k T approaches in Drell-Yan dilepton

Confronting color dipole and intrinsic k T approaches in Drell-Yan dilepton production E.G. de Oliveira a, M.B. Gay Ducati a and M.. Betemps ab emmanuel.deoliveira@ufrgs.br a High Energy Physics Phenomenology Group (GFPE), Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto legre, RS, Brazil http://www.if.ufrgs.br/gfpae b Conjunto grotécnico Visconde da Graça (CVG), Universidade Federal de Pelotas, Pelotas, RS, Brazil Based on work Phys. Rev. D. 74, 09400 (2006) and in progress. E.G. de Oliveira II LWHEP 2007 p.

Motivation In this work it is provided a study of the dilepton production in the proton-nucleus and proton-proton collisions at backward rapidities. Since dileptons do not interact strongly with the final environment, they are relevant to understand initial state effects. In a collision like p, there is an asymmetry between forward and backward rapidities, which gives new possibilities of measurements and study. lso, to understand how dilepton transverse momentum arises in hadron collisions is a important research subject. Two different phenomenological models that take into account the transverse momentum spectrum of dilepton distributions are studied here: intrinsic parton transverse momentum framework and color dipole approach. Furthermore, the nuclear effects are one of our subjects: as it will be seen, these effects are very important and produce visible changes in the nuclear modification ratio at backward rapidities. E.G. de Oliveira II LWHEP 2007 p. 2

Dilepton in the dipole approach Dilepton production at backward rapidities in the color dipole framework considers, in p collisions, the proton at rest and the nucleus as the projectile. The scattering is understood in the following way (B. Z. Kopeliovich, J. Raufeisen,. V. Tarasov, M. B. Johnson, Phys. Rev. C 67, 04903, 2003): The nucleus emits a quark. The emitted quark fluctuates into a state of a quark plus a massive photon. The quark interacts with a parton from the proton, freeing the massive photon. The virtual photon subsequently decays into a lepton pair. The dipole cross section arises as the interference of the two different diagrams involved, as shown in detail in J. Raufeisen, J.C. Peng, G.C. Nayak, Phys. Rev. D 66, 034024 (2002). Nucleus Nucleus q γ l + l q γ Proton Proton The interaction time between the projectile quark and the proton must be much shorter than the time of fluctuation of the quark-photon state (small x ). E.G. de Oliveira II LWHEP 2007 p. 3

Dilepton at negative rapidities The differential cross section in p T is written as (M.. Betemps, M.B. Gay Ducati, M.V.T. Machado, J. Raufeisen, Phys. Rev. D 67, 4008; B. Kopeliovich, [hep-ph/9609385]): dσ DY dm 2 dyd 2 p T = α2 em 6π 3 M 2 Z 0 dρw(x 2, ρ, p T )σ dip (x, ρ), in which p T is the dilepton transverse momentum, M is the dilepton mass, y is the rapidity, and ρ is the dipole transverse separation. q The variables x and x 2 are given by x,2 = (M 2 + p 2 T )/s exp[±y], and s is the squared center of mass energy. Backward rapidities (y < 0) imply x 2 > x. W(x 2, ρ, p T ) depends on a nuclear structure function F 2 ( x 2 α, M 2 ), which encloses the nuclear effects: W(x 2, ρ, p T ) = Z x 2 dα α 2 F 2 ( x 2 α, M2 ) + [ + ( α) 2 ] " ( " # [m 2 qα 2 + 2M 2 ( α) 2 ] p 2 T + T (ρ) η2 4η T 2(ρ) ηp T p 2 T + η2 T 3(ρ) 2 T (ρ) + η 4 T 2(ρ) where α is the momentum fraction of the quark carried by the virtual photon, η 2 = ( α)m 2 + α 2 m 2 E.G. de Oliveira II LWHEP 2007 p. 4 q and m q is the quark mass (m q = 0.2 GeV). #),

Dilepton at negative rapidities The functions T i are given by: T (ρ) = ρ α J pt ρ ηρ 0 K 0 α α T 2 (ρ) = ρ2 α 2 J pt ρ ηρ 0 K α α T 3 (ρ) = ρ α J pt ρ ηρ K. α α lso, the nuclear structure function, given by F 2 (x, M 2 ) = X q e 2 q[xf q (x, M 2 ) + xf Ā q (x, M 2 )], () is considered to take into account the nuclear projectile content. For pp collisions the nuclear structure function F 2 (x 2/α, M 2 ) needs to be replaced by the proton structure function F p 2 (x 2/α, M 2 ). E.G. de Oliveira II LWHEP 2007 p. 5

Nuclear parton distributions Nuclear parton distribution functions (NPDFs) are calculated from free proton PDFs. The parametrization GRV98 is used to determine the latter ones. Two different approaches are used: Eskola, Kolhinen and Salgado (EKS) parametrization gives NPDFs simply by multiplying proton PDFs by a factor: fq (x, Q 2 0 ) = R q (x, Q 2 0 )fp q (x, Q 2 0 ). D. de Florian and R. Sassot (nds) parametrization obtains NPDFs from proton PDFs by a convolution: fq (x, Q 2 0 ) = R dy x y W q(y, )fq p x y 0, Q2. The ratio between nuclear structure functions RF 2 = F2 /F p 2 is used to compare NPDFs. EKS predicts smaller ratios in both ECM and shadowing regions than nds parametrization:.8.6 nds EKS M=6 GeV.4 /.F 2 p =F 2 R F2.2 0.8 shadowing small x 0.6 large x 0.4 0 5 0 4 0 3 0 2 0 0 0 x E.G. de Oliveira II LWHEP 2007 p. 6

Dipole cross section σ dip The phenomenological model proposed by Golec-Biernat and Wüsthoff (GBW) is used for the dipole cross section. σ dip (x, r) = σ 0» exp r2 Q 2 «0 4(x/x 0 ) λ, where Q 2 0 = GeV2 and fitted parameters σ 0 = 23.03 mb, x 0 = 3.04 0 4 and λ = 0.288. This model presents two asymptotic behaviors: Color transparency behavior σ dip ρ 2 for small ρ Flat (saturated) behavior σ dip σ 0 for large ρ. 30 GBW 20 σ dip (x,r) (mb) 0 0 0 0.5.5 2 r (GeV) E.G. de Oliveira II LWHEP 2007 p. 7

Color dipole results (RHIC-EKS) Ratio,00,075,050,025,000 0,975 0,950 0,925 0,900 0,875 0,850 0,825 0 2 p T 3 RHIC - EKS 4 5 6 7 -,0 -,2 -,4 -,6-2,2-2,0 -,8 y -2,4-2,6 Nuclear modification ratio R p = dσ(p) dp 2 T dydm ffi dσ(pp) dp 2 T dydm. Dilepton mass: M = 6 GeV. RHIC energies: s = 200GeV. 0.08 < x 2 < 0.5; large x effect. Lower y larger x 2 ;.8.6.4 nds EKS M=6 GeV Larger p T larger x 2 ; The ratio R F 2 decreases at large x 2 large x nuclear effect. /F 2 p =F 2 R F2.2 0.8 M.. Betemps, M. B. Gay Ducati, EGO; Phys. Rev. D. 74, 09400 (2006). 0.6 0.4 0 5 0 4 0 3 0 2 0 0 0 x E.G. de Oliveira II LWHEP 2007 p. 8

Color dipole results (RHIC-nDS),00 0.08 < x 2 < 0.5; Ratio,075,050,025,000 0,975 0,950 0,925 0,900 0,875 0,850 0,825 0 2 p T 3 4 RHIC nds 5 6 7 -,0 -,2 -,4 -,6-2,2-2,0 -,8 y -2,4-2,6 large x effect. Lower y larger x 2 ; Larger p T larger x 2 ; R F 2 decreases at large x 2 large x effect less intense than the EKS case; Comparison EKS nds (large x effect predictions)..8.6.4 nds EKS M=6 GeV Conclusion: Rapidity and p T distributions at RHIC in the backward rapidities present large x nuclear effects. /F 2 p =F 2 R F2.2 0.8 0.6 0.4 0 5 0 4 0 3 0 2 0 0 0 x Ratio,00,075,050,025,000 0,975 0,950 0,925 0,900 0,875 0,850 0,825 0 2 p 3 -,0 -,2 -,4 -,6 -,8-2,0 E.G. de Oliveira II LWHEP 2007 p. 9

Color dipole results (LHC-EKS) /F 2 p =F 2 R F2.8.6.4.2 0.8 0.6 Ratio,00,075,050,025,000 0,975 0,950 0,925 0,900 0,875 0,850 0,825 0,800 0,775 LHC EKS nds EKS -5-4 -3 y -2 - M=6 GeV 0 23 4 567 p T 8 LHC energies s = 8800 GeV. 0.002 < x 2 < 0.3; antishadowing and shadowing nuclear effects. Peak at y 4.5 antishadowing effect; Two behaviors with p T : Suppression in p T large x effect (very backward); Decreasing with p T shadowing effect; M.. Betemps, M. B. Gay Ducati, EGO; Phys. Rev. D. 74, 09400 (2006). 0.4 0 5 0 4 0 3 0 2 0 0 0 x E.G. de Oliveira II LWHEP 2007 p. 0

Color dipole results (LHC-nDS) /F 2 p =F 2 R F2.8.6.4.2 0.8 0.6 Ratio,00,075,050,025,000 0,975 0,950 0,925 0,900 0,875 0,850 0,825 0,800 0,775 LHC nds nds EKS -5-4 y -3-2 3 456 p T - 0 2 0.4 0 5 0 4 0 3 0 2 0 0 0 x M=6 GeV 7 8 0.002 < x 2 < 0.3. antishadowing and shadowing nuclear effects; Peak at y 5 antishadowing effect; Two behaviors with p T : Suppression in p T large x effect (only at very backward); Decreasing with p T shadowing effect; Weak p T dependence; EKS nds (similar behavior) Conclusion: Rapidity and p T distributions at LHC in the backward rapidities, present large and small x nuclear effects. E.G. de Oliveira II LWHEP 2007 p.

Dilepton at backward-forward Y The ratio R p for dilepton production at backward (EKS and nds nuclear parametrizations) and forward (CGC predictions M.. Betemps, M.B. Gay Ducati, Phys. Rev. D 70, 6005 (2004)) rapidities (RHIC energies)...05 increasing p T 0.95 increasing p T R p 0.9 0.85 0.8 0.75 R p p T behavior. Back p T =2 GeV (EKS) Back p T =2 GeV (nds) Back p T =4 GeV (EKS) Back p T =4 GeV (nds) Back p T =6 GeV (EKS) Forw p T =2 GeV (CGC) Forw p T =4 GeV (CGC) Forw p T =6 GeV (CGC) 0.7 3 2 0 2 3 y 8 < : Forward p T increases R p enlarged ( saturation) Backward p T increases R p reduced ( large x effects) E.G. de Oliveira II LWHEP 2007 p. 2

Drell-Yan process in IMF X q l q γ l X t leading order in the infinite momentum frame, it is the annihilation of a quark-antiquark pair into a virtual boson that splits into the dilepton. gain, PDFs (NPDFs) are needed. This time, we are going to use CTEQ PDFs. The differential cross-section for the Drell-Yan process is (at LO): dσ = X q [f q (x )f q (x B ) + f q (x )f q (x B )] dx dx B e 2 qσ 0 σ 0 = 4πα2 3M 2 E.G. de Oliveira II LWHEP 2007 p. 3

Next-to-leading order diagrams Next-to-leading order diagrams that do not create transverse momentum: Next-to-leading order diagrams that do create transverse momentum: E.G. de Oliveira II LWHEP 2007 p. 4

Intrinsic transverse momentum Other source of transverse momentum can be the intrinsic transverse momentum of the partons. G. ltarelli, G. Parisi, and R. Petronzio, Phys. Lett. 76B, 35 (978); 356 (978). It is usually parameterized by a Gaussian distribution: h(k 2 T ) = 4πb 2 exp «kt 2 4b 2. One can combine intrinsic transverse momentum with partonic cross section transverse momentum with the following integral: Z σ S = h(p 2 T ) dσ dm 2 dy + d 2 q T σ P (s, M 2, q 2 T )[h(( p T q T ) 2 ) h(p 2 T )]. σ tot is the total double differential cross section at NLO and σ P is the contribution from annihilation and Compton diagrams (x a min = (x τ)/( x 2 )): σ P (s, M 2, q 2 T ) = Z x a min dx a x b x a x a x X +[P gq (x a, x b, M 2 ) + P g q (x a, x b, M 2 )] π q ( P q q (x a, x b, M 2 ) 8 α 2 α s e 2 q 2M 2 ŝ + û 2 + ˆt 2 π 27 M 2 ŝ 2 ˆtû ) α 2 α s e 2 q 2M 2 û + ŝ 2 + ˆt 2 9 M 2 ŝ 2 ŝˆt E.G. de Oliveira II LWHEP 2007 p. 5

NLO cross section The double differential Drell-Yan cross section at next-to-leading order is given by: dσ dm 2 dy = ˆσ Z 0 dx dx B dzδ(x x B z τ)δ y s 0 2 ln x «x B 82 3 < 4 X» e 2 : q(f q (x, M)f q (x B, M) + x x B ) 5 δ( z) + α s(m 2 ) 2π q 2 3 + 4 X» e 2 q [f g (x, M)(f q (x B, M) + f q (x B, M)] + x x B 5 αs (M 2 ) 2π q D q (z) 9 = D g (z) ;. In the modified minimum subtraction renormalization scheme (MS), functions D q (z) and D g (z) are given by (C F = 4/3, T R = /2): 2π 2 «D q (z) = C F "δ( z) 3 8 2 + «z2 ln( z) z ln z + 4( + z2 ) z» D g (z) = T R (z 2 + ( z) 2 ( z)2 )ln + z 2 + 3z 7 2 z2. + # E.G. de Oliveira II LWHEP 2007 p. 6

Intrinsic k T results (RHIC-EKS) Ratio..05 Results in the intrinsic transverse momentum formalism (b = 0.48 GeV, mean intrinsic k T 0.6 GeV). 0.95 0.9 0.85 0.80 Ratio 2 p_t,00,075,050,025,000 0,975 0,950 0,925 0,900 0,875 0,850 0,825 0 3 2 p T 4 3 RHIC - EKS 5 4 5 6 6-2.2-2.4 7-2.6 7-2 -,0 -,2 -,4 -,6-2,2-2,0 -,8 y -2,4-2,6 - -.2 -.4 -.6 -.8 y pproximately the same behavior of the ratio is obtained considering RHIC energies and EKS parameterization. For large p T, the intrinsic k T can be neglected and both approaches are similar. For small p T, the Gaussian parameterization of intrinsic k T changes the p T dependence. E.G. de Oliveira II LWHEP 2007 p. 7

Intrinsic k T results (RHIC-nDS) Ratio..05 0.95 0.9 Now we are considering NLO nds parametrization. Results in the intrinsic transverse momentum formalism (b = 0.48 GeV, mean intrinsic k T 0.6 GeV). 0.85 0.80 Ratio 2 p_t,00,075,050,025,000 0,975 0,950 0,925 0,900 0,875 0,850 0,825 0 3 4 2 3 p T RHIC nds 5 4 5 6 6-2.2-2.4 7-2.6 7-2 -,0 -,2 -,4 -,6-2,2-2,0 -,8 y -2,4-2,6 - -.2 -.4 -.6 -.8 y pproximately the same behavior of the ratio is obtained again. For small p T, the Gaussian parameterization of intrinsic k T changes the p T dependence again. E.G. de Oliveira II LWHEP 2007 p. 8

Conclusions The strong dependence of the nuclear structure function ratio R F 2 on the nuclear effects at negative rapidities has been observed. Therefore, the dilepton production at backward rapidities is suitable to understand and quantify the nuclear effects at large and small Bjorken x. For example, at LHC energies and backward rapidities, the p T distribution for the ratio R p presents distinct behaviors in the regions of very backward (large x effects) and of more central rapidities (shadowing). Results in the intrinsic transverse momentum formalism are in qualitative agreement with results in the color dipole formalism. However, for small p T, the Gaussian parameterization of intrinsic k T changes the p T dependence, providing a way to distinguishes both approaches. Following studies will move to consider resummation techniques to improve the model used in the infinite momentum frame. E.G. de Oliveira II LWHEP 2007 p. 9

References M.. Betemps, M.B. Gay Ducati, E.G. de Oliveira, Phys. Rev. D 74, 09400 (2006) BRHMS collaboration, R. Debbe, J. Phys. G 30, S759 (2004). I. rsene et al. The BRHMS Collaboration, Phys. Rev. Lett. 93, 242303 (2004). M.. Betemps, M.B. Gay Ducati, Phys. Rev. D 70, 6005 (2004); Eur. Phys. J. C 43, 365 (2005); Phys. Lett. B 636, 46 (2006). F. Gelis, J. Jalilian-Marian, Phys. Rev. D 66, 09404 (2002). R. Baier,.H. Mueller and D. Schiff, Nucl. Phys. 74, 358 (2004). S.S. dler, et al. PHENIX Collaboration, Phys. Rev. Lett. 94, 082302 (2005). B. Z. Kopeliovich, J. Raufeisen,. V. Tarasov, and M. B. Johnson, Phys. Rev. C 67, 04903 (2003). J. Raufeisen, J.C. Peng, G.C. Nayak, Phys. Rev. D 66, 034024 (2002). M.. Betemps, M.B. Gay Ducati, M.V.T. Machado, J. Raufeisen, Phys. Rev. D 67, 4008 (2003). B.Z. Kopeliovich, In proceedings Workshop Hirschegg 95: Dynamical Properties of Hadrons in Nuclear Matter. Ed. by H. Feldmeier and W. Nörenberg, GSI, Darmstadt, p. 02 (995) [hep-ph/9609385]. S.J. Brodsky,. Hebecker, E. Quack, Phys. Rev. D 55, 2584 (997). M. Glück, E. Reya,. Vogt, Eur. Phys. J. C 5, 46 (998). K.J. Eskola, V.J. Kolhinen, C.. Salgado, Eur. Phys. J. C 9, 6 (999). K.J. Eskola, V.J. Kolhinen, P.V. Ruuskanen, Nucl. Phys. B 535, 35 (998). D. de Florian, R. Sassot, Phys. Rev. D 69, 074028 (2004). K. Golec-Biernat, M. Wüsthoff, Phys. Rev. D 59, 0407 (999); Phys. Rev. D 60, 4023 (999). E.G. de Oliveira II LWHEP 2007 p. 20

References S.D. Drell, T.M. Yan, Phys. Rev. Lett. 25, 36 (970). R.D. Field, pplications of Perturbative QCD, ddison-wesley, Reading, 989. W. Greiner,. Shäfer, Quantum Cromodynamics, Springer, Berlin, 994. R.K. Ellis, W.J. Stirling, B.R. Webber, QCD and Collider Physics, Cambridge University Press, Cambridge, 996. O. Linnyk, S. Leupold, U. Mosel, Phys. Rev. D 75, 0406 (2007) [arxiv:hep-ph/0607305]. E605 collaboration, H.L. Lai et al., Phys. Rev. D50 (994). CDF collaboration, F. be et al., Phys. Rev. D49 (994). W.J. Stirling, M.R. Whalley, J. Phys. G 9 (993). P.L. McGaughey, J.M. Moss, J.C. Peng, nnu. Rev. Nucl. Part. Sci. 49 999. E.G. de Oliveira II LWHEP 2007 p. 2