Inclusive diffraction in DIS and the dipole picture

1. Inclusive diffraction in DISand the dipole picture arXiv:0706.2682 Cyrille MarquetRIKEN BNL Research Center

2. Contents • Introductionthe dipole picture in deep inelastic scattering (DIS) • Geometric scaling and saturation- the qq dipole scattering amplitude- the saturation regime of QCD- the geometric scaling of the total cross-section in DIS- the geometric scaling of diffractive observables in DIS • Inclusive diffraction in DIS- description in the dipole picture - new improvement of with respect to the standard approach- consequences for the data description

3. ep center-of-mass energyS = (k+P)2*p center-of-mass energyW2 = (k-k’+P)2 k’ k size resolution 1/Q p Mueller (1990), Nikolaev and Zakharov (1991) (QED wavefunction ψ(r,Q²)), then the dipole interacts with proton at small x, the dipole cross-section is comparable to that of a pion, even though r ~ 1/Q << 1/QCD Deep inelastic scattering (DIS) probing small distances in the proton photon virtualityQ2 = - (k-k’)2 > 0

4. Geometric scaling and saturation

5. The dipole scattering amplitude the dipole is probing small distances inside the proton: r ~ 1/Q r he sees the proton in the transverse plane: the physics is invariant along any line parallel to the saturation line T = 1 T << 1

6. The geometric scaling of DIS(x, Q2) saturation models fit well F2 data Golec-Biernat and Wüsthoff (1999) Bartels, Golec-Biernat and Kowalski (2002) Iancu, Itakura and Munier (2003) and they give predictions which describe accurately a number of observables at HERA (F2D, FL, DVCS, vector mesons) and RHIC (nuclear modification factor in d-Au) this is seen in the data with  0.3 Stasto, Golec-Biernat and Kwiecinski (2001) update

7. k’ k’ some events are diffractive k k when the hadron remains intact p p p’ rapidity gap in the dipole picture, the diffractive final state is decomposed: Diffractive DIS (DDIS) momentum transfert = (p-p’)2 < 0diffractive mass of the final stateMX2 = (p-p’+k-k’)2 diffractive structure functions

8. contribution of the different r regions in the hard regime hard diffraction is directly sensitive to the saturation region  non-linear weakly-coupled QCD DIS dominated by relatively hard sizes DDIS dominated by semi-hard sizes Hard diffraction and small-x physics the dipole sees the proton in the transverse plane the dipole scattering amplitudfe dipole size r

9. Geometric scaling in diffraction  scaling also for vector meson production : Marquet and Schoeffel (2006)

10. Inclusive diffraction in DIS

11. Fourier transform to MX2 comes from overlap of wavefunctions Fourier transform to t dipole amplitudes The actual contribution double differential cross-section (proportional to structure function) for a given photon polarization:

12. flaws: - what is used is - the data are not at large Q2 only valid for N << 1, not good when using a saturation model using is better the contribution is overestimated The contribution at large Q2 Levin and Wusthoff (1994) , Wusthoff (1997) the large-Q2 formula is what is used in all dipole model descriptions of DDIS Golec-Biernat and Wüsthoff (1999) Forshaw, Sandapen and Shaw (2004) Golec-Biernat and Sapeta (2006) Kormilitzin (2007) gluonic dipole

13. The contribution at small β Bartels, Jung and Wusthoff (1999), Kovchegov (2001), Munier and Shoshi (2004), Marquet (2005) the term with two dipoles comes from until now, it has not been implemented in the structure functions description

14. dominates what about a resummation of multi gluon final states? with linear BFKL evolutionwith mean-field non-linear evolution Bialas and Peschanski (1996)Kovchegov and Levin (2000) Hatta, Iancu, Marquet, Soyez and Triantafyllopoulos (2006) Kovner, Lublinsky and Weigert (2006) at small , this is feasible in the dipole picture with evolutionbeyond mean-field approximation Unified contribution

15. The saturation model for N Iancu-Itakura-Munier model extended to include heavy quarks Soyez (2007) α and β such that N and its derivative are continuous at the saturation scale : fixed numbers: matching point size of scaling violations quark masses 3 parameters : (~250 points)

16. Diffractive DIS without proton tagging e p  e X Y with MY cut H1 LRG data (2006) MY < 1.6 GeV: ZEUS FPC data (2005) MY < 2.3 GeV: Inclusive diffraction at HERA Diffractive DIS with proton tagging e p  e X p H1 FPS data (2006) ZEUS LPS data (2004)

17. prediction for : Comparison with HERA data parameter free prediction comparison with latest data: description of DIS (~250 points) and diffractive DIS (~450 points)

18. Conclusions - saturation phenomenology is very successful at both HERA and RHIC - the same dipole scaterring amplitude describes DIS and DDIS for both and contributions to the diffractive final state - after fitting a few parameters on DIS data, the parameter free predictions for DDIS 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 - global (DIS+DDIS+VM) description with very few parameters - the improvements presented for inclusive diffraction can be used with any dipole model and are necessary for a satisfactory description Marquet, Peschanski and Soyez (2007)