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Effect of Dynamical SU(2) Gluons to the Gap Equation of Nambu--Jona-Lasinio Model in Constant Background Magnetic Field

Masaru Ishi-i·Taro Kashiwa·Naoki Tanimura
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Abstract

In order to estimate the effect of dynamical gluons to chiral condensate, the gap equation of SU(2) gauged Nambu--Jona-Lasinio model, under a constant background magnetic field, is investigated up to the two-loop order in 2+1 and 3+1 dimensions. We set up a general formulation allowing both cases of electric as well as magnetic background field. We rely on the proper time method to maintain gauge invariance. In 3+1 dimensions chiral symmetry breaking ($χ$SB) is enhanced by gluons even in zero background magnetic field and becomes much striking as the background field grows larger. In 2+1 dimensions gluons also enhance $χ$SB but whose dependence on the background field is not simple: dynamical mass is not a monotone function of background field for a fixed four-fermi coupling.

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Masaru Ishi-i, Taro Kashiwa, Naoki Tanimura. 2001-08-30. Effect of Dynamical SU(2) Gluons to the Gap Equation of Nambu--Jona-Lasinio Model in Constant Background Magnetic Field. https://doi.org/10.1103/physrevd.65.065025

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