Open Charm Production

With the HERA-II luminosity and new detector components enhanced systematic precision and increased kinematic reach will be provided by both increased statistics and also by the use of the upgraded detector components described in section 7.1. The statistics can be used to reduce the statistical errors or to increase the number of measured cross section points. Figure 59 illustrates the kinematic reach for reconstructed $D^*$ events as a function of the transverse momentum $p_t$ of the charm quark. Double and triple-differential cross section measurements, e.g.as functions of $Q^2$, $p_t$ and $\eta$, allow to probe the theoretical predictions at a deeper level and better accuracy and characteristic effects in specific regions of the phase space can be isolated.

In HERA-I, differential measurements of exclusive final states with charm (e.g. identified by the reconstruction of $D$-meson) were performed in the central rapidity regions ( $\vert\eta(D^*)<1.5\vert$) up to transverse momenta of the $D^*$ of 20 GeV (see section 6.1.1). While the data are generally described by pQCD calculations, discrepancies of order 20% are seen among different theory predictions and with the data in particular at large transverse momenta and in the forward direction.

Figure: a) Projected number of $D^*$ events in the central H1 detector acceptance as a function of transverse momentum $p_t$ of the charm quark for an integrated luminosity of 400 pb$^{-1}$. The solid line shows the rate for photoproduction while the light (dark) shaded histograms refer to cuts of $Q^2 > 5 (100)$ GeV$^2$, respectively.

This is illustrated in fig.60 in which the H1 data are compared to predictions from different models as a function of the pseudo-rapidity of $D^*$ mesons and of the transverse energy $E_t$ of jets in charm events. In general, the cross section predictions from CASCADE are higher towards large values of $\eta$ and $p_t$ of the charm quark than those from calculations in the collinear factorization scheme using the DGLAP evolution equations. The HERA-II data are expected to provide sufficient precision to unambiguously discriminate between the different models. The upgraded forward detectors of H1 and ZEUS and more luminosity will make the forward region, i.e.regions of pseudo-rapidity larger than 1.5, more accessible than it has been so far.

Figure: a) Comparison of the cross section predictions for the inclusive charm cross section as a function of pseudo-rapidity, from NLO calculation HVQDIS in the collinear factorization approach using the DGLAP evolution equation (light shaded) and from CASCADE using the $k_t$ factorization approach and the CCFM evolution equation (dark shaded). b) Charm dijet cross sections as a function of $E_t$ of the leading jet in the event as predicted by the RAPGAP Monte Carlo generator (solid line) and by CASCADE (dashed line). In both figures the theory predictions are shown together with the H1 data [8] (see also fig.23 in section 6.1.2 and fig.25 in section 6.1.3).

Measurements of exclusive final states with jets give access to a number of aspects of heavy quark production and fragmentation as the jets contain information about the kinematics and type of the hard partonic interaction. In photoproduction and at small values of $Q^2$, $Q^2 \lesssim m_{c~{\rm or}~b}^2$ the measurement of jet correlations gives access to the hadronic structure of resolved photons. As explained in section 2.3 the particular role of heavy quarks in resolved photon processes is yet to be clarified. The measurement of the shape of the $x_{\gamma}^{OBS}$ distribution and of dijet angular distributions of charm jets in different regions of $x_{\gamma}^{OBS}$ have given first insights into the relative fractions of the processes of gluon-gluon fusion and charm-excitation. High statistics measurements will allow to obtain details at better precision and to determine the dependence on the external scales $Q^2$ and $p_t$, where $p_t$ is the transverse momentum of the final state jets.

The measurement of dijet correlations gives access to the distribution of gluons from the proton in the initial state. In the $k_t$ factorization scheme, the $k_t$ of the gluon can be determined. Predictions in the $k_t$ factorization scheme (CCFM-evolution equation) differ from those using the DGLAP evolution equation in particular in the forward region, i.e. at large values of pseudo-rapidity. Measurements in the forward direction will provide for valuable tests of the different approaches.

The HERA-I data have already provided precise input to the issue of fragmentation. Comparisons of the HERA-data with results from LEP have shown that the assumption of universality is justified. This is all the more interesting as the typical jet energies at HERA are around 10 GeV, and thus significantly lower than those at LEP. One useful question to be addressed with high statistics HERA-II data is to confirm the finding that the fragmentation is independent of the energy by measuring the fragmentation for different processes and at different energies within the same experiment. Furthermore, a fit of the fragmentation distributions could help to discriminate between different fragmentation models, e.g. Lund, [108], Peterson [109], Kartvelishvili [113]. These studies should be performed for both fragmentation fractions and fragmentation functions of charm. For beauty, the production cross sections and branching ratios are too small to allow a full reconstruction of a sufficiently large sample of $B$-hadrons with the statistics expected at HERA.

The analysis of charm and beauty events in which both quark and anti-quark are explicitly identified is particularly useful for the study of heavy quark production at small transverse momenta. Due to the double-tag the background from $uds$ events is strongly suppressed. This allows to perform measurements at small transverse momenta and small invariant masses $M(Q\bar{Q})$ where present results indicate an excess of the data over the expectations. These data samples allow to make measurements to very small transverse momenta of the quark and anti-quarks, such that the total cross section can be measured with few or no model assumptions.