Exclusive vs. Diffractive VM production in DIS at small-x or off nuclei

1. Exclusive vs. DiffractiveVM production in DIS at small-x or off nuclei Cyrille Marquet Columbia University based on F. Dominguez, C.M. and B. Wu, Nucl. Phys. A823 (2009) 99, arXiv:0812.3878 + work in progress

2. proton vs. nucleus target in e+p collisions at HERA, both 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/LHeC, at accessible values of |t|, the nucleus is broken up it is crucial to understand and quantify the transition from exclusive to diffractive scattering  predictions of what happens with nuclei work in progress Motivations • low vs. high momentum transfer upper part described with the overlap function: interaction at small : exclusive process diffractive process the target is intact (low |t|)saturation models work well the target has broken-up (high |t|)BFKL Pomeron exchange works well  description of both within the same framework ? possible at low-x Dominguez, C.M. and Wu, (2009)

3. Outline • Saturation and the Color Glass Condensatescattering off a high-energy hadron/nucleus VM production off the CGC the McLerran-Venugopalan model • The process ep → eVYunified formula (low and high t) comparison with HERA data • The process eA → eVYthe Woods-Saxon averagingthree distinct momentum-transfer regimes

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 k², 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 space transverse coordinate y: antiquark space transverse coordinate this is the most common average for instance it determines deep inelastic scattering 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. the exclusive part obtained by averaging at the level of the amplitude: one needs to compute a 4-point function, possible in the MV model for 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

8. ep → eVY

9. 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

10. the x dependence can also be consistently included, andshould be obtained from the BK equation (now available at NLO) for now, we are just using models • recovering known limits linearizing, we recover the BFKL formula → high-t OK the exclusive part is also contained→ low-t OK Analytical results • the 4-point function (using transverse positions and not sizes here)

11. Exclusive vs. diffractive 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

12. The eA → eVY case

13. the dipole-nucleus cross-section Kowalski and Teaney (2003)  averaged with the Woods-Saxon distribution position of the nucleons application for inclusive DIS off nuclei (F2): Kowalski, Lappi and Venugopalan (2007) 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| how to bring nucleons in the picture ?

14. 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 Hard diffraction off nuclei Kowalski, Lappi, C.M. and Venugopalan (2008) • the Woods-Saxon averaging in diffraction, averaging at the level of the amplitude corresponds to a final state where the nucleus is intact results for t-integrated structure functions averaging at the cross-section level allows the breakup of the nucleus into nucleons

15. Conclusions • 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 function • VM production off the proton understood, preliminary results for the nucleus case 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|