Inclusive diffraction in DIS and the dipole picture Cyrille Marquet RIKEN BNL Research Center arXiv:

Contents Introduction the 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

Deep inelastic scattering (DIS) ep center-of-mass energy S = (k+P) 2  *p center-of-mass energy W 2 = (k-k’+P) 2 k k’ p size resolution 1/Q photon virtuality Q 2 = - (k-k’) 2 > 0 probing small distances in the proton (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 Mueller (1990), Nikolaev and Zakharov (1991)

Geometric scaling and saturation

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

Stasto, Golec-Biernat and Kwiecinski (2001) The geometric scaling of  DIS (x, Q 2 ) this is seen in the data with  0.3 saturation models fit well F 2 data and they give predictions which describe accurately a number of observables at HERA (F 2 D, F L, DVCS, vector mesons) and RHIC (nuclear modification factor in d-Au) Golec-Biernat and Wüsthoff (1999) Bartels, Golec-Biernat and Kowalski (2002) Iancu, Itakura and Munier (2003) update

Diffractive DIS (DDIS) k k’ p k p p’ when the hadron remains intact rapidity gap some events are diffractive momentum transfer t = (p-p’) 2 < 0 diffractive mass of the final state M X 2 = (p-p’+k-k’) 2 diffractive structure functions in the dipole picture, the diffractive final state is decomposed:

Hard diffraction and small-x physics dipole size r the dipole scattering amplitudfe 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 the dipole sees the proton in the transverse plane

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

Inclusive diffraction in DIS

The actual contribution comes from Fourier transform to M X 2 overlap of wavefunctions Fourier transform to t dipole amplitudes double differential cross-section (proportional to structure function) for a given photon polarization:

The contribution at large Q 2 Levin and Wusthoff (1994), Wusthoff (1997) Golec-Biernat and Wüsthoff (1999) Forshaw, Sandapen and Shaw (2004) Golec-Biernat and Sapeta (2006) Kormilitzin (2007) the large-Q 2 formula is what is used in all dipole model descriptions of DDIS only valid for N << 1, not good when using a saturation model using is better flaws: - what is used is - the data are not at large Q2 the contribution is overestimated gluonic dipole

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

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

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

Inclusive diffraction at HERA Diffractive DIS with proton tagging e p  e X p H1FPS data (2006) ZEUSLPS data (2004) Diffractive DIS without proton tagging e p  e X Y with M Y cut H1LRG data (2006) M Y < 1.6 GeV: ZEUSFPC data (2005) M Y < 2.3 GeV:

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

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)