Jet-Muon Analyses

Both H1 and ZEUS have presented measurements in which the events containing beauty are identified using high $p_t$ muons from semileptonic $b$ decays [36,37,38,39,40,41,44]. The beauty signal events are distinguished from the charm and light quark background by means of observables which exploit the large mass (H1 and ZEUS, see section 5.6) and the long lifetime of the $b$ quarks (H1, see section 5.5).

Figure 32 shows the differential photoproduction cross-sections as a function of the muon pseudo-rapidity for the process $ep \rightarrow eb\bar{b}X \rightarrow e\,\,$jet$\,$jet$\,\mu\,$. The H1 [44] and ZEUS [40] data, which are in reasonable agreement, are compared to NLO calculations in the massive scheme[80]. The same scales and parton density distributions are used in both analyses. While the ZEUS data are well described by the theory, the H1 data at low transverse momenta are observed to be somewhat higher than the expectations. The errors of the theory prediction are dominated by the uncertainties of the renormalization scale and the $b$ quark mass. In the calculations different parameter choices, e.g.for the modeling of the hadronization and decay of the $B$ hadron, lead to variations of the prediction of up to $\sim 12\%$.

Figure 32: Differential beauty photoproduction cross sections from H1 [44] and ZEUS [40] as a function of a) the pseudo-rapidity and b) the transverse momentum of the muon. The shaded bands reflect the predictions from FMNR as calculated for the ZEUS data (dark shaded) and H1 data (light shaded).

Figure 33: Ratio of beauty production cross section measurements at HERA [40,41,43,44] to the NLO QCD predictions FMNR (photoproduction) and HVQDIS (DIS).

ZEUS [41] and H1 [44] have also measured the jet-muon beauty cross section in DIS events with at least one hard jet in the Breit frame, $p^{jet}_{t,Breit} > 6$ GeV, together with a muon for photon virtualities $Q^2 > 2$ GeV$^2$. The measurements from H1 and ZEUS are performed in slightly different kinematic regions (see table 3). Comparisons of the data with the NLO QCD calculation in the massive scheme [81] show that the data are higher than the predictions by about 2 standard deviations.

The results of the beauty measurements with jets and muons at HERA are summarized in fig.33 where the ratios between the measured beauty production cross sections and the corresponding next-to-leading order predictions in the massive scheme [80,81] are shown as a function of the photon virtuality $Q^2$. The data tend to be somewhat higher than the predictions but still in agreement.

In earlier measurements [36,39] NLO QCD predictions were used to extrapolate the measured visible cross sections for dijet events with a lepton to more inclusive $\mu$ or b-quark production cross sections. In these measurements softer jet and muon cuts were used in order to overcome statistical limitations. In [40] ZEUS extracted the $b$ quark differential cross section as a function of the quark transverse momentum for a $b$ quark pseudo-rapidity range in the laboratory frame $\vert\eta_b \vert< 2$ and the result was found to be consistent with the previous ZEUS result from semi-leptonic $B$ decays into electrons [39], translated into the $b$ quark cross section for $p^b_t>5$ GeV and $\vert\eta\vert<2$ and also with the most recent results. In a previous measurement by H1 [36] the inclusive $b\rightarrow \mu X$ cross section was found to be $2.3$ standard deviations higher than the new measurement [44] when extrapolated into the same kinematic range using the same model assumptions. In this early measurement the cuts on the jet and muon transverse momenta were comparably loose (see table 3). It can be concluded that the difference between this measurement and the later measurements is not due to extrapolation effects, as suggested e.g.in [162,163], but mainly results from experimental effects which may occur when going to small values of $p_t$ of the $b$-quark. Similar excesses of the cross section above expectation appear to be visible in other measurements of the beauty cross sections which probe the region of small $p_t$ of the beauty quark (see sections 6.3.1 and 6.3.2).