, αr q q (dipole) transverse separation, α quark light-cone momentum fraction carried by the photon, x 1 /α projectile momentum fraction carried by the quark, x 2 target momentum fraction carried by the gluon. tranverse momentum of the lepton pair. M 2 squared lepton pair mass. x F = x 1 x 2. = d 2 r Ψ T,L γ q (α, r) 2 σ q q dip (x 2, αr) The differential Drell-Yan cross section can be written as d σ DY dm 2 dx F d 2 = α em 6 πm 2 1 (x 1 +x 2 ) 1 x 1 dα α F p 2 ( x1 α ) dσ(qn qγ N) d ln αd 2 M.B. Gay Ducati - DIS April / St. Petersburg p.4

5 Drell-Yan in the dipole approach We can write such cross section as, d σ DY dm 2 dx F d 2 = α2 em 6 π 3 M 2 1 (x 1 +x 2 ) 0 dρw (ρ, )σ dip (ρ) Explicit dependence on the dipole cross section. ρ αr dependence of the cross section large αr non-perturbative sector small αr perturbative sector σ dip W (ρ, ) should be considered as a weight function M.B. Gay Ducati - DIS April / St. Petersburg p.5

6 Weight Function W (ρ, ) = 1 dα x 1 x 1 α 2 α F 2(x 1 /α, M 2 ) { [ [m 2 qα 4 + 2M 2 (1 α) 2 ] + [1 + (1 α) 2 ] 1 p 2 T + T 1(ρ) 1 η2 [ ηpt p 2 T + T 3(ρ) T 1(ρ) η2 2 ] 4η T 2(ρ) ]} + η 4 T 2(ρ) where with T 1 (ρ) = ρj 0 ( ρ/α)k 0 (ηρ/α)/α T 2 (ρ) = ρ 2 J 0 ( ρ/α)k 1 (ηρ/α)/α 2 T 3 (ρ) = ρj 1 ( ρ/α)k 1 (ηρ/α)/α. η = (1 α)m 2 + α 2 m 2 q M.B. Gay Ducati - DIS April / St. Petersburg p.6

7 Drell-Yan cross section features For the integrated weight function we obtain W (ρ,m 2 ) (GeV) 2e 04 2e 04 1e 04 5e 05 0e e 06 Transverse M = 5 GeV M = 7 GeV M = 10 GeV Longitudinal Large ρ contribution are suppressed Small contribution of the non-perturbative piece a 4e 06 2e 06 0e ρ (fm) a M.A. Betemps,MBGD, M.V.T. Machado, Phys. Rev. D (2002) M.B. Gay Ducati - DIS April / St. Petersburg p.7

8 Drell-Yan cross section features Concerning W (ρ, ) W(ρ, ) (GeV 1 ) 3e 04 2e 04 1e 04 0e+00 1e 04 = 0 GeV = 1 GeV = 4 GeV s 1/2 = 500 GeV Large ρ contribution are not highly suppressed. Significative contribution from the nonperturbative sector. 2e ρ (fm) M.B. Gay Ducati - DIS April / St. Petersburg p.8

9 Dipole cross section In the double logarithmic approximation, σ GM dip (x, r) = π2 α s 3 r2 xg GM (x, Q 2 ), Q 2 = λ/r 2, λ = 4 xg GM (x, Q) is the Glauber-Mueller gluon distribution xg GM (x, Q 2 )= 4 π 2 1 x dx x 4 Q 2 d2 r πr 4 S(b) (Gaussian parametrization) σ GG (x, r) = 3α s(4/r 2 ) 4 0 d 2 b π {1 e 1 2 σgg (x,r)s(b) }. π 2 r 2 [ xg DGLAP ( x, 4 r 2 )]. GRV 94 AGL (A.L. Ayala, MBGD and E. Levin) approach a. Non-perturbative sector r freezing. a Nucl. Phys. B511, 355 (1998) M.B. Gay Ducati - DIS April / St. Petersburg p.9

10 Dipole cross section The phenomenological saturation model of Bartels et al. (BGBK) b σ dip (x, ρ) = σ 0 {1 exp ( π2 ρ 2 α s (µ 2 )xg(x, µ 2 )} ) 3σ 0, µ 2 = C + µ 2 ρ 2 0, xg(x, Q2 0 ) = A gx λ g (1 x) 5.6 There are five free parameters (σ 0, C, µ 2 0, A g and λ g ), which have been determined by fitting ZEUS, H1 and E665 data with x < We employ parameters from FIT 1. (σ 0 = mb is fixed, C = 0.26, µ 2 0 = 0.52, A g = 1.2, λ g = 0.28.) b Phys. Rev. D66, (2002) M.B. Gay Ducati - DIS April / St. Petersburg p.10

11 Low energy data Current data on DY reactions x 2 is around 0.1, Low energy non-asymptotic quark-like content (Reggeon contribution) added to the GM dipole cross section The suitable Reggeon parametrization for all ranges is σdip IR (x, r) = N IR r 2 x q val (x, 4/r 2 ), Good description of the mass distribution (E772 data). E772 data N IR = 7 a a M.A.Betemps,MBGD, M.V.T. Machado. Phys. Rev. D66, (2002) M.B. Gay Ducati - DIS April / St. Petersburg p.11

12 Low energy distribution data s 1/2 =62 GeV 5<M<8 GeV Good agreement with (cm 2 /GeV 2 ) dσ/d CERN R209 data GM (+ reggeon) BGBK (fit 1) the distribution data s = 62 GeV (σ0 = 7) Regge contribution GM GRV (GeV) BGBK CTEQ At these energies, negligible unitarity corrections are in the Glauber-Mueller approach M.B. Gay Ducati - DIS April / St. Petersburg p.12

13 RHIC and LHC DY distribution 10 1 At RHIC and LHC energies the DY distribution in pp collision (x F = 0.625) M 2 d 4 σ/dx F dm 2 d 2 (pb GeV 2 ) RHIC GRV94 GM distribution GRV 98 BGBK s 1/2 =500 GeV M=6.5 GeV x F =0.625 M 2 d 4 σ/dx F dm 2 d 2 (pb GeV 2 ) GRV94 GM distribution GRV98 BGBK LHC s 1/2 =14 TeV M=6.5 GeV x F = (GeV) (GeV) Large unitarity effects at high small ρ. Negligible Regge contribution. M.B. Gay Ducati - DIS April / St. Petersburg p.13

14 RHIC and LHC DY distribution 10 4 At RHIC and LHC energies the DY distribution in pp collision (x F = 0) M 2 d 4 σ/dx F dm 2 d 2 (pb GeV 2 ) RHIC GM distribution BGBK s 1/2 =500 GeV M=6.5 GeV x F =0 M 2 d 4 σ/dx F dm 2 d 2 (pb GeV 2 ) GRV94 GM distribution GRV98 BGBK LHC s 1/2 =14 TeV M=6.5 GeV x F = (GeV) (GeV) Small unitarity effects at x F = 0. Small Regge contribution at RHIC energies. M.B. Gay Ducati - DIS April / St. Petersburg p.14

15 Conclusions Investigation of the gluon content through the Drell-Yan process at high energies. Good description of the low energy data using GM + Regge (all range). At RHIC energies the unitarity effects can be absorbed if we consider updated parametrizations (x at large x F ). The unitarity effects are quite sizeable at high energies (LHC), at both large and x F (rapidity). Unitarity corrections are not sizeable in the central rapidity region (y = 0) even at LHC energies. M.B. Gay Ducati - DIS April / St. Petersburg p.15