Saturation in Diffractive Deep Inelastic Scattering

TL;DR

The paper extends a perturbative QCD saturation model, previously used to describe inclusive DIS at low x, to diffractive deep inelastic scattering. By modeling the γ*p interaction with a dipole cross section that saturates at large dipole sizes, it predicts a consistent x-dependence for both inclusive and diffractive cross sections and a roughly constant diffractive-to-inclusive ratio, without introducing new parameters. The diffractive structure functions are computed in both momentum and impact-parameter space, incorporating three components (qq̄ with transverse and longitudinal photons, and qq̄g) and an unintegrated gluon distribution. The approach yields good agreement with H1 and ZEUS data across β, x_IP, and Q^2, and suggests diffraction at small x is semi-hard with an elevated effective Pomeron intercept. It also sets the stage for diffractive charm production and diffractive parton distributions in future work.

Abstract

We successfully describe the HERA-data on diffractive deep inelastic scattering using a saturation model which has been applied in our earlier analysis of the inclusive $ep$-scattering data. No further parameters are needed. Saturation already turned out to be essential in describing the transition from large to small values of $Q^2$ in inclusive scattering. It is even more important for diffractive processes and naturally leads to a constant ratio of the diffractive versus inclusive cross sections. We present an extensive discussion of our results as well as detailed comparison with data.

Figures (12)

• Figure 1: The integrand of the inclusive cross section $\sigma_T$ in (\ref{['eq:1']}) (solid lines) after the integration over $\alpha$ and the azimuthal angle, plotted for two values of $Q^2$. The dotted lines show the dipole cross section (\ref{['sigmahat']}). The dashed vertical lines correspond to the characteristic scales $r=2 R_0$ and $r=2/Q$. The values for $2 R_0$ at a fixed energy $W=245~\hbox{\rm GeV}$ are: $0.36~\hbox{\rm fm}$ for $Q^2=10~\hbox{\rm GeV}^2$ and $0.25~\hbox{\rm fm}$ for $Q^2=0.8~\hbox{\rm GeV}^2$.
• Figure 2: The integrands of the inclusive (Inc) and diffractive (DD) cross sections at $Q^2=10~GeV^2$ for the following two cases: (a) saturation according to Eq. (\ref{['sigmahat']}) (dotted line) and (b) no saturation, i.e. $\hat{\sigma} \sim r^2$.
• Figure 3: Diffractive production of a $q\bar{q}$-pair (left) and the emission of an additional gluon (right).
• Figure 4: Gluon radiation.
• Figure 5: Effective triple gluon couplings.