Neutral and charged mesons in magnetic fields A resonance gas in a non-relativistic quark model

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 B << Lambda(2)(QCD) (Lambda(QCD) similar to 200 MeV: the QCD scale), the analyses proceed as in usual quark models, while special precautions are needed for strong fields, B << Lambda(2)(QCD) , 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 similar to 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 similar to 100 MeV, but our results at higher energy scale suffer from artifacts of our confining potential and non-relativistic treatments.

Automated summary

Analyzing mesons in constant magnetic fields using a non-relativistic constituent quark model, the study explores the internal quark dynamics and the effects of magnetic translations on neutral and charged mesons. The phase space enhancement for mesons at low temperatures significantly increases entropy, aiding the transition from a hadron gas to a quark gluon plasma.