Abstract
We consider the propagation of a neutrino or an antineutrino in a medium composed of fermions () and scalars () interacting via a Yukawa-type coupling of the form , for neutrino energies at which the processes like or , and the corresponding ones for the antineutrino, are kinematically accessible. The relevant energy values are around or , where and are the masses of and , respectively. We refer to either one of these regions as a resonance energy range. Near these points, the one-loop formula for the neutrino self-energy has a singularity. From a technical point of view, that feature is indicative that the self-energy acquires an imaginary part, which is associated with damping effects and cannot be neglected, while the integral formula for the real part must be evaluated using the principal value of the integral. We carry out the calculations explicitly for some cases that allow us to give analytic results. Writing the dispersion relation in the form , we give the explicit formulas for and for the cases considered. When the neutrino energy is either much larger or much smaller than the resonance energy, reduces to the effective potential that has been already determined in the literature in the high or low momentum regime, respectively. The virtue of the formula we give for is that it is valid also in the resonance energy range, which is outside the two limits mentioned. As a guide to possible applications we give the relevant formulas for and , and consider the solution to the oscillation equations including the damping term, in a simple two-generation case.
- Received 24 January 2022
- Accepted 24 April 2022
DOI:https://doi.org/10.1103/PhysRevD.105.095022
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society