Dijet Production in DIS at HERA

A major area of study at HERA is dijet production in DIS, which has earlier been used to determine $\alpha_S$ and constrain the gluon density. Previously, data have been compared to NLO semi-analytic calculations using JADE-type algorithms. Now, with the flexible NLO Monte Carlo programs MEPJET [32] and DISENT [33] available, comparisons with various jet schemes are possible. Results were presented at this workshop using the cone [34,35], JADE [36] and k_T [37] algorithms.

In order to measure the cross sections, detailed comparisons with models incorporating parton showers/dipole chains and a hadronisation phase have been made. In general, these data are well described by the ARIADNE [38] program and are reasonably well described by LEPTO [39] or HERWIG [6]. The next stage in the development of ARIADNE by the Lund group is the Linked Dipole Chain (LDC) model, which was reported at this workshop [40].

A problem highlighted at the workshop relates to various attempts which have been made to correct to parton level in an attempt to determine the gluon density or the strong coupling constant directly. However, the relationship between the NLO partons and ARIADNE/LEPTO/HERWIG partons is far from clear and this introduces an uncertainty for theorists who wish to compare with published data. A presentation of the data corrected to hadron level is therefore required.

The general observation in various analyses, with a range of different kinematic cuts, is that the measured dijet cross sections/rates tend to be higher than those predicted by the NLO calculations incorporating a default coupling constant and parton densities which describe the total DIS cross sections.

  

Figure: ZEUS preliminary dijet cross section as a function of $\xi$, compared to LO and NLO predictions.

This is illustrated in Fig. 8 where the ZEUS preliminary dijet cross section, corrected to parton level, is compared to the NLO and LO predictions [34]. The cross section is measured as a function of $\xi = x(1+M_{\rm JJ}/Q^2)$, the momentum fraction of the parton entering the hard scattering process. The data are $\simeq$ 30% higher than the NLO calculation and this difference persists after taking into account variations in calorimeter energy scale, jet energy resolution, the Monte Carlo used to correct to parton level, the input parton densities or the factorisation/renormalisation scale. However, the shape of the cross section is well described by the NLO calculations and this can be used to extract the power dependence of the gluon at low-$\xi$, $\xi g(\xi) \propto \xi^{-\lambda}$. This results in a value of $\lambda = 0.38 \pm 0.04 \pm 0.18$ at Q²=4 GeV².

A further development has been taken in the H1 analysis. Using the k_T algorithm in the Breit frame [37], a global fit has been performed of the H1 and NMC DIS cross section measurements as well as the H1 preliminary dijet rates. In order to account for hadronisation effects, an additional power correction term is incorporated into the fit of the dijet rates. Although the functional form of these power corrections has not yet been calculated, it is clear from the fits to the data that such a term is required. An empirical function $h(x) = \alpha+\beta\ln(x/x_o) +\gamma\ln^2(x/x_o)+\delta\ln^3(x/x_o)$ is introduced, where $\alpha, \beta, \gamma$ and $\delta$ are additional parameters in the fit and x_o=10^-4. The additional contribution to the dijet cross section is determined as $\Delta\sigma(x,Q^2) = h(x)/Q^2$. The fitted form of h(x) is shown in Fig. 9 together with the results of the global fit incorporating this power correction term. A calculation of the power corrections would therefore enable a simultaneous determination of its magnitude and provide further constraints on $\alpha_S$ as well as the parton densities.

  

Figure 9: Analysis of H1 dijet data.