Abstract
We compute the magnetic field-induced modifications to the boson self-coupling and the boson-fermion coupling, in the static limit, using an effective model of QCD, the linear sigma model with quarks. The former is computed for arbitrary field strengths as well as using the strong field approximation. The latter is obtained in the strong field limit. The arbitrary field result for the boson self-coupling depends on the ultraviolet renormalization scale and this dependence cannot be removed by a simple vacuum subtraction. Using the strong field result as a guide, we find the appropriate choice for this scale and discuss the physical implications. The boson-fermion coupling depends on the Schwinger's phase and we show how this phase can be treated consistently in such a way that the magnetic field induced vertex modification is both gauge invariant and can be written with an explicit factor corresponding to energy-momentum conservation for the external particles. Both couplings show a modest decrease with the field strength.
Highlights
The effects of magnetic fields on the properties of strongly interacting matter have gathered a great deal of interest over the last several years
Field intensities in the linear sigma model with quarks (LSMq), it is important to compute the magnetic-field-induced corrections to the interaction vertices. We address this question and compute the one-loop magnetic field corrections to the boson selfcoupling and the boson-fermion coupling in the LSMq
We have computed the magnetic-fieldinduced corrections to the boson self-coupling and to the boson-fermion coupling in the LSMq, in the static limit
Summary
The effects of magnetic fields on the properties of strongly interacting matter have gathered a great deal of interest over the last several years. The recent LQCD results for the magnetic-field-driven modifications of neutral and charged mesons show that the neutral pion mass monotonically decreases, whereas the mass of the charged pions monotonically increases, both as functions of the field intensity [57,72] The former cannot be fully reproduced by calculations within effective models that do not consider accounting for magnetic field modifications of the couplings [73,74]. We address this question and compute the one-loop magnetic field corrections to the boson selfcoupling and the boson-fermion coupling in the LSMq. In doing so, we address some important details involving the effects introduced by the renormalization scale, as well as those introduced by the Schwinger phase in calculations involving three particles propagating within loops in the presence of magnetic fields. VI, leaving for the appendixes the details of the calculation of the boson self-coupling and the bosonfermion coupling
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