arXiv 2104.003762021-04hep-phhep-latnucl-th

磁场中的中性和带电介子：非相对论性夸克模型中的共振气体

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

Toru Kojo

备注：: 14 pages, 9 figures; A contribution to the topical issue "The QCD Phase Diagram in Strong Magnetic Fields"; v2 revised, 18 pages, 10 figures, comparisons with the lattice results were added

摘要：

本文在非相对论组分夸克模型中分析了恒定磁场中的介子。我们的夸克模型包含一个谐振子类型的限制势，我们微扰处理短程关联来解释自旋味能量分裂。我们研究中性和带电介子考虑到内部夸克动力学。中性态用二维磁动量表示，带电态用两个离散的角动量表示。对于$B \ll Λ_{\rm QCD}^2$（$Λ_{\rm QCD} \sim 200$ MeV：QCD标度），分析与通常的夸克模型一样进行，而对于强场$B \sim Λ_{QCD}^2$，特别是当我们处理短程关联，如费米-布莱特-泡利相互作用时，需要特别注意。我们计算了能量达到$\sim 2.5$ GeV的介子能谱，并利用它们来构造介子共振气体。假设夸克质量对磁场不敏感，介子的相空间增强显著增加了熵，有助于从强子气体到夸克-胶子等离子体的转变。我们面对我们的结果与晶格数据，发现合理的协议，在低温低于$\sim 100$兆电子伏的低位谱和熵密度，但我们的结果在更高的能量尺度受到我们的限制势和非相对论处理的文物。

英文摘要：

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 $B \ll Λ_{\rm QCD}^2$ ($Λ_{\rm QCD} \sim 200$ MeV: the QCD scale), the analyses proceed as in usual quark models, while special precautions are needed for strong fields, $B \sim Λ_{QCD}^2$, 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 $\sim 2.5$ 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 low-lying 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 non-relativistic treatments.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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