Mikheyev-Smirnov-Wolfenstein matter potential at the one-loop level in the Standard Model
Jihong Huang, Shun Zhou
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. First, we carry out the one-loop renormalization of the Standard Model in the on-shell scheme, where the electromagnetic fine-structure constant $\ensuremath{\alpha}$, 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 $\overline{\text{MS}}$ scheme and compared with previous results in the literature.