Gauge independence of pion masses in a magnetic field within the Nambu–Jona-Lasinio model
Gauge independence of pion masses in a magnetic field within the Nambu–Jona-Lasinio model
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DOI：
10.1103/physrevd.104.074026
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发表时间：
2020-09
影响因子：
5
通讯作者：
Jianing Li;G. Cao;Lianyi He
中科院分区：
文献类型：
--
作者：
Jianing Li;G. Cao;Lianyi He
We investigate the properties of neutral and charged pions in a constant background magnetic field mainly at zero temperature within the Nambu–Jona-Lasinio model. In the previous calculations, the Ritus method, involving Schwinger phases in a fixed gauge, was employed within the momentum-space random phase approximation (RPA) [Phys. Lett. B 782, 155-161 (2018)]. However, gauge invariance of the charged pion masses has not yet been examined. In this work, by adopting the linear response theory based on the imaginary-time path integral formalism, we derive the correlation functions for pions in the coordinate space, where the corresponding Schwinger phases show up automatically. At sufficiently large imaginary time τ, the meson correlation function approaches an exponential form ∼ exp(−EGτ), where EG is the ground-state energy of the one-meson state and hence determined as the meson mass. Furthermore, we show that the mass of the charged pions is gauge independent, i.e., independent of the choice of the vector potential for the magnetic field. Actually, we also find that the momentum-space RPA is equivalent to the imaginary-time method used here.
