Abstract
We improve the pNRQCD approach to annihilation processes of heavy quarkonium and make first pNRQCD predictions for exclusive electromagnetic production of heavy quarkonium. We consider strongly coupled quarkonia, i.e., quarkonia that are not Coulombic bound states. Possible strongly coupled quarkonia include excited charmonium and bottomonium states. For these, pNRQCD provides expressions for the decay and exclusive electromagnetic production NRQCD matrix elements that depend on the wavefunctions at the origin and few universal gluon field correlators. We compute electromagnetic decay widths and exclusive production cross sections, and inclusive decay widths into light hadrons for P -wave quarkonia at relative order v2 and leading order, respectively. We also compute the decay widths of 2S and 3S bottomonium states into lepton pairs and their ratios with the inclusive widths into light hadrons at relative order v2.
Highlights
Are well under control from the theoretical side, but more difficult to determine experimentally as contributions from decay channels into leptons, photons or heavy quarks have to be subtracted from the total width
Nonrelativistic QCD (NRQCD) is the effective field theory, suited to describe states made of a heavy quark and a heavy antiquark, that follows from QCD by integrating out modes of energy and momentum of order m [3]
From eqs. (2.24) and (3.1) it follows that the LDME of a generic four-fermion operator of the type listed in appendix A, which includes decay and exclusive electromagnetic production LDMEs but excludes hadronic production LDMEs, for a strongly coupled quarkonium H of quantum numbers n, J, L and S, at rest (P = 0), can be expressed in strongly coupled Potential NRQCD (pNRQCD) by means of the master formula [14]: 1 H|On|H = P = 0|P = 0
Summary
We compute the LDMEs of NRQCD assuming that the quarkonium states that we consider are well below the open flavor threshold and satisfy the condition mv ΛQCD. We further assume that higher gluonic excitations of the heavy quark-antiquark pair are separated by an energy gap of order ΛQCD or larger from the ground state; this assumption is supported by lattice calculations that show the excitation spectrum of the gluon field around a static quark-antiquark pair separated by a large energy gap from the ground state [10,11,12] It follows that we can picture the distribution of the energy levels as illustrated in figure 1. Such picture allows us to describe the quarkonium spectrum in an effective field theory where all modes associated to the excitations of the heavy quark-antiquark pair induced by gluons or light quarks and separated by an energy gap of order ΛQCD from the quarkonium spectrum have been integrated out. The Wilson loop and field insertions on it are traced in color space
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