Abstract
Practical calculations in light-front dynamics are, as a general rule, complicated, since there is no consensus about how to treat the poles which come from the instantaneous parts of Feynman's propagators of the fields. An alternative to solve this difficulty is null-plane causal perturbation theory, a recent developed framework which prevents the appearance of the mentioned poles by avoiding the usage of Feynman's propagators in ``loop distributions,'' requiring no regularization of the amplitudes. In this study, we treat the radiative corrections in the neutral Yukawa's model in that framework. Particularly, we explicitly calculate the boson and fermion self-energies and show that the results obtained with this approach are equivalent to that of the instant dynamics.
Highlights
As is well known, Yukawa’s model [1,2,3,4] is a phenomenological model for the interaction between nucleons and pions
The problem of finding the fermion self-energy for an analogous model, with scalar instead of pseudoscalar mesons [6], in light-front dynamics was recently considered by Karmanov, Mathiot, and Smirnov [7]; these investigators pointed out some difficulties: (i) the cutoffs of the null-plane variables lead to a dependence of the amplitudes on the null-plane orientation in some regularization techniques; (ii) such a dependence is very sensitive because each partial amplitude in light-front dynamics usually diverges more strongly than the corresponding Feynman’s amplitude; (iii) that dependence disappears in the renormalized amplitudes, but the renormalization procedures are drastically different for different regularization schemes
In the causal approach, being finite by construction, those operations are not needed; since they are identified as the origin of some problems, we hope that nullplane causal perturbation theory (CPT) could make simpler the comparison of light-front quantum field theory (QFT) with the usual instant dynamics formulation
Summary
Yukawa’s model [1,2,3,4] is a phenomenological model for the interaction between nucleons and pions. Bakker and Ji [8] have considered box diagrams for light-front (scalar) Yukawa’s model; they conclude that the question of what regularization scheme is the one which would lead to an invariant S-matrix remains, to date, without an answer. Another study in this problem was done by Grang, Mathiot, Mutet, and Werner [9,10,11],. In the causal approach, being finite by construction, those operations are not needed; since they are identified as the origin of some problems, we hope that nullplane CPT could make simpler the comparison of light-front QFT with the usual instant dynamics formulation. In order to familiarize the reader with null plane CPT we present a very brief summary at —the details of the construction of the theory can be found in Ref. [13]
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