Abstract
In the framework of the Nambu--Jona-Lasino (NJL) model, we study the effect of an intense external uniform magnetic field on neutral and charged pion masses and decay form factors. In particular, the treatment of charged pions is carried out on the basis of the Ritus eigenfunction approach to magnetized relativistic systems. Our analysis shows that in the presence of the magnetic field three and four nonvanishing pion-to-vacuum hadronic form factors can be obtained for the case of the neutral and charged pions, respectively. As expected, it is seen that for nonzero magnetic field the $\pi^0$ meson can still be treated as a pseudo Nambu-Goldstone boson, and consequently the corresponding form factors are shown to satisfy various chiral relations. For definite parametrizations of the model, numerical results for $\pi^0$ and $\pi^\pm$ masses and decay constants are obtained and compared with previous calculations given in the literature.
Highlights
In recent years a significant effort has been devoted to the study of the properties of strongly interacting matter under the influence of strong magnetic fields
In the framework of the Nambu–Jona-Lasino (NJL) model, we study the effect of an intense external uniform magnetic field on neutral and charged pion masses and decay form factors
The analysis in Ref. [16] considers a regularization procedure in which only the vacuum contributions to different quantities at zero external magnetic field are regularized. This scheme, that goes under the name of “magnetic field independent regularization” (MFIR), has been shown to provide more reliable predictions in comparison with other regularization methods often used in the literature [39]
Summary
In recent years a significant effort has been devoted to the study of the properties of strongly interacting matter under the influence of strong magnetic fields (see e.g., [1,2,3] and references therein). This is mostly motivated by the realization that large magnetic fields might play an important role in the physics of the early Universe [4], in the analysis of high energy noncentral heavy ion collisions [5], and in the description of physical systems such as magnetars [6]. This issue has been studied in the last years following various theoretical approaches for low energy QCD, such as Nambu-Jona-Lasinio (NJL)-like models [7,8,9,10,11,12,13,14,15,16,17,18], quark-meson models [19,20], chiral perturbation
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