The dipole picture in DIS: saturation and heavy quarks

Abstract

We discuss the description of the proton structure function within the dipole factorisation framework. We parametrise the forward dipole amplitude to account for saturation as predicted by the small-x QCD evolution equations. Contrarily to previous models, the saturation scale does not decrease when taking heavy quarks into account. We show that the same dipole amplitude also allows to reproduce diffractive data and exclusive vector meson production.In these proceedings [1] we shall concentrate on Deep Inelastic Scattering (DIS) at small x. In this regime, the photon-proton cross-section can be factorised as a convolution between the wavefunction for a virtual photon to fluctuate into a quark-antiquark pair and the interaction T between this colourless dipole and the proton:where the factor 2πR 2 p arises from integration over the impact parameter. The photon wavefunction can be computed from perturbative QED and we are left with the parametrisation of the hadronic dipole amplitude. To that aim, we usually rely on the observation that the small-x DIS data satisfy geometric scaling [2], meaning that, instead of being a function of both Q 2 and x, they appear to be a function of τ = log(Q 2 /Q 2 s (x)) = log(Q 2 /Q 2 0 )−λ log(1/x) only, where Q s (x) is known as the saturation scale. Since r ∼ 1/Q in (1), this property suggests that the dipole amplitude is a function of rQ s (x) only.Since the small-x domain extends down to small Q 2 , the dipole amplitude is sensitive to the unitarity bound T < 1. There are two broad classes of models which differ by their way to implement that boundary. The first approach is to use an eikonal form as initially proposed in [3], followed by more precise analysis to incorporate DGLAP evolution and masses for the heavy quarks [4].The second approach, that we follow through these proceedings, is to use predictions directly from the Balitsky-Kovchegov equation describing the QCD evolution to small x. It resums the BFKL logarithms of 1/x and satisfies unitarity by including saturation effects.In contrast with the eikonal models which include it by hand, it has been proven [5] that the solutions of the BK equation satisfy the property of geometric scaling. More precisely, T (r, x) rQs 2