Causal approach for the electron-positron scattering in generalized quantum electrodynamics

Abstract

In this paper we study the generalized electrodynamics contribution to the electron-positron scattering process e − e þ → e − e þ , i.e., Bhabha scattering. Within the framework of the standard model and for energies larger than the electron mass, we calculate the cross section for the scattering process. This quantity is usually calculated in the framework of Maxwell electrodynamics and (for phenomenological reasons) is corrected by a cutoff parameter. On the other hand, by considering generalized electrodynamics instead of Maxwell's, we show that the Podolsky mass plays the part of a natural cutoff parameter for this scattering process. Furthermore, by using experimental data on Bhabha scattering we estimate its lower bound. Nevertheless, in order to have a mathematically well-defined description of our study we shall present our discussion in the framework of the Epstein-Glaser causal theory.

Reduced Order Podolsky Model

“…In our case, since we have isolated the gauge symmetry in the A µ sector and have introduced the gauge invariant auxiliary vector field B µ we expect also second-class constraints. In the following we apply the Dirac-Bergmann algorithm to system (7) by going to the phase space and considering its instant-form time evolution as a constrained system. The quantization will then be achieved by fixing the gauge, calculating Dirac brackets, and sending them to quantum operator commutators.…”

“…As a starting point, in order to calculate the conjugated momenta and perform a Legendre transformation, we split the Lagrangian (7) into two parts with respect to the occurrance of time derivatives writing…”

“…We have successfully calculated the Dirac brackets among the phase space variables for the model (7). From this point on the canonical quantization follows the usual procedure promoting the classical variables of phase space to quantum operators and associating the DB's to the commutation relations.…”

“…Additionally, from the known experimental value of the electron magnetic moment, a numerical bound for Podolsky's parameter was obtained in [4]. In [7], Bufalo, Pimentel and Souto have calculated the generalized electrodynamics contribution to the Bhabha scattering cross section attempting to address known discrepancies between usual QED predictions and experiment.…”

Casimir effect in Podolsky electrodynamics: A functional approach

“…The term with the gauge parameter ξ comes from the Fadeev-Popov-DeWitt method for quantization of gauge systems and we call it as non-mixing gauge fixing term. [21][22][23][24] Although, initially, Podolsky used the standard Lorenz gauge fixing term to fix the physical degrees of freedom, sometimes it is more convenient to use the so called generalized Lorenz gauge fixing term.…”