{
  "id": "2209.01872",
  "version": "v1",
  "published": "2022-09-05T10:10:09.000Z",
  "updated": "2022-09-05T10:10:09.000Z",
  "title": "Mass splitting and spin alignment for $φ$ mesons in a magnetic field in NJL model",
  "authors": [
    "Xin-Li Sheng",
    "Shu-Yun Yang",
    "Yao-Lin Zou",
    "Defu Hou"
  ],
  "comment": "11 pages, 8 figures",
  "categories": [
    "nucl-th",
    "hep-ph"
  ],
  "abstract": "Based on the Nambu-Jona-Lasinio (NJL) model, we develop a framework for calculating the spin alignment of vector mesons and applied it to study $\\phi$ mesons in a magnetic field. We calculate mass spectra for $\\phi$ mesons and observe mass splitting between the longitudinally polarized state and the transversely polarized state. The $\\phi$ meson in a thermal equilibrium system is preferred to occupy the state with spin $\\lambda=0$ than those with spin $\\lambda=\\pm1$, because the former state has smaller energy. As a consequence, we conclude that the spin alignment will be larger than 1/3 if one measures along the direction of the magnetic field, which is qualitatively consistent with the recent STAR data. Around the critical temperature $T_{C}=150$ MeV, the positive deviation from 1/3 is proportional to the square of the magnetic field strength, which agrees with the result from the non-relativistic coalescence model. Including the anomalous magnetic moments for quarks will modify the dynamical masses of quarks and thus influence the mass spectra and spin alignment of $\\phi$ mesons. The discussion of spin alignment in the NJL model may help us better understand the formation of hadron's spin structure during the chiral phase transition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-05T10:10:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spin alignment",
      "njl model",
      "mass splitting",
      "mass spectra",
      "hadrons spin structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}