https://doi.org/10.1140/epjc/s10052-024-12643-7
Regular Article - Theoretical Physics
Mass splitting and spin alignment for 
mesons in a magnetic field in NJL model
1
Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, 430079, Wuhan, China
2
INFN Sezione di Firenze, Via G. Sansone 1, Sesto Fiorentino, 50019, Florence, Italy
Received:
12
January
2024
Accepted:
3
March
2024
Published online:
22
March
2024
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 mesons in a magnetic field. We calculate mass spectra for mesons and observe mass splitting between the longitudinally polarized state and transversely polarized states. The meson in a thermal equilibrium system is preferred to occupy the state with spin 
than those with spin 
, because the former state has a 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 
, 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 affect the mass spectra and spin alignment of 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.
© The Author(s) 2024
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