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arXiv 2009.04697nucl-thhep-ph
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Nambu-Jona-Lasinio模型中磁场中π介子质量的规范无关性

Gauge independence of pion masses in a magnetic field within the Nambu--Jona-Lasinio model

Jianing Li, Gaoqing Cao, Lianyi He

发表信息：
Phys.Rev.D 104, 074026 (2021)
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摘要：

本文在Nambu-Jona-Lasinio模型下研究了中性和带电π介子在零温恒定背景磁场中的性质。在以前的计算中，Ritus方法，包括Schwinger相位在一个固定的规范，采用动量空间无规相位近似（RPA）~[物理Lett. B $\textbf{782}$，155-161（2018）]。然而，带电π介子质量的规范不变性还没有得到检验。本文采用基于时间-时间路径积分的线性响应理论，导出了π介子在坐标空间中的关联函数，并在此对应的Schwinger相位自动出现。在足够大的虚时间$τ$下，介子关联函数接近指数形式的$\sim\exp(-E_{\rm G}τ)$，其中$E_{\rm G}$是单介子态的基态能量，因此被确定为介子质量。此外，我们还证明了带电π介子的质量是与规范无关的，即，而与磁场的矢势的选择无关。实际上，我们还发现动量-空间RPA与本文所用的时间-空间方法是等价的。

英文摘要：

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 $\textbf{782}$, 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 $\sim\exp(-E_{\rm G}τ)$, where $E_{\rm G}$ 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.

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