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

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 $\overline{\mathrm{MS}}$ scheme and compared with previous results in the literature.

Comments: 33 pages, 12 figures, 3 tables, more discussions and references added, version accepted by PRD