Diffractive structure functions of nuclei

1. Diffractive structure functionsof nuclei Cyrille Marquet Physics Department, Columbia University and RIKEN BNL Research Center

2. k’ k p p’ Diffractive deep inelastic scattering eh center-of-mass energyS = (k+p)2*h center-of-mass energyW2 = (k-k’+p)2photon virtualityQ2 = - (k-k’)2 > 0 momentum transfert = (p-p’)2 < 0diffractive mass of the final stateMX2 = (p-p’+k-k’)2 x~ momentum fraction of the struck parton with respect to the hadron/nucleus ~ momentum fraction of the struck parton with respect to the Pomeron xpom~ momentum fraction of the Pomeron with respect to the hadron/nucleus

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

4. diffractive DIS (DDIS): in the dipole picture, the diffractive final state is decomposed: important only at small β or large Q2 The QCD dipole picture in DIS in the limit x  0withQ²fixed 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 thoughr ~ 1/Q << 1/QCD • deep inelastic scattering (DIS):

5. at small β: the log(1/β) enhancement comes from the configurations: Bartels, Jung and Wusthoff (1999), Kovchegov (2001), Munier and Shoshi (2004), Marquet (2005) the wavefunction ψ(r,Q²) factorizes, the hadronic scattering effectively involves two quark-antiquark dipoles  until recently, it had not been implemented in the structure functions description The contribution at large Q2 : the log(Q2) enhancement comes from the configuration: Levin and Wusthoff (1994) , Wusthoff (1997) in coordinate space, the gluon is well separated from the quark and antiquark the hadronic scattering effectively involves a gluon dipole  the large-Q2 formula is what was used in all dipole model descriptions of DDIS Bartels, Jung and Wusthoff (1999), Kovchegov (2001), Munier and Shoshi (2004), Marquet (2005)

6. dominates Unified contribution C. Marquet (2007) Contributions of the different final states to the diffractive structure function: at large  : quark-antiquark (L) tot =F2D at intermediate  : quark-antiquark (T) at small  : quark-antiquark-gluon large  measurements FLD

7. Comparison with HERA data with proton tagging e p  e X p H1 FPS data (2006) ZEUS LPS data (2004) without proton tagging e p  e X Y H1 LRG data (2006) MY < 1.6 GeV ZEUS FPC data (2005) MY < 2.3 GeV parameter-free predictions description of DIS (~250 points) and diffractive DIS (~450 points)

8. Geometric scaling in diffraction with Marquet and Schoeffel (2006) Stasto, Golec-Biernat and Kwiecinski (2001)

9. other approaches : numerical solution of the Kovchegov-Levin equation Levin and Lublinsky (2002) with nuclear DPDFs (leading-twist shadowing) Frankfurt, Guzey and Strikman (2004) in the dipole picture with Kugeratski, Goncalves and Navarra (2006) From protons to nuclei following the approach of Kowalski-Teaney (2003):  averaged with the Woods-Saxon distribution position of the nucleons averaging allows to evaluate the saturation scale Kowalski, Lappi and Venugopalan (2007) 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

10. as a function of Q2 : the quark-antiquark contributions for β values at which they dominate: the decrease (with increasing Q2) of the diffractive cross-section is slower for a nucleus than for a proton Hard diffraction on nuclei in progress with Kowalski, Lappi and Venugopalan the ratios FAD / Fp Dfor each contributions: as a function of β: quark-antiquark-gluon < 1 and ~ const. quark-antiquark (T) > 1 and ~ const. quark-antiquark (L) > 1 and decreases with β the decrease with (decreasing β) of is slower for a nucleus than for a proton for Au nucleus, without breakup

11. comparison breakup / no breakup: for Au nucleus, one gets a 15 % bigger structure function when allowing breakup into nucleons next step: compute The ratio F2D,A / F2 D,p the ratio of the structure functions: the quark-antiquark-gluon contribution dominates only for very small values of , the ratio gets constant and decreases with A decreases with A the quark-antiquark contribution dominates