2/10/20161 What can we learn with Drell-Yan in p(d)-nucleus collisions Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory Collaborations with Dominguez, Kang, Marquet, Xiao

Outline Drell-Yan lepton pair production at small-x Universality of the Quark distribution between DIS and Drell-Yan Unique opportunity for Drell-Yan process in p(d)-nucleus collisions 2/10/20162

Beautiful data from HERA Both Parton Model with DGLAP and Dipole can describe the data 2/10/20163 GBW 98’

Twist expansion Leading twist expansion of the dipole formalism contains large Log(Q 2 )  Bartels et al, 2009  Stasto et al, 2010, Anna’s talk Saturation scale in proton is small at HERA energy, both DGLAP and dipole (CGC) can describe the DIS data 2/10/20164

Equivalently, quark distribution in dipole Integrated quark distribution has Ultraviolet divergence 2/10/20165 GBW model McLerran-Venugopalan 99 Mueller 1999 Xiao-Yuan, 2010

Parton distributions contain the non- perturbative (saturation) physics  As an input in the DGLAP fit  Model in the dipole formalism Saturation will be manifest when hard scale Q in order of Qs  Inclusive observables Or the processes which are sensitive to kt-dependent parton distributions  Semi-inclusive observables 2/10/20166

Inclusive observables Q in the same order of Qs, and both have to be large Dipole (CGC) formalism Taking Q->0 limit will lead to infrared divergence 2/10/20167 GBW model

Sensitive to the quark mass when Q=0  GBW 98, Log(mq^2) Associated with the real photon splitting to quark pair  Can be absorbed into the quark distribution in real photon (resolved photon) Small Q prediction is strongly model- dependent (wrong practice)  It works amazing well though, which might have nothing to do with saturation physics 2/10/20168

Pt dependent observables Inclusive pt spectrum in pA collisions  Requires large transverse momentum, probes the perturbative region of unintegrated gluon distributions Semi-inclusive processes, additional hard scale  Probe the broader range of UGD  However, Couple with other pt-dependent quantities 2/10/20169 Al’s talk

Inclusive cross section  Invariant mass not so large compared to the saturation scale Pt dependent observables  Directly probe the unintegrated gluon distributions  Correlation of DY-hadron Al’s, Bowen’s talks 2/10/201610

How relevant is the saturation scale at RHIC 2/10/ A 1/3 For typical Range of lepton Pair mass at RHIC, Saturation Is going to Be important DGLAP shadowing Will not be enough Jamal’s talk Anna’s talk

Advantage of Low Pt Drell-Yan Direct probe for the transverse momentum dependence of partons  Saturation effects explicitly show up in the transverse momentum distribution Factorization can be argued for large Q Related to the TMD factorization Complementary study in SIDIS 2/10/201612

Drell-Yan Process at small-x What are the relevant scales  Q, virtuality of the photon  Pt, transverse momentum of hadron  Qs, saturation scale We are interested in the region of Q>>Qs, Pt  TMD factorization makes sense 2/10/201613

Color-dipole, CGC formalism 2/10/ Al and Jamal’s talks

Keep the leading power contribution, transverse momentum decouples from the mass of the lepton pair M Small kt limit: M>>p T 2/10/201615

Quark distribution can be calculated The same quark distribution appears in SIDIS cross section, Marquet-Xiao-Yuan 08 It’s Universal 2/10/ McLerran-Venugopalan 98

TMD factorization 2/10/201617

Up to this order Trivial factors from  Soft factor  Fragmentation function  Hard factor These effects and the Sudakov form factor will be important when go beyond this order 2/10/201618

Interesting properties 2/10/ Mueller 99; McLerran-Venugopalan 99

Quark distribution at different x 20 Ratio relative to that at 10 -2

Applications: simple TMD 2/10/ Spin-average one: Spin-dependent one: Calculated from CGC

Pt dependence of the Nuclear suppression 2/10/ With smearing effects See also, Guo,Qiu,Zhang, 00

SSA at low P T Cross section dominated by low transverse momentum UGD 2/10/201623

SSA at high P T Cross section is dominated by large pt UGD Ratios 2/10/201624

Pt dependence for A N 2/10/ pp pA Illustration purpose Trivial assumption For the Sivers Function Full calculations Underway Similar analysis for Pion A N

26 Summary Drell-Yan lepton pair production in p(d)nucleus collisions provide opportunities to detailed studying saturation physics, in particular, the pt dependence in  Very clean place to test the Nuclear shadowing  Spin asymmetries

Scaling in Forward hadron production 2/10/ H Quark distribution From the projectile Dense medium Dumitru-Jalilian-Marian, 02 Dumitru-Hayashigaki-Jalilian-Marian, 06

Simple power counting Forward region is dominated by the valence quark distribution (1-x) 3 Similar power behavior for the fragmentation function, (1-z) 1~2, Pt-dependent-Geometric scaling, Similar study by McLerran- Praszalowicz, 10 2/10/201628

Scaling in pp collisions 2/10/ BRAHMS: 2 rapidity bins STAR: 3 rapidity bins

Geometric Scaling for R pA ? 2/10/ R ratio depends on the difference in the saturation scales More data are needed to draw conclusion

Phenomenology: quark distributions ratios 31 Transverse Mometum Broading with Q GBW model for dipole Cross section

Dipole picture for DIS 2/10/ Fragmentation function

Dipole picture for DIS 2/10/ Fragmentation function

SIDIS Differential Cross section 2/10/ Unintegrated gluon dis.

TMD limit: Q>>p T Keep the leading power contribution, neglect all higher power corrections 2/10/201635