eA eRHIC Raju Venugopalan Brookhaven National Laboratory eRHIC discussion group, Oct. 18th 2006

eRHIC at BNL THE PROPOSAL A high energy, high intensity polarized electron/positron beam facility at BNL to colliding with the existing heavy ion and polarized proton beam would significantly enhance RHIC’s ability to probe fundamental, universal aspects of QCD Main Design Ring Ring OptionLinac Ring Option

eRHIC vs. Other DIS Facilities New kinematic region New kinematic region E e = 10 GeV (~5-12 GeV variable) E e = 10 GeV (~5-12 GeV variable) E p = 250 GeV (~ GeV variable) E p = 250 GeV (~ GeV variable) E A = 100 GeV E A = 100 GeV Sqrt[S ep ] = GeV Sqrt[S ep ] = GeV Kinematic reach of eRHIC: Kinematic reach of eRHIC: X = > 0.7 (Q 2 > 1 GeV 2 ) X = > 0.7 (Q 2 > 1 GeV 2 ) Q 2 = 0 --> 10 4 GeV 2 Q 2 = 0 --> 10 4 GeV 2 Polarization of e,p beams (~70%) and He 3 beams ~30-40% polarized Polarization of e,p beams (~70%) and He 3 beams ~30-40% polarized Heavy ions of ALL species at RHIC Heavy ions of ALL species at RHIC Luminosity Goal: Luminosity Goal: L(ep) ~ cm -2 sec - 1 L(ep) ~ cm -2 sec - 1 eRHIC DIS

CM vs. Luminosity eRHIC eRHIC Variable beam energy Variable beam energy P-U ion beams P-U ion beams Light ion polarization Light ion polarization Huge luminosity Huge luminosity eRHIC ELIC-Jlab

Kinematics: Cross-section: g_1,…g_5 - polarized structure functions in pol. e - pol. p scattering

DIS highlights:  Bjorken scaling: the parton model.  Scaling violations: QCD- asymptotic freedom, renormalization group; precision tests of pQCD.  Rapid growth of gluon density at small x, significant hard diffraction.  Measurement of polarized structure functions: scaling violations, the “spin crisis”.  QCD in media: the EMC effect, shadowing, color transparency,..

How can we probe glue with a high luminosity lepton-ion collider ? Key Measurements Precision inclusive measurements of structure functions -wide sweep of nuclei from Protons to Uranium Direct (photon-gluon fusion) semi-inclusive and exclusive probes of final states Deeply virtual Compton scattering - observables in blue will be measured for the first time in a wide kinematic domain - CGC/saturation models predict significant differences from DGLAP type pQCD models for Q_s > (p_t, M)

Lego plots a la Bjorken and Khoze et al. Such multi-gap events can also be studied in DIS Bj, hep-ph/

Bj-scaling - apparent scale invariance of structure functions… Nobel to Friedman, Kendall, Taylor

 Feynman and Bjorken explanation of scaling puzzle… Parton model Parton constituents of proton are “quasi-free” on interaction time scale 1/q Fraction of hadron momentum carried by a parton…

Puzzle resolved in QCD QCD Parton model Logarithmic scaling violations

The Hadron at high energies: I Parton model QCD-logarithmic corrections

“X”-QCD--RG evolution # of valence quarks # quarks… “sea” quarks Valence quarks

DGLAP evolution: Linear RG in Q^2 Dokshitzer-Gribov-Lipatov-Altarelli-Parisi # of gluons grows rapidly at small x…

 Coefficient functions - C - computed to NNLO for many processes, e.g., gg -> H Harlander, Kilgore; Ravindran,Van Neerven,Smith; …  Splitting functions -P - computed to 3-loops recently! Moch, Vermaseren, Vogt + higher twist (power suppressed) contributions… STRUCTURE OF HIGHER ORDER CONTRIBUTIONS IN DIS

increasing But… the phase space density decreases -the proton becomes more dilute Resolving the hadron -DGLAP evolution

RG evolution…

- Large x - Small x Gluon density saturates at f= Resolving the hadron -BFKL evolution

Proton Proton is a dense many body system at high energies QCD Bremsstrahlung Non-linear evolution: Gluon recombination

Mechanism for parton saturation: Competition between “attractive” bremsstrahlung and “repulsive” recombination effects. Maximal phase space density => Saturated for

Need a new organizing principle- beyond the OPE- at small x.  Higher twists (power suppressed-in ) are important when :  Leading twist “shadowing’’ of these contributions can extend up to at small x.

F_L is a positive definite quantity- more sensitive to higher twists than F_2 ? - clarify comparision with leading twist NLO pQCD at low x and moderate

Golec-Biernat & Wusthoff’s model where & Parameters:

Geometrical scaling at HERA Scaling seen for all x < 0.01 and ( Golec-Biernat,Kwiecinski,Stasto)

Comparison with Data FS model with/without saturation and IIM CGC model hp-ph/ Fit F 2 and predict x IP F 2 D(3 ) F2F2 F2F2 FS(nosat) x CGC FS(sat)

Comparison with Data Exclusive J/Psi production: Kowalski-Teaney

R_{A1,A2} = 1 => Pomeron flux is A -independent = f(A1,A2) - universal form Diffractive Vector Meson Production: Very sensitive to small x glue! Brodsky,Gunion,Mueller, Frankfurt,Strikman

III: Hard diffractive processes “Pomeron” exchange 30 % of eRHIC eA events may be hard diffractive events- Study sizes and distributions of Rapidity Gaps

Viewing the hadron in the transverse plane at high energies… Y_0 ---> Y+Y_0 Gluon radiation Gluon radiation & recombination

 Overlapping gluon clouds… at large impact parameters, interplay between perturbative (hard Pomeron) and non-perturbative (soft Pomeron) physics…  By studying the “t” dependence of diffractive final states, can we learn more about the transition regime ? S-matrix:

Shadowing and diffraction: Is shadowing a non-perturbative leading twist phenomenon, or is generated by weak coupling, high parton density effects? What is the relation of shadowing to diffraction? AGK rules relating the two are valid at low parton densities-how do these generalize to large parton densities? Armesto,Capella,Kaidalov, Salgado

Cartoon of ratio of nuclear structure functions Uncertainity in ratio of Ca to nucleon gluon distributions -Hirai,Kumano,Nagai, hep-ph/ Armesto

Ratio of Gluon densities in Lead to Proton at x in x range Factor 3 uncertainity in glue => Factor 9 uncertainity in Semi-hard HI-parton cross-sections at LHC!

The nuclear “oomph” factor! eA at eRHIC same parton density as ep at LHC energies! ?

Reasonable agreement with forward spectra Hayashigaki et al.

Virtual photon coherence length:  x_Bj << 0.01 : Photon coherence length exceeds nuclear size  0.01 < x_Bj < 0.1: Intermediate length scale between R_p & R_A  x_Bj >> 0.1: Photon localized to longitudinal size smaller than nucleon size

Strong hints from AA multiplicity dists. and D Au forward data of novel physics of strong color fields A dependence of saturation scale ? Numbers on “phase” diagram ? Breakdown of linear QCD evolution eqns. ?

II: Extracting gluon distributions in pA relative to eA Direct photons Open charm Drell-Yan As many channels…but more convolutions, kinematic constraints-limit precision and range.

Drell-Yan But very difficult to see scaling violations Impressive reach…