Introduction

Heavy quark production is a key process for the study of the theory of strong interactions, quantum chromodynamics (QCD). At the HERA storage ring at DESY, electrons of 27.6 GeV of energy are collided with 920 GeV protons, providing an $ep$ center-of-mass energy of 318 GeV. HERA offers ample opportunities to study the production mechanisms of heavy quarks and to test all aspects of QCD, in both perturbative and non-perturbative regimes. In perturbative approaches the mass of the heavy quark $m_q$ defines a 'hard' scale at which the strong interaction coupling constant $\alpha_S$ is evaluated and the condition $m_q \gg \Lambda_{QCD}$ implies that calculations in the framework of perturbative QCD should give reliable results. However, the steep energy dependence of the strength of the coupling constant (running of $\alpha_s$) makes precise predictions difficult and leads to relatively large scale uncertainties. Processes in which no hard scale is present and $\alpha_S$ is large, e.g.the hadronization of heavy quarks into hadrons, are often described in phenomenological non-perturbative approaches.

The understanding of QCD, as one of the four fundamental forces of nature, is not only of principal interest in itself, it is also crucial for the search for physics beyond the Standard Model (SM). At many experiments the interpretation of the data depends on the precise knowledge of the rate of QCD processes, which are expected to form the most significant background at hadron colliders. The importance of a precise understanding of QCD is apparent when considering current and future accelerators, e.g.the Large Hadron Collider (LHC) which is anticipated to start in 2007. Many of these accelerators will have protons or photons as colliding particles with hadronic properties to be described in QCD.

Measurements of inclusive cross sections and exclusive final states have been performed both for electroproduction, often called Deep Inelastic Scattering (DIS), where the photon virtuality $Q^2 \gg \Lambda_{QCD}^2$, and for photoproduction ($Q^2\sim 0$). The cross section in electron proton collisions is strongly dependent on $Q^2$. It is largest in photoproduction where the virtuality of the photon exchanged between the electron and the proton is very small, and the electron beam serves as a source of quasi-real photons with a wide energy distribution spanning the range between close to zero and the electron beam energy of 27.6 GeV. The photoproduction mechanism was previously studied extensively in fixed-target experiments using photon and lepton beams [1]. At HERA, the available center-of-mass energy is about one order of magnitude larger than at fixed-target facilities.

In the regime of deep inelastic scattering, the photon virtuality is large, $Q^2 \gg \Lambda_{QCD}^2$. Experimentally, the value of $Q^2$ is directly measurable at HERA at values larger than $Q^2 > 0.1$ GeV$^2$ up to values as large as 50000 GeV$^2$, the kinematic limit of $Q^2$ being the $ep$ center of mass energy squared $s \approx 100000$ GeV$^2$. Heavy quark analyses have reached values of $Q^2$ as large as 1000 GeV$^2$. In the DIS regime, the photon virtuality $Q^2$ can be used as an energy scale for perturbative calculations and the validity of theoretical predictions as a function of the photon virtuality can be studied. Although the total rates are much smaller than those in photoproduction, the hadronic component of the photon is suppressed and more reliable theoretical and experimental results can be obtained.

Different theoretical approaches exist to describe the HERA data which are based on the factorization of the cross section into a hard scattering process, described by perturbative QCD, and a non-perturbative part, given by the input distributions for the initial state partons in the proton and the exchanged photon and the hadronization of the final state particles.

Measurements of heavy quark production processes give access to a large number of theoretical and phenomenological issues and help to discriminate between the various models. Specifically, at HERA, heavy quark production processes can be used as a probe of the structure of the proton, and also the photon. The production of heavy quarks is directly sensitive to the gluon density in the colliding hadron which is most precisely determined from the scaling violations of inclusive structure function measurements. Measurements of heavy quark production, and also of other processes with exclusive final states, thus allow to test the universality of the parton density distributions. Furthermore, the fragmentation of the heavy quarks into the final state hadrons can be investigated and compared to existing results from other experiments.

In particular charm quarks are produced copiously at HERA. At sufficiently high photon virtualities, $Q^2$, the production of charm quarks constitutes up to $30\%$ of the total cross section. In contrast, the inclusive beauty cross section is suppressed by the largeness of the $b$-quark mass and only becomes sizable ($\sim 10\%$) at $Q^2 \gtrsim 100$ GeV$^2$ where $Q^2 \sim (2 m_b)^2$ or at large transverse momenta of the final state particles.

Heavy quark processes have been identified primarily using the 'golden channels' of resonance decays, $D^{*\pm} \rightarrow D^0 \pi^{\pm} \rightarrow K^{\mp}\pi^{\pm}\pi^{\pm}$ [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] and $J/\psi\rightarrow \ell^+\ell^-$ [27,28,29,30,31,32,33,34]. Other resonances, such as $D^+$, $D_s$ and $\Lambda_c$ have also been reconstructed [35,6,20,26]. More recently, charm and beauty analyses have been published using semi-leptonic decay channels [36,37,38,39,40,41,42] and/or lifetime tags using inclusive data samples [43,44,45,46]. Furthermore, first measurements in which both heavy quarks are identified [47,48,42] have been performed, the results of which provide sensitivity to further details of the heavy quark production process. Finally, the HERA experiments have been able to perform a number of spectroscopic analyses in which the wealth of charm events is exploited to perform searches for higher excitation resonances, such as $D_1$, $D_2$, [50,49] and exotic bound states, such as pentaquarks [51,52,53,54]. $D^{*\pm}$ mesons have also been used to measure the production of charm in diffractive processes [57,55,56,58]. A discussion of the physics of open charm production in diffraction is however not included in this report.

Experimentally, the measurements of heavy quark production at HERA require extensive use of precision information from many parts of the detector. While the total cross section for heavy flavour production is relatively large, the small branching ratios for specific decay channels and limited detector acceptances usually lead to a substantial reduction of the size of the event samples useful for the heavy quark analyses. Various experimental techniques to identify heavy quark processes and to measure specific properties have been established and are discussed in this report.

This report is structured as follows: An overview of the theory of heavy quark production is given in section 2. Event generator programs for the simulation of heavy quark events and the calculation of cross sections are presented in section 3. The H1 and ZEUS detectors are described in section 4 and the experimental techniques are discussed in section 5. The experimental results obtained so far are presented and confronted with theory calculations (section 6). Finally, in section 7, future opportunities for further studies with heavy quarks at HERA are discussed.