Simple predictions from ALCOR_c for rehadronisation of charmed quark matter

We study the production of charmed hadrons with the help of ALCOR_c, the algebraic coalescence model for rehadronisation of charmed quark matter. Mesonic ratios are introduced as factors connecting various antibaryon to baryon ratios. The resulting simple relations could serve as tests of quark matter formation and coalescence type rehadronization in heavy ion collisions.

The description of the charmed baryons has to deal with the fact that two possible (1/2) + baryon multiplets exist containing c, s and u (or d) quarks, one being flavor symmetric under s and d (or u) exchange and the other being antisymmetric [10]. The heavier (symmetric) states decay into the lighter (antisymmetric) one by emission of a γ or a π meson. However, if quark clusterization is the basic hadronization process, then the effect of these decay processes will be cancelled from charmed antibaryon to baryon ratios. Neglecting the difference between the light u and d quarks and using the notation q for them, the 10 different types of produced quark clusters can be connected to the 40 lowest lying SU(4)-flavor baryon species in the following way (see e.g. Ref. [11,12] for precise quark content, hadron names and masses): In ALCOR, the algebraic coalescence model of rehadronization it is assumed that the number of directly produced hadrons is given by the product of the the number of quarks (or anti-quarks) from which those hadrons are produced, multiplied by coalescence coefficients C h and by non-linear normalization coefficients b q , that take into account conservation of quark numbers during quark coalescence, as will be explained subsequently. The number of various hadrons and quarks is denoted by the symbol usual for that type of particles, e.q. q, s and c denote the number of light, strange and charmed quarks, respectively, N denotes the number of protons, neutrons and deltas etc.
In this paper, we will evaluate only the simplest predictions from ALCOR c , by considering ratios of the number of particles to the number of anti-particles and by assuming the symmetry of the coalescence process for charge conjugation, extending the results of ref. [6] to the case of charmed quarks, mesons and baryons.
Assuming that the coalescence coefficients C for hadrons are equal to that for the corresponding anti-particles, e.g. C Λ = C Λ , the following relations were obtained for the ratio of light and strange antibaryons and baryons [6]: Inspecting eqs. (11)-(14) one can recognize, that the kaon to anti-kaon ratio S qs has a special role as it acts as a stepping factor that connects various antibaryon to baryon rations, This factor S qs substitutes a light quark with a strange quark in the antibaryon to baryon ratios. Thus it shifts the antibaryon to baryon ratios and changes their strangeness content by one unit, as the following relations display: The inverse factor, S sq = (S qs ) −1 decreases the strangeness content and increases the number of light quarks in the antibaryon to baryon ratios. Note that these relations hold between the ratios of the directly produced anti-baryons to baryons and that the number of observed anti-baryons and baryons have to be corrected to the various chains of resonance decays [6].
Extending the above ALCOR model to the case of charmed baryons and antibaryons, further relations are obtained: These ratios and the ratios from eqs. (11)-(14) can be organized into a special structure displayed in Fig.1. We can introduce two more factors S sc and S cq constructed as in eq.(15) but from the ratios of charmed mesons: The factor S sc substitutes a strange quark with a charm one and the factor S cq changes the charm quark into a light one. These properties lead to the following identity: This identity can be rewritten as an identity between the mesonic ratios: A comparison of this simple relation with experimental data could serve as test of quark matter formation and coalescence type rehadronization in heavy ion collisions.
The inverse of the step factors is defined as S ji = (S ij ) −1 . The structure of the antibaryon to baryon ratios in ALCOR c is visualized in a geometric manner in Fig. 1. This way, more complicated but definitely interesting relations can be obtained. Since the baryons with one charm quark (or antiquark) can be measured most easily, one may consider the following relations as candidates for an experimental test: These yield the following simple relation between baryonic and mesonic ratios: A number of similar expressions can be derived from Figure 1, picking up a given ratio and following all the paths to reach that from its neighbors.
In summary , we have made simple predictions from the ALCOR c model, extending the ALCOR model of algebraic coalescence and rehadronization of quark matter to the case when charmed quarks and final state hadrons are present in a significant number. We found that the various M /M mesonic ratios connect different B/B ratios. The agreement between the obtained theoretical relations and those in the measured data could serve as proof or disproof of the formation of quark matter in heavy ion collisions followed by a fast hadronization via quark coalescence. The predictions made in this paper are independent from the detailed values of coalescence coefficients, we have assumed only their symmetry for charge conjugation. The calculations of the absolute numbers of produced particles from ALCOR c requires the specification of these coalescence coefficients from calculations of cross-sections.