Resonance Reconstruction

In most analyses signals for charm quarks have been obtained by full reconstruction of the decay particles of the charmed hadrons into which the quarks fragment. From the decay particles the invariant mass is reconstructed, such that the number of signal events can be determined from the resonance spectrum, above a non-resonant combinatorial background. The reconstruction of the invariant mass works particularly well in hadronic decays in which all final state particles are measured as charged particles in the tracking detectors. Calorimeter energy deposits are sometimes used for decay channels containing $\pi^0$ or $\gamma$.

Figure: $D^*$ signal from ZEUS in the decay channel $D^{*\pm }\rightarrow (D^0\rightarrow K^{\mp } \pi ^{\pm }) \pi ^{\pm }$. Events are selected in which the invariant mass of the $K\pi$ system is consistent with the mass of the $D^0$ (taken from [19]).

The most widely used method to identify events containing charm is the reconstruction of events in the so-called 'golden decay' channel, in which the invariant mass of the $D^{*\pm}$ meson is reconstructed in the decay $D^{*\pm} \rightarrow D^0 \pi^{\pm} \rightarrow K^{\mp}\pi^{\pm}\pi^{\pm}$. In fig.11 the difference $\Delta M$ between the measured masses of the $K\pi\pi$ system and of the $D^0$ meson decaying into $K\pi$ is shown. The number of signal events and the amount of non-resonant background in the mass window is usually determined by a fit to the signal and the side bands. The width of the $\Delta M$ peak is governed by the experimental resolution of the pion track from the $D^*$ decay, as resolution effects from the measurement of the two $D^0$ decay particles largely cancel in the subtraction. The $\Delta M$ distribution is therefore the preferred way to determine the number of $D^*$ mesons in the sample.

The advantage of the full resonance reconstruction method is that all details about the heavy quark resonance and decay kinematics are known and the number of events can be determined precisely. The disadvantage comes from small branching ratios, $BR(D^{*\pm} \rightarrow D^0\pi^{\pm} \rightarrow K^{\mp}\pi^{\pm}\pi^{\pm}) \simeq 2.6\%$ [144] and limited detector capabilities such as finite detector acceptances and/or poor resolution. At small $Q^2$ the detector acceptance constrains measurements in which samples of fully reconstructed $D^*$ mesons are used to about one third of the total phase space for charm production [5]. Limited detector resolution leads to the need for wide mass windows or large combinatorial background. Bad resolution is a particular issue for the identification and measurement of neutral particles at low energies as neither experiment, H1 nor ZEUS, have been designed for this purpose.