---
address: |
    DESY, Notkestr. 85, D-22603 Hamburg, Germany\
    E-mail: fpschill@mail.desy.de
author:
- 'F.-P. Schilling  \[H1 Collaboration\]'
title: |
    Diffractive Jet Production in DIS\
    – Testing QCD Factorisation 
---

Overview
========

At HERA, colour singlet exchange or [*diffractive*]{} processes are studied in deep-inelastic $ep$ scattering (DIS), where the exchanged photon with virtuality $Q^2$ provides a probe to determine the QCD (i.e. quark and gluon) structure of diffractive exchange. In [@collins], it was proven that QCD hard scattering factorisation is valid in diffractive DIS, so that [*diffractive parton distributions*]{} $p_i^D$ in the proton can be defined as quasi-universal objects. The hypothesis of a factorising $x_{{I\!\!P}}$ dependence ([*Regge factorisation*]{}) is often used in addition.

Measurements of inclusive diffractive DIS in terms of the [ *diffractive structure function*]{} $F_2^{D(3)}(x_{{I\!\!P}},\beta,Q^2)$ mainly constrain the diffractive quark distribution. By contrast, diffractive dijet production is directly sensitive to the gluon distribution $g^D(z,\mu^2)$ (Fig. \[fig2\]), which can be inferred only indirectly from the scaling violations of $F_2^{D(3)}$. QCD factorisation can be tested by predicting the dijet cross sections using the pdf’s extracted from $F_2^{D(3)}$.

![Inclusive diffractive scattering at HERA [*(left)*]{} and diffractive dijet production [*(right)*]{}, viewed in a partonic picture.[]{data-label="fig2"}](djets-kine.grey.eps){height="3.0cm"}

Furthermore, the predictions of a variety of phenomenological models for diffractive DIS such as soft colour neutralisation or 2-gluon exchange can be confronted with the dijet cross sections.

Data Selection and Cross Section Measurement
============================================

The data sample corresponds to an integrated luminosity of $\mathcal{L}=18.0 \rm\ pb^{-1}$ and was obtained with the H1 detector at HERA. Dijet events were identified using the CDF cone algorithm and diffractive events were selected by the requirement of a large rapidity gap in the outgoing proton direction. The kinematic range of the measurement is $4<Q^2<80 \ \mathrm{GeV^2}$, $p^*_{T, jet}>4 \ 
\mathrm{GeV}$, $x_{{I\!\!P}}<0.05$, $M_Y<1.6 \ \mathrm{GeV}$ and $|t|<1.0 \ 
\mathrm{GeV^2}$. The cross sections were corrected for detector and QED radiative effects and the systematic uncertainties, which dominate the total errors, were carefully evaluated.

Diffractive Parton Distributions
================================

Parton distributions for the diffractive exchange[^1] were extracted from DGLAP QCD fits to $F_2^{D(3)}(x_{{I\!\!P}},\beta,Q^2)$ in [@h1f2d94]. The parton distributions were found to be dominated by gluons ($80-90\%$ of the exchange momentum).

If these parton distributions, which evolve according to the DGLAP equations, are used to predict the diffractive dijet cross sections, a very good agreement is obtained (Fig. \[fig5ab\]). Fig. \[fig7\] shows the measurement of the dijet cross section as a function of $z_{{I\!\!P}}^{(jets)}$, an estimator for the parton momentum fraction of the diffractive exchange which enters the hard process (Fig. \[fig2\] right). A very good agreement in shape and normalisation is obtained if the [ *fit 2*]{} parton distributions from [@h1f2d94] are used. The [*fit 3*]{} parameterisation, in which the gluon distribution is peaked towards high $z_{{I\!\!P}}$ values, is disfavoured[^2]. Using different factorisation scales ($\mu^2=Q^2+p_T^2$ in Fig. \[fig7\]a, $\mu^2=p_T^2$ in Fig. \[fig7\]b) or including a resolved virtual photon contribution (Fig. \[fig7\]a) in the model prediction does not alter these conclusions. The dijet data thus strongly support the validity of QCD factorisation in diffractive DIS and give tight constraints on the diffractive gluon distribution in both shape and normalisation.

The measured $z_{{I\!\!P}}^{(jets)}$ cross sections in bins of the scale $\mu^2=Q^2+p_T^2$ (Fig. \[fig8\]a) are in good agreement with the prediction based on a DGLAP evolution of the diffractive parton distributions. The $z_{{I\!\!P}}^{(jets)}$ cross sections in bins of $x_{{I\!\!P}}$ (Fig. \[fig8\]b) demonstrate consistency with Regge factorisation.

In a Regge framework, the energy dependence of the cross section is determined in terms of an effective [*pomeron intercept*]{} $\alpha_{{I\!\!P}}(0)=1.17\pm0.07$ (stat.+syst.) from the $x_{{I\!\!P}}$ cross section (Fig. \[fig6\]a), consistent with the result from [@h1f2d94]. The cross section as a function of $\beta$ is shown in Fig. \[fig6\]b.

Soft Colour Neutralisation Models
=================================

In Fig. \[fig10\], the cross sections are compared with models based on the ideas of soft colour neutralisation to produce large rapidity gaps. These are the original version of the ‘soft colour interactions’ model (SCI) [@sci], the improved version of SCI based on a generalised area law [@scinew] and the ‘semi-classical model’ [@semicl]. The original SCI and the semi-classical models give good descriptions of the differential distributions. However, none of these models is yet able to simultaneously reproduce shapes and normalisations of the dijet cross sections.

Colour Dipole and 2-gluon Exchange Models
=========================================

Models for diffractive DIS based on the diffractive scattering of $q\bar{q}$ or $q\bar{q}g$ photon fluctuations off the proton by 2-gluon exchange are confronted with the data in Fig. \[fig11\] for the limited kinematic range of $x_{{I\!\!P}}<0.01$, where contributions from quark exchange can be neglected. The ‘saturation model’ [@sat], which takes only $k_T$-ordered configurations of the final state partons into account, reproduces the shapes of the differential distributions, but underestimates the cross sections by a factor of two. The model of Bartels et al. [@bartels], in which also non-$k_T$-ordered configurations are taken into account, is found to be in reasonable agreement with the data if a free parameter $p_{T,g}^{cut}$ is fixed to $1.5
\rm\ GeV$[^3].

Conclusions
===========

Diffractive dijet production has been shown to be a powerful tool to gain insight into the underlying QCD dynamics of diffraction, in particular the role of gluons. Factorisable, gluon-dominated diffractive parton distributions successfully describe diffractive jet production and inclusive diffraction in DIS at the same time, in agreement with QCD factorisation.

[99]{}

H1 Collaboration, C. Adloff [*et al.*]{}, .

F.-P. Schilling, Ph.D. thesis, Univ. Heidelberg (2001), DESY-THESIS-2001-010.

J. Collins, , err.-ibid. [**D 61**]{} (2000) 19902.

H1 Collaboration, C. Adloff [*et al.*]{}, .

A. Edin, G. Ingelman, J. Rathsman, .

J. Rathsman, .

W. Buchmüller, T. Gehrmann, A. Hebecker, .

K. Golec-Biernat, M. Wüsthoff, .

J. Bartels, H. Lotter, M. Wüsthoff, ;\
J. Bartels, H. Jung, M. Wüsthoff, .

[^1]: The assumption of Regge factorisation was found to be compatible with the data.

[^2]: The corresponding gluon distributions are shown above the cross sections.

[^3]: $p_{T,g}^{cut}$ corresponds to the minimum $p_T$ of the final state gluon in the case of $q\bar{q}g$ production.
