Open questions in QCD at high parton density: EIC vs LHeC Cyrille Marquet Centre de Physique Théorique Ecole Polytechnique

Contents gluon saturation: status and open questions - what we know - what we would like to know - what questions can(not) be answered with e+A (p+A) - connections with Quark-Gluon-Plasma physics e+(p)A measurements: EIC/LHeC highlights - structure functions F2 and FL - hard diffraction - di-hadron production - exclusive vector meson production - cold nuclear matter effects

Gluon saturation: status and open questions

What we know for sure fundamental consequence of QCD dynamics: at asymptotically small x: - QCD evolution becomes non-linear - particle production becomes non-linear - QCD stays weakly coupled both in terms of practical applicability and phenomenological success the Color Glass Condensate (CGC) has emerged as the best candidate to approximate QCD in the saturation regime the energy dependence of the saturation scale, and more generally of observables, can be computed from first principles although in practice, the predictivity will depend on the level of accuracy of the calculation (LO vs NLO, amount of non-perturbative inputs needed, …)

A big open question is this relevant at today’s colliders ? in other words: can we get away with using such a gluon distribution (with ad hoc cutoff if necessary) ? or do we need to properly take into account the QCD dynamics at kT ~ QS and below ? the CGC phenomenology is successful for every collider process that involves small-x partons and kT ~ QS , i.e. for a broad range for high-energy observables: multiplicities in p+p, d+Au, Au+Au and Pb+Pb; forward spectra and correlations in p+p and d+Au; total, diffractive and exclusive cross sections in e+p and e+A, … - for each of these observables, there are alternatives explanations - the applicability of the theory can be questioned when values of QS start to drop below 1 GeV (e.g. p+p and peripheral d+Au at RHIC) the CGC is not widely accepted because

What EICs can do provide golden measurements EICs = EIC stage 1, EIC stage 2, LHeC provide golden measurements the kind that will prove non-linear QCD evolution to be indispensable, or irrelevant twice one thought one had found such observables modification of particle production at forward rapidities in p+A versus p+p EICs would provide smoking guns for saturation, something that very likely cannot be done with p+A (let alone A+A) single inclusive di-hadron correlations

Bigger open questions (I) EICs would also provide data that can help us address the following questions the impact parameter dependence of the gluon density and of QS this has always been the main non-perturbative input in CGC calculations in the case of a proton, using an impact-parameter averaged saturation scale is enough most of the time, but in the case of a nucleus it is not modeling what is done in the most advanced CGC phenomenological studies, is to treat the nucleus as a collection of Woods-Saxon distributed CGCs, and to evolve (down in x) the resulting gluon density at different impact parameters independently but is this good enough ? (in principle not)

Bigger open questions (II) the transition from the saturation to the high-pT (leading-twist) regime rcBK evolution (down in x) does not contain the DGLAP limit, hence after some evolution (at forward rapidities), RpA predictions reach unity only at unrealistically large values of pT Albacete, Dumitru how RpA goes back towards unity at high-pT ? the transition from the saturation regime to confinement how does it happen ? does the coupling run with Qs ? are classical fields still the right degrees of freedom ? p+A and e+A collisions offer special opportunities to explore this many-body system of strongly-correlated gluons universality properties of the saturation regime here I focus on what is unique to e+A, p+A provides great possibilities as well see e.g. Salgado et al, 1105.3919

Connections with QGP physics bulk observables in heavy-ion collisions reflect the properties of the initial state as much as those of the hydro evolution of the QGP see François’s talk next new sources of uncertainties keep emerging, for instance even two CGC models predict different eccentricities the main source of error in the extraction of medium parameters (e.g. η/s) is our insufficient understanding of initial state fluctuations QGP properties cannot be precisely extracted from data without a proper understanding of the initial state; e+A collisions: access to a precise picture

e+p and e+A measurements: EIC and LHeC highlights

Deep inelastic scattering (DIS) photon virtuality Q2 = - (k-k’)2 = - q2 > 0 *A center-of-mass energy W2 = (q+p)2 e+A @ EIC e+Pb @ LHeC NOT all processes require Q2 ~ QS2 in order to probe saturation effects

Inclusive structure functions measures quark distributions gluon distribution precisely measuring FL is crucial, and this requires an e+A energy ( ) scan Albacete, Lamont can NLO DGLAP simultaneously accommodate F2 and FL data if saturation sets in according to current models ?

Hard diffraction in DIS a surprising QCD feature at HERA: a proton in its rest frame hit by a 25 TeV electron remains intact 15% of the time clean and unambiguous signal of saturation, already at EIC stage-1 this enhancement is specific to e+A (there is no equivalent in p+A) Guzey, Lamont, CM observable subject to strong non-linear effects even with Q2 values significantly bigger than QS2 at HERA the NLO DGLAP description breaks down already at Q2 ~ 8 GeV2

Exclusive Vector Meson production @ LHeC energy dependence momentum transfer dependence @ EIC Toll, Ullrich Newman, Watt through a Fourier transformation, one can extract the spatial gluon distribution (and correlations), this is not feasible in p+A

Di-hadrons in DIS directly sensitive to the kT dependence of the gluon distribution at the qualitative level: similar effects as in p+A Lee, Xiao, Zheng unique access to Weizsacker-Williams gluon distribution (a different operator definition is involved in p+A) but at the quantitative level, this process involves a different unintegrated gluon distribution

Conclusions all detailed studies can be found in - the INT report on the Physics case for the Electron-Ion Collider, arXiv:1108.1713 e+A conveners : A. Accardi, M. Lamont and CM - the upcoming EIC white paper e+A conveners: Y. Kovchegov and T. Ullrich - the LHeC Conceptual Design Report, arXiv:1206.2913 small-x conveners: N. Armesto, B. Cole, P. Newman and A. Stasto thanks to the EIC task forces at Brookhaven and Jefferson labs thanks to the LHeC small-x working group