https://doi.org/10.1140/epja/s10050-021-00629-y
Regular Article - Theoretical Physics
Neutral and charged mesons in magnetic fields
A resonance gas in a non-relativistic quark model
Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, 430079, Wuhan, China
Received:
1
April
2021
Accepted:
11
November
2021
Published online:
29
November
2021
We analyze mesons in constant magnetic fields (B) within a non-relativistic constituent quark model. Our quark model contains a harmonic oscillator type confining potential, and we perturbatively treat short range correlations to account for the spin-flavor energy splittings. We study both neutral and charged mesons taking into account the internal quark dynamics. The neutral states are labelled by two-dimensional momenta for magnetic translations, while the charged states by two discrete indices related to angular momenta. For 
(
MeV: the QCD scale), the analyses proceed as in usual quark models, while special precautions are needed for strong fields, 
, especially when we treat short range correlations such as the Fermi-Breit-Pauli interactions. We compute the energy spectra of mesons up to energies of 
GeV and use them to construct the meson resonance gas. Within the assumption that the constituent quark masses are insensitive to magnetic fields, the phase space enhancement for mesons significantly increases the entropy, assisting a transition from a hadron gas to a quark gluon plasma. We confront our results with the lattice data, finding reasonable agreement for the low-lying spectra and the entropy density at low temperature less than 
MeV, but our results at higher energy scale suffer from artifacts of our confining potential and non-relativistic treatments.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
