Dirac sea effects on Heavy Quarkonia decay widths in magnetized matter -- a field theoretic model of composite hadrons

Abstract

We study the partial decay widths of charmonium (bottomonium) states to $\mathrm{D}\bar{\mathrm{D}}(\mathrm{B}\bar{\mathrm{B}})$ mesons in magnetized (nuclear) matter using a field theoretical model of composite hadrons with quark (and antiquark) constituents. These are computed from the mass modifications of the decaying and produced mesons within a chiral effective model, including the nucleon Dirac sea effects. The mass modifications of the open charm (bottom) mesons are calculated from their interactions with the nucleons and the scalar mesons, whereas the mass shift of the heavy quarkonium state is obtained from the medium change of a scalar dilaton field, $\chi$, which mimics the gluon condensates of QCD. The Dirac sea contributions are observed to lead to a rise (drop) in the quark condensates as the magnetic field is increased, an effect called the (inverse) magnetic catalysis. These effects are observed to be significant and the anomalous magnetic moments (AMMs) of the nucleons are observed to play an important role. For ${\rho }_B$=0, there is observed to be magnetic catalysis (MC) without and with AMMs, whereas, for ${\rho }_B={\rho }_0$, the inverse magnetic catalysis (IMC) is observed when the AMMs are taken into account, contrary to MC, when the AMMs are ignored. In the presence of a magnetic field, there are also mixings of spin 0 (pseudoscalar) and spin 1 (vector) states (PV mixing) which modify the masses of these mesons. The magnetic field effects on the heavy quarkonium decay widths should have observable consequences on the production the heavy flavour mesons, which are created in the early stage of ultra-relativistic peripheral heavy ion collisions, at RHIC and LHC, when the produced magnetic fields can still be extremely large.

42 pages, 7 figures, version published in Phys. Rev. D 107 (2023) 074003

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