Charm Jet Cross Sections

The measurement of $D^*$ mesons in events with dijets enhances the sensitivity to higher order effects. Figure 25 shows the H1 cross sections in the DIS regime for the production of dijets in association with a $D^*$ meson versus the $D^*$ meson production cross section [8]. A transverse momentum of at least 4(3) GeV is required for the highest (second highest) $p_t$ jet, respectively. The Monte Carlo simulations RAPGAP, AROMA, CASCADE all reproduce the inclusive cross section but do not describe the cross section of dijets in association with a $D^*$ meson. While RAPGAP and AROMA (based on the DGLAP evolution equations) are too low in normalization, the CASCADE Monte Carlo generator (based on the CCFM equation) is too high. HERWIG fails to describe the data for both the inclusive and the dijet selection.

In dijet processes the contribution from resolved processes can be measured. The variable $x_{\gamma}^{\rm obs}$ gives the energy fraction in the proton rest frame, of the parton from the photon entering the hard subprocess. It is reconstructed using the two highest transverse energy jets as

$$x^{\rm obs}_{\gamma} = \frac{\sum_{\rm jet1,2} (E-p_z)}{2yE_{e}}$$ (6)

where $E_{e}$ is the electron beam energy and $y$ is the photon inelasticity, i.e.the fractional electron energy carried by the exchanged photon. For the direct process (fig5a in section 2.3), $x_{\gamma}^{obs}$ approaches unity, as the hadronic final state consists of only the two hard jets and the proton remnant in the forward region. Energy depositions of the proton remnant in the forward direction contribute little to $x_{\gamma}^{obs}\,$since $\sum_{h}(E-p_z) \approx \sum_{h} E(1-cos\theta)$ and $\theta_{p-\rm remnant}$ is close to 0. In resolved processes (fig.5b-d in section 2.3) $x_{\gamma}^{obs}$ can be small. Other effects that lead to values of $x_{\gamma}^{obs}\,$smaller than unity are jet splitting, i.e.when two jets are reconstructed which originate from the same mother parton, and higher order effects, e.g.when hard gluons are radiated off the quarks.

Figure: The $D^*$ dijet cross section versus the inclusive $D^*$ cross section in comparison with various models [8]. The dijet cross sections as a function of $E_t$ of the leading jet are shown in fig.60.

The ZEUS dijet photoproduction cross section [17] as a function of $x_{\gamma}^{\rm obs}$ is shown in the figures 26a and b compared with predictions from PYTHIA [108], HERWIG [125] and CASCADE [104], as well as a fixed order massive calculation [80] in NLO QCD. A significant part of the cross section is situated at low values of $x_{\gamma}^{\rm obs}$. In the approach of collinear factorization at leading order this is consistent with the presence of resolved photon processes.

Figure: Differential $D^*$ dijet photoproduction cross sections from ZEUS [17], a) $d\sigma /dx_{\gamma }^{obs}$ in comparison with Monte Carlo generators CASCADE, PYTHIA and HERWIG, b) $d\sigma /dx_{\gamma }^{obs}$ in comparison with NLO FO predictions after hadronization correction (full lines) and at parton level (dashed lines). c-f) $d\sigma/d\cos\theta^{*}$ as a function of $\cos\theta^{*}$ for the region of $x_{\gamma }^{\rm obs} < 0.75$ (resolved-enhanced, c and e) and $x_{\gamma }^{\rm obs} > 0.75$ (direct-enhanced, d and f) (see text). Also shown are predictions from Monte Carlo generators (c and d) which are individually scaled in normalization and from a NLO fixed order QCD calculation (e and f). The dashed-dotted lines show the jet-energy-scale uncertainty of the data.