Relative Transverse Momentum Distribution $p_t^{rel}$

Events with heavy quarks are often identified using semi-leptonic decays of heavy hadrons. In these events the decay lepton is typically one of the leading particles in the event. While a fraction of the decay particles, e.g.the neutrino escape detection such that the mass of the heavy hadrons can not precisely be measured, it is nevertheless possible to reconstruct distributions which reflect the mass of the heavy hadron. These distributions are significantly different for charm and for beauty and therefore allow the determination of the relative contributions from charm and from beauty in a given event sample. The observable $\,p_t^{rel}\,$, i.e. the transverse momentum of the decay lepton relative to the direction of the parent quark, as estimated by the jet axis, provides a clear signature for beauty. Due to their larger mass, events with decays of $B$-hadrons populate higher values of $\,p_t^{rel}\,$as shown in fig.20.

Figure 20: Distribution of the transverse momentum of the decay muon track candidate for a sample of photoproduction events with two jets and an identified muon. The solid line shows the distribution of the PYTHIA Monte Carlo simulation after a fit of the normalization of light quark (dash-dotted), charm quark (dotted) and beauty quark (dashed) events (see text).

The transverse momentum $p_t^{rel}$ of the muon with respect to the axis of the associated jet exhibits a much harder spectrum for muons from $b$ decays than for the other sources. At HERA, several analyses of beauty production have made use of the $\,p_t^{rel}\,$distribution and are described in section 6.2.1.