Neutral and charged mesons in magnetic fields: A resonance gas in a nonrelativistic quark model
Abstract
We analyze mesons in constant magnetic fields ($B$) within a nonrelativistic constituent quark model. Our quark model contains a harmonic oscillator type confining potential, and we perturbatively treat short range correlations to account for the spinflavor energy splittings. We study both neutral and charged mesons taking into account the internal quark dynamics. The neutral states are labelled by twodimensional momenta for magnetic translations, while the charged states by two discrete indices related to angular momenta. For $B \ll \Lambda_{\rm QCD}^2$ ($\Lambda_{\rm QCD} \sim 200$ MeV: the QCD scale), the analyses proceed as in usual quark models, while special precautions are needed for strong fields, $B \sim \Lambda_{QCD}^2$, especially when we treat short range correlations such as the FermiBreitPauli interactions. We compute the energy spectra of mesons up to energies of $\sim 2.5$ 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 lowlying spectra and the entropy density at low temperature less than $\sim 100$ MeV, but our results at higher energy scale suffer from artifacts of our confining potential and nonrelativistic treatments.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 DOI:
 10.48550/arXiv.2104.00376
 arXiv:
 arXiv:2104.00376
 Bibcode:
 2021arXiv210400376K
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Lattice;
 Nuclear Theory
 EPrint:
 14 pages, 9 figures