Neutrino propagation in noncommutative spacetimes

TL;DR

This paper calculates one-loop quantum corrections to neutrino propagation in noncommutative gauge theories, revealing UV/IR mixing effects, potential superluminal speeds, and the impact of Seiberg-Witten map choices.

Contribution

It provides explicit one-loop corrections in noncommutative U*(1) gauge theory, showing how to mitigate UV/IR mixing and explore neutrino dispersion modifications.

Findings

UV divergence and IR logarithmic divergence in corrections

Certain noncommutative parameters eliminate problematic divergences

Neutrino dispersion relations can exhibit superluminal behavior

Abstract

One-loop theta-exact quantum corrections to the neutrino propagator are computed in noncommutative U*(1) gauge-theory based on Seiberg-Witten maps. Our closed form results show that the one-loop correction contains a hard 1/epsilon UV divergence, as well as a logarithmic IR-divergent term of the type ln sqrt(theta p)^2, thus considerably softening the usual UV/IR mixing phenomenon. We show that both of these problematic terms vanish for a certain choice of the noncommutative parameter theta which preserves unitarity. We find non-perturbative modifications of the neutrino dispersion relations which are assymptotically independent of the scale of noncommutativity in both the low and high energy limits and may allow superluminal propagation. Finally, we demonstrate how the prodigious freedom in Seiberg-Witten maps may be used to affect neutrino propagation in a profound way.