The Mikheyev-Smirnov-Wolfenstein Matter Potential at the One-loop Level in the Standard Model

TL;DR

This paper provides a comprehensive one-loop calculation of the MSW matter potential in the Standard Model, revealing significant corrections that impact neutrino flavor conversion analyses.

Contribution

It presents the first complete one-loop renormalization and correction calculation of the MSW matter potential in the Standard Model, including scheme comparisons.

Findings

One-loop corrections to the charged-current potential are about 6%.

Neutral-current potential corrections can reach up to 8%.

Results are consistent with previous literature but include new finite corrections.

Abstract

When neutrinos are propagating in ordinary matter, their coherent forward scattering off background particles results in the so-called Mikheyev-Smirnov-Wolfenstein (MSW) matter potential, which plays an important role in neutrino flavor conversions. In this paper, we present a complete one-loop calculation of the MSW matter potential in the Standard Model (SM). First, we carry out the one-loop renormalization of the SM in the on-shell scheme, where the electromagnetic fine-structure constant $\alpha$, the weak gauge-boson masses $m^{}_W$ and $m^{}_Z$, the Higgs-boson mass $m^{}_h$ and the fermion masses $m^{}_f$ are chosen as input parameters. Then, the finite corrections to the scattering amplitudes of neutrinos with the electrons and quarks are calculated, and the one-loop MSW matter potentials are derived. Adopting the latest values of all physical parameters, we find that the relative size of one-loop correction to the charged-current matter potential of electron-type neutrinos or antineutrinos turns out to be $6\%$, whereas that to the neutral-current matter potential of all-flavor neutrinos or antineutrinos can be as large as $8\%$. The calculations are also performed in the $\overline{\rm MS}$ scheme and compared with previous results in the literature.