Exclusive vs. Diffractive VM production in nuclear DIS Cyrille Marquet Institut de Physique Théorique CEA/Saclay based on F. Dominguez, C.M. and B. Wu, Nucl. Phys. A823 (2009) 99, arXiv: work in progress

Outline Saturation, the CGC and the dipole picture the CGC picture of the nuclear wave function at small x high-energy dipole scattering off the CGC and geometric scaling Lessons from HERA diffractive data the success of the dipole picture geometric scaling and other hints of parton saturation The process eA → eVY VM production off the CGC and dealing with the nuclear break-up explicit calculation in the MV model results and work in progress

Parton saturation, the CGC and the dipole picture in DIS

The saturation momentum gluon kinematics recombination cross-section gluon density per unit area it grows with decreasing x recombinations important when for a given value of, the saturation regime in a nuclear wave function extends to a higher value of x compared to a hadronic wave function McLerran and Venugopalan (1994) the CGC: an effective theory to describe the saturation regime lifetime of the fluctuations in the wave function ~ high-x partons ≡ static sources low-x partons ≡ dynamical fields  the idea in the CGC is to take into account saturation via strong classical fields gluon recombination in the hadronic wave function the saturation regime: for with

The Color Glass Condensate  small x gluons as radiation field valence partons as static random color source separation between the long-lived high-x partons and the short-lived low-x gluons CGC wave function classical Yang-Mills equations the CGC wave function the solution gives the evolution of with x is a renormalization-group equation Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner ( ) from, one can obtain the unintegrated gluon distribution, as well as any n-parton distributions the small-x evolution in the A + =0 gauge

Scattering off the CGC scattering of a quark: this is described by Wilson lines dependence kept implicit in the following in the CGC framework, any cross-section is determined by colorless combinations of Wilson lines, averaged over the CGC wave function x : quark transverse coordinate y : antiquark transverse coordinate the dipole scattering amplitude: this is the most common Wilson-line average the 2-point function or dipole amplitude or

The dipole factorization dipole-hadron cross-section inclusive DIS at small x, the dipole cross section is comparable to that of a pion, even though r ~ 1/Q << 1/  QCD overlap of splitting functions exclusive diffraction the overlap function: instead of  access to impact parameter

r the dipole is probing small distances inside the hadron/nucleus: r ~ 1/Q what does the proton look like in (Q², x) plane: Geometric scaling geometric scaling can be easily understood as a consequence of large parton densities lines parallel to the saturation line are lines of constant densities along which scattering is constant T = 1 T << 1

Hard diffraction and saturation dipole size r the dipole scattering amplitude the total cross sections in inclusive DIS in diffractive DIS contribution of the different r regions in the hard regime  DIS dominated by relatively hard sizes  DDIS dominated by semi-hard sizes diffraction directly sensitive to saturation

Things we learned with HERA

Inclusive diffraction in DIS k k’ p k p p’ when the hadron remains intact rapidity gap some events are diffractive momentum fraction of the exchanged object (Pomeron) with respect to the hadron diffractive mass M X 2 = (p-p’+k-k’) 2 the measured cross-section momentum transfer t = (p-p’) 2 < 0

Inclusive Diffraction (DDIS) (~450 points) parameter-free predictions with IIM model at fixed , the scaling variable is C.M. and Schoeffel (2006)C.M. (2007)

Important features of DDIS tot = F 2 D contributions of the different final states to the diffractive structure function: at small  : quark-antiquark-gluon at intermediate  : quark-antiquark (T) at large  : quark-antiquark (L) the β dependence saturation naturally explains the constant ratio the ratio F 2 D,p / F 2 p

Munier, Stasto and Mueller (2001)  HERA is entering the saturation regime the scattering probability (S=1-T ) is extracted from the  data S(1/r  1Gev, b  0, x  )  0.6 Exclusive processes: ep → eVp rhoJ/Psi success of the dipole models t-CGC b-CGCappears to work well also but no given DVCS predictions checked by H1 C.M., Peschanski and Soyez (2007) Kowalski, Motyka and Watt (2006)

for the total VM cross-section Geometric scaling C.M. and Schoeffel (2006) scaling at non zero transfer C.M., Peschanski and Soyez (2005) predicted checked H1 collaboration (2008)

Diffractive Vector Meson production in nuclear DIS eA → eVY

Dealing with the target break-up from a proton target to a nucleus in e+p collisions at HERA, both exclusive and diffractive processes can be measured already at rather low |t| (~0.5 GeV2), the diffractive process is considered a background in e+A collisions at a future EIC, at accessible values of |t|, the nucleus is broken up it is crucial to understand and quantify the transition from exclusive to diffractive scattering  this can be calculated in the CGC framework work in progress exclusive vs. diffractive process the target is intact (low |t|) upper part described with the overlap function: exclusive processdiffractive process the target has broken-up (high |t|) interaction at small :  description of both within the same framework ? possible at low-x Dominguez, C.M. and Wu, (2009)

VM production off the CGC the diffractive cross section overlap functions amplitude target average at the cross-section level: contains both broken-up and intact events conjugate amplitude r : dipole size in the amplitude r’ : dipole size in the conjugate amplitude one needs to compute a 4-point function, possible in the MV model for the exclusive part obtained by averaging at the level of the amplitude: one recovers

The MV model µ 2 characterizes the density of color charges along the projectile’s path with this model for the CGC wavefunction squared, it is possible to compute n-point functions a Gaussian distribution of color sources is the two-dimensional massless propagator applying Wick’s theorem when expanding in powers of α and averaging, all the field correlators can be expressed in terms of the difficulty is to deal with the color structure Fujii, Gelis and Venugopalan (2006)

Analytical results the 4-point function (using transverse positions and not sizes here) it can also be consistently included, and should be obtained from (almost) the BK equation but for now, we are just using models the x dependence

Results and work in progress

The case of a target proton as a function of t exclusive production: the proton undergoes elastic scattering dominates at small |t| diffractive production : the proton undergoes inelastic scattering dominates at large |t| exclusive → exp. fall at -t < 0.7 GeV 2 diffractive → power-law tail at large |t| two distinct regimes Dominguez, C.M. and Wu, (2009) the transition point is where the data on exclusive production stop

exclusive production is called coherent diffraction the nucleus undergoes elastic scattering, dominates at small |t| intermediate regime (absent with protons) the nucleus breaks up into its constituents nucleons, intermediate |t| then there is fully incoherent diffraction the nucleons undergo inelastic scattering, dominates at large |t| From protons to nuclei qualitatively, one expects three contributions coherent diffraction → steep exp. fall at small |t| breakup into nucleons → slower exp. fall at 0.05 < -t < 0.7 GeV 2 incoherent diffraction → power-law tail at large |t| three regimes as a function of t: next step: computation for vector mesons Kowalski, Lappi and Venugopalan (2008)

Including small-x evolution our calculation can be used as an initial condition a stage-I EIC can already check this model, and constrain the A dependence of the saturation scale at values of x moderately small with higher energies, the x evolution (which is the robust prediction) can be tested too actual CGC x evolution instead of modeled x evolution this is what should be done now that running-coupling corrections have been calculated see for instance the recent analysis of F 2 with BK evolution Albacete, Armesto, Milhano and Salgado (2009) the complication in our case is that the BK approximation of JIMWLK cannot be used: it has no target dissociation ( ) and is useful for the exclusive part only one needs a better approximation of JIMWLK that keeps contributions to all order in Nc this can be done and running-coupling corrections can be implemented too C.M. and Weigert, in progress

Conclusions Diffractive vector meson production is an important part of the physics program at an eA collider it allows to understand coherent vs. incoherent diffraction The CGC provides a framework for QCD calculations in the small-x regime explicit calculations possible in the MV model for the CGC wave function consistent implementation of the small-x evolution is also possible VM production off the proton understood, preliminary results for the nucleus case a stage-I EIC will constrain initial conditions at moderate values of x with higher energies the small-x QCD evolution will be tested coherent diffraction → steep exp. fall at small |t| breakup into nucleons → slower exp. fall at 0.05 < -t < 0.7 GeV 2 incoherent diffraction → power-law tail at large |t|