$D^*\mu$ Correlations

Table: Measured $D^*\mu$ cross sections for charm and beauty production in comparison with results from theory predictions.

		Cross section [pb]
H1 Charm	Data	$250 \pm 57 \pm 40$
	PYTHIA (direct)	$242(142)$
	CASCADE	$253$
	FMNR	$286^{+159}_{-59}$
H1 Beauty	Data	$206 \pm 53 \pm 35$
	PYTHIA (direct)	$57(44)$
	CASCADE	$56$
	FMNR	$52^{+14}_{-9}$
ZEUS Beauty	Data	$214 \pm 52 (stat.) ^{+96}_{-84} (syst.)$
	PYTHIA (direct)	$80$
	HERWIG	$38$

ZEUS and H1 have performed analyses of $D^*\mu$ correlations [47,48] in which the $D^*$ is reconstructed in the decay $D^{*\pm} \rightarrow D^0\pi^\pm \rightarrow (K^\mp\pi^\pm)\pi^\pm$. The separation of charm and beauty production exploits the charge and azimuthal angle correlations of the $D^*$ meson and the muon. Four different correlation regions are defined which are populated differently by charm and beauty events (see fig.36), thus allowing to separate the cross section contributions from charm and beauty quark pairs.

In the approximation in which the directions of the $D^*$ meson and the muon are identified with those of the quark and antiquark, only one correlation is possible for $c\bar{c}$ pairs, and the events populate region IV. In contrast, beauty events populate regions II,III, and IV depending on whether the muon originates from the same $b$ quark as the $D^*$ or from the opposite $\bar{b}$. The correlations for the $D^*$ and the muon are smeared out by the leptonic decay spectrum and by fragmentation effects. Higher order QCD effects like gluon radiation and/or an initial transverse momentum of the gluon should also be visible. Possible physics backgrounds come from $B^0\bar{B^0}$ mixing and Cabibbo suppressed decays $b \rightarrow cW^-$, $W^- \rightarrow \bar{c}s$. Experimentally, background contributions originate from events with fake $D^*$ mesons, i.e.from combinatorial background, or from fake muons.

Monte Carlo simulations are used to account for smearing effects and backgrounds. The normalization of the combinatorial background is fitted using right and wrong charge combinations of the $D^0$ decays in each region separately. Here, wrong charge combinations are given by $D^{*\pm} \rightarrow (K^\pm\pi^\mp)\pi^\pm$. The relative fractions of beauty and charm are then extracted from a fit to the four correlation regions.

The analysis does not depend on the reconstruction of jets and is thus capable of accessing a kinematic region of lower invariant masses $M(Q\bar{Q})$ than the measurements of the beauty cross section for events with jets in the final state (see fig.37).

Figure: Normalized differential $D^*\mu$ cross sections for the azimuthal angle difference $\Delta \Phi$ between the muon and the $D^*$ meson. The data are compared with predictions from a) the LO+PS Monte Carlo generators Pythia and Cascade and b) with LO and NLO predictions from the FMNR program.

The normalized differential cross section of the $D^*\mu$ sample is compared with LO+PS predictions from Pythia and Cascade (fig.38a) and with predictions from FMNR at LO and at NLO (fig.38b). The data show the expected deviations from the LO calculations due to higher order effects: the observed $\Delta \Phi$ peak around $180^{\circ}$ is broader than the LO computation. The data are in good agreement with the NLO calculation and also with PYTHIA and CASCADE. Although different approaches are used in PYTHIA and CASCADE to compute the evolution of the partons from the proton and the hard interaction, the differences between the two simulations are smaller than the experimental errors.

The visible beauty and charm cross sections as measured using $D^*\mu$ correlations by H1 [47] and by ZEUS [48] are compared with theory predictions. The results are listed in table 4 and are also shown in fig.40. Comparison of the measurement with the theory predictions shows that the beauty cross sections extracted from the $D^*\mu$ data are consistently higher by roughly a factor 3 to 4 than the expectations from theory. In contrast, the corresponding charm cross sections are generally well described by theory.