Exclusive vs. D iffractive VM production in nuclear DIS

1. Exclusive vs. DiffractiveVMproduction 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:0812.3878 + work in progress

2. 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

3. Parton saturation, the CGCand the dipole picture in DIS

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

5. from , one can obtain the unintegrated gluon distribution, as well as any n-parton distributions • the small-x evolution the evolution of with x is a renormalization-group equation Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner (1997-2002) the solution gives The Color Glass Condensate • the CGC wave function  CGC wave function valence partons as static random color source separation between the long-lived high-x partons and the short-lived low-x gluons small x gluons as radiation field classical Yang-Mills equations in the A+=0 gauge

6. the 2-point function or dipole amplitude the dipole scattering amplitude: x: quark transverse coordinate y: antiquark transverse coordinate or this is the most common Wilson-line average Scattering off the CGC • this is described by Wilson lines scattering of a quark: 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

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

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

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

10. Things we learned with HERA

11. k’ k’ some events are diffractive k k when the hadron remains intact p p p’ rapidity gap diffractive mass MX2 = (p-p’+k-k’)2 momentum transfert = (p-p’)2 < 0 momentum fraction of the exchanged object (Pomeron) with respect to the hadron • the measured cross-section Inclusive diffraction in DIS

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

13. the ratio F2D,p / F2p saturation naturally explains the constant ratio Important features of DDIS • the βdependence contributions of the different final statesto the diffractive structure function: tot =F2D at small  : quark-antiquark-gluon at intermediate  : quark-antiquark (T) at large  : quark-antiquark (L)

14. success of the dipole models t-CGC C.M., Peschanski and Soyez (2007) b-CGC appears to work well also but no given Kowalski, Motyka and Watt (2006) rho J/Psi DVCS predictions checked by H1 Exclusive processes: ep→ eVp Munier, Stasto and Mueller (2001) the scattering probability (S=1-T ) is extracted from the  data S(1/r 1Gev, b  0, x  5.10-4)  0.6  HERA is entering the saturation regime

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

16. Diffractive Vector Mesonproduction in nuclear DISeA→ eVY

17. 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 Dealing with the target break-up • exclusive vs. diffractive process upper part described with the overlap function: interaction at small : exclusive process diffractive process the target is intact (low |t|) the target has broken-up (high |t|)  description of both within the same framework ? possible at low-x Dominguez, C.M. and Wu, (2009)

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

19. applying Wick’s theorem Fujii, Gelis and Venugopalan (2006) when expanding in powers of α and averaging, all the field correlators can be expressed in terms of is the two-dimensional massless propagator the difficulty is to deal with the color structure The MV model • a Gaussian distribution of color sources µ2 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

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

21. Results and work in progress

22. The case of a target proton Dominguez, C.M. and Wu, (2009) • 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| • two distinct regimes exclusive→ exp. fall at -t < 0.7 GeV2 diffractive→power-law tail at large|t| the transition point is where the data on exclusive production stop

23. three regimes as a function of t: coherent diffraction→ steep exp. fall at small |t| breakup into nucleons→slower exp. fall at 0.05 < -t < 0.7 GeV2 incoherent diffraction→power-law tail at large |t| next step: computation for vector mesons Kowalski, Lappi and Venugopalan (2008) From protons to nuclei • qualitatively, one expects three contributions 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|

24. 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 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 F2 with BK evolution Albacete, Armesto, Milhano and Salgado (2009)

25. Conclusions • Diffractive vector meson production is an important part of the physics program at an eA colliderit allows to understand coherent vs. incoherent diffraction • The CGC provides a framework for QCD calculations in the small-x regimeexplicit calculations possible in the MV model for the CGC wave functionconsistent implementationof the small-x evolution is also possible • VM production off the proton understood, preliminary results for the nucleus casea stage-I EIC will constrain initial conditions at moderate values of xwith 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 GeV2 incoherent diffraction→power-law tail at large |t|