A Note on the J/ψ Strong Couplings

In this note we present an evaluation of the couplings JD(∗)D(∗) and JD(∗)D(∗)π in the Constituent Quark Model. These couplings are a crucial ingredient in the calculation of cross sections for the processes πJ/ψ → D(∗)D̄(∗), an important background for the J/ψ suppression signal in quark-gluon plasma. BARI-TH/02-450 CERN-TH/2002-343 LYCEN-2002-68 November 2002 in Workshop on Hard Probes in Heavy Ion Collisions at the LHC A NOTE ON THE J/ψ STRONG COUPLINGS A. Deandrea, G. Nardulli and A.D. Polosa Abstract In this note we present an evaluation of the couplings JD(∗)D(∗) and JD(∗)D(∗)π in the Constituent Quark Model. These couplings are a crucial ingredient in the calculation of cross sections for the processes πJ/ψ → D(∗)D̄(∗), an important background for the J/ψ suppression signal in quark-gluon plasma. This note is a preliminary report on a study of absorption effects of the J/ψ resonance due to its interaction with the hot hadronic medium formed in relativistic heavy ion scattering. We will give the full analysis elsewhere [1]; here we limit the presentation to the study of the strong couplings of J/ψ, low mass charmed mesons and pions. In the calculation of the relevant cross sections one encounters tree-level diagrams such as those depicted in Fig. 1. Previous studies of these effects can be found in [2]-[5]. Besides the g(DDπ) couplings, for which both theoretical [7],[8] and experimental [9] results are available, in Fig. 1 the JD(∗)D(∗) and JD(∗)D(∗)π couplings appear. They have been estimated by different methods, that are, in our opinion, unsatisfactory. For example the use of the SU(4) symmetry puts on the same footing the heavy quark c and the light quarks, which is at odds with the results obtained within the Heavy Quark Effective Theory (HQET), where the opposite approximation mc ≫ ΛQCD is used (for a short review of HQET see [8]). Similarly, the rather common approach based on the Vector Meson Dominance (VMD) should be considered critically, given the large extrapolation p2 = 0 → mJ/ψ that is involved. A different evaluation, based on QCD Sum Rules can be found in [10] and presents the typical theoretical uncertainties of this method. In this note we will use another approach, based on the Constituent Quark Model (CQM), which is a quark-meson model taking into account explicitly the HQET symmetries (for more details on the CQM see [11]). The CQM model has turned out to be particularly suitable for the study of exclusive heavy meson decays. Since its Lagrangian contains the Feynman rules for vertices formed by a heavy meson, a heavy quark and a light quark, transition amplitudes are computable via simple (constituent) quark loop diagrams where mesons enter as external legs. The model is relativistic and incorporates, besides the heavy quark symmetries, also the chiral SU2 symmetry of the light quark sector. The calculation of the g(DDπ) coupling constant in the CQM can be found in [11]. Here we will consider the calculation of the JD(∗)D(∗) and JD(∗)D(∗)π vertices and, to begin with, the JD(∗)D(∗) vertex, whose calculation proceeds via a VMD ansatz (see Fig. 2). In the CQM the evaluation of the loop diagram depicted on the l.h.s. of the VMD equation in Fig. 2 amounts to the calculation of the Isgur-Wise function, which can be found in [11]. The result is