Generalized two-point tree-level amplitude j f → j′ f′ in a magnetized medium

Abstract

The tree-level two-point amplitudes for the transitions jf → j f , where f is a fermion and j is a generalized current, in a constant uniform magnetic field of an arbitrary strength and in charged fermion plasma, for the jf f interaction vertices of the scalar, pseudoscalar, vector and axial-vector types have been calculated. The generalized current j could mean the field operator of a boson, or a current consisting of fermions, e.g. the neutrino current. The particular cases of a very strong magnetic field, and of the coherent scattering off the real fermions without change of their states (the "forward" scattering) have been analysed. The contribution of the neutrino photoproduction process, γe → eνν, to the neutrino emissivity has been calculated with taking account of a possible resonance on the virtual electron. October 21, 2018 23:18 WSPC/INSTRUCTION FILE Kuzn˙Rum˙Shlen˙Gen˙Compt˙corr 2 A. V. Kuznetsov, D. A. Rumyantsev, D. M. Shlenevwhere P is the rotational period. It is well-known that strong magnetic field and/or plasma could have an essential influence on various quantum processes, 3-6 because the external active medium catalyses the processes, by changing their kinematics and inducing new interactions. Therefore, the effects of magnetized plasma on microscopic physics should be incorporated in the magnetosphere models of strongly magnetized neutron stars. In the present paper we consider the two-point processes, because such reactions can have possible resonant behavior, and therefore they could be very interesting for astrophysical applications. 7The investigation of the two-point processes in an external active medium (electromagnetic field and/or plasma) has a rather long history. The most general expression for a two-vertex loop amplitude of the form j → ff → j in a pure constant uniform magnetic field and in a crossed field was obtained previously in Ref. 8, where all possible combinations of scalar, pseudoscalar, vector, and axial-vector interactions of the generalized currents j and j with fermions were considered. The generalized current j could mean the field operator of a boson, or a current consisting of fermions, e.g. the neutrino current.The typical example of a tree-level process with two vector vertices in the presence of magnetized plasma is the Compton scattering, γe → γe, as a possible channel of the radiation spectra formation. In this case, both generalized currents j and j mean the photon field operators. This process was studied in a number of papers, see e.g. Refs. 9-15, but the results were presented there in the form without taking account of the photon dispersion properties. In Ref. 16 this neglect was corrected. The expression for the Compton scattering amplitude, with the initial and final electrons being on the lowest Landau level was presented in Ref. 16 in the explicit Lorentz invariant form. The other example of the Compton like process with the vector and axial-vector vertices, the photon transition into the neutrino pair in the presence of magnetized plasma, γe → eνν,...

Neutrino photoproduction on the electron in dense magnetized medium

“…Obtained results coincide up to notation with obtained earlier in [24]. They also generalize the results of recent studies [13] to the case, when initial and final electron occupy arbitrary Landau level.…”

“…The obtained luminocity (31) coincides up to notation with results of [24]. It also generalizes obtained in [13] expression to the case of arbitrary initial and final electron Landau level.…”

“…n + iI s Σ (P)(X 1 ) Assuming that the main contribution to amplitude is given by resonance region, we can approximately replace the part of the amplitude by the δ-function [13]:…”