1. Diffractive structure functions in e-A scattering Cyrille Marquet Columbia University based on C. Marquet, Phys. Rev. D 76 (2007) 094017 + paper in preparation with Henri Kowalski, Tuomas Lappi and Raju Venugopalan

2. Motivations - diffraction probes QCD in a different way than inclusive measurements colorless t-channel exchanges, Pomerons, …, the large fraction of events (10 %) observed at HERA was not expected  a challenge for QCD - proposal for an electron-ion collider (at BNL or Jlab) by the EIC collaboration an important part of the physics program is diffraction: a first measurement of the nuclear diffractive structure functions - this talk: predictions in the Color Glass Condensate (CGC) framework Nikolaev, Schaefer, Zakharov and Zoller (2002) Frankfurt, Guzey and Strikman (2004) with nuclear DPDFs (leading-twist shadowing) an effective theory for QCD at high partonic density where the leading-twist approximation is not justified  the non-linear weakly coupled regime of QCD - other existing predictions: for diffractive dijets

3. Diffractive deep inelastic scattering  ~ momentum fraction of the struck parton with respect to the Pomeron x pom ~ momentum fraction of the Pomeron with respect to the hadron/nucleus k k’ p p’ eh center-of-mass energy S = (k+p) 2  *h center-of-mass energy W 2 = (k-k’+p) 2 photon virtuality Q 2 = - (k-k’) 2 > 0 momentum transfer t = (p-p’) 2 < 0 diffractive mass of the final state M X 2 = (p-p’+k-k’) 2 x ~ momentum fraction of the struck parton with respect to the hadron/nucleus

4. Collinear factorization in the limit Q²   with x fixed perturbative non perturbative for inclusive DIS a = quarks, gluons Dokshitzer-Gribov-Lipatov-Altarelli-Parisi perturbative evolution of  with Q 2 : not valid if x is too small when the hadron becomes a dense system of partons for diffractive DIS another set of pdf’s, same Q² evolution higher twists ~

5. Dipole factorization deep inelastic scattering (DIS): in the limit x  0 with Q² fixed the photon split into a dipole (QED wavefunction ψ(r,Q²) ) the dipole then interacts with the target at small x, the dipole cross-section is comparable to that of a pion, even though r ~ 1/Q << 1/  QCD in principle, two parameters: the saturation scale and the maximum dipole cross-section in practice, depending how many practical approximations are made: 1 to 3 extra parameters diffractive DIS (DDIS) : the structure functions are also expressed in terms of  no additional parameter I take the parameters from the recent F 2 analysis (by G. Soyez), and make predictions for F 2 D in e-p scattering C. Marquet (2007) computed in CGC contributions from all twists

6. Comparison with HERA data description of DIS (~250 points) and diffractive DIS (~450 points) parameter-free predictions with proton tagging e p  e X p H1FPS data (2006) ZEUSLPS data (2004) without proton tagging e p  e X Y H1LRG data (2006) M Y < 1.6 GeV ZEUSFPC data (2005) M Y < 2.3 GeV

7. The β dependence 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) large  measurements  F L D tot = F 2 D

8. From protons to nuclei Kowalski, Lappi and Venugopalan (2007) following the approach of Kowalski-Teaney (2003): averaging allows to evaluate the saturation scale in diffraction, averaging at the level of the amplitude corresponds to a final state where the nucleus is intact averaging at the cross-section level allows the breakup of the nucleus into nucleons averaged with the Woods-Saxon distribution  position of the nucleons Kugeratski, Goncalves and Navarra (2006) Levin and Lublinsky (2002) numerical solution of the Kovchegov-Levin equation other approaches : in the dipole picture with

9. Hard diffraction on nuclei in progress with Kowalski, Lappi and Venugopalan the ratios F A D / F p D for each contributions: quark-antiquark-gluon quark-antiquark (T) quark-antiquark (L) > 1 and ~ const. > 1 and decreases with β < 1 and ~ const. for Au nucleus, without breakup the decrease with (decreasing β ) of is slower for a nucleus than for a proton as a function of β : the quark-antiquark contributions for β values at which they dominate: the decrease (with increasing Q 2 ) of the diffractive cross-section is slower for a nucleus than for a proton as a function of Q 2 :

10. The ratio F 2 D,A / F 2 D,p the quark-antiquark contribution dominates the quark-antiquark-gluon contribution is important only for very small values of , the ratio gets constant and decreases with A decreases with A the ratio of the structure functions: for Au nucleus, one gets a 15 % bigger structure function when allowing breakup into nucleons comparison breakup / no breakup: next step: compute

11. Conclusions - CGC (saturation) phenomenology is very successful at both HERA and RHIC - the same dipole scattering amplitude describes inclusive and diffractive DIS global description with very few parameters - after fitting a few parameters on inclusive data, the parameter free predictions for diffraction agree very well with the HERA data - the model also describes vector meson (ρ, Φ, J/ψ) production (total cross- sections and t-spectra) with 2 additional parameters Marquet, Peschanski and Soyez (2007) Why do these high-energy QCD computations work so well at HERA ? we would understand better if this could be tested with a future EIC depending on the energy options, one could reach Qs ~ 2 GeV