Abstract
We consider the calculation of the thermal self-energy of a neutrino that propagates in a medium composed of fermions and scalars interacting via a Yukawa-type coupling, in the case that the neutri no energy is much larger than the fermion and scalar masses, as well as the temperature and chemical potentials of the background. In this kinematic regime the one-loop contribution to the imaginary part of the self-energy is negligible. We consider the two-loop contribution and we encounter the so-called pinch singularities which are known to arise in higher loop self-energy calculations in Thermal Field Theory. With a judicious use of the properties and parametrizations of the thermal propagators the singularities are treated effectively and actually disappear. From the imaginary part of the self-energy, we obtain a precise formula for the damping matrix expressed in terms of integrals over the background particle distributions. The formulas predict a specific dependence of the damping terms on the neutrino energy, depending on the background conditions. For guidance to estimating the effects in specific contexts, we compute the damping terms for several limiting cases of the momentum distribution functions of the background particles. We discuss briefly the connection between the results of our calculations for the damping matrix and the decoherence effects described in terms of the Lindblad equation.
Highlights
AND SUMMARYIn several models and extensions of the standard electroweak theory, the neutrinos interact with scalar particles (φ) and fermions (f) via a coupling of the formLint 1⁄4 Xgaf RνLaφ þ H:c: a ð1:1ÞFor definiteness we are assuming the presence of only one f and φ, while the indices a; b; c; ... label the neutrino flavors
Similar effects occur due to neutrinoneutrino-scalar interactions of the form νcRbνLaφ when a neutrino propagates in a neutrino background. This can occur in the environment of a supernova, where the neutrino-neutrino interactions lead to the collective neutrino oscillations and related phenomena, and it can occur in the hot plasma of the early Universe before the neutrinos decouple [12,13]
We determine the contribution of those processes to the damping matrix Γ from the two-loop calculation of the imaginary part of the thermal neutrino self-energy using the methods of thermal field theory (TFT)
Summary
In several models and extensions of the standard electroweak theory, the neutrinos interact with scalar particles (φ) and fermions (f) via a coupling of the form. We calculated the real part (or more precisely the dispersive part) of the neutrino thermal self-energy, denoted by Σr, from which the dispersion relation and effective potential are determined Those interactions can induce processes such as ν þ φ ↔ f and ν þ f ↔ φ , depending on the kinematic conditions, that produce damping terms in the neutrino dispersion relation and index of refraction. The two-loop diagrams for the selfenergy, from which the damping matrix is determined, suffer from the so-called pinch singularities [28] These arise from the fact that in the present case some of the diagrams contain a product of two thermal propagators with the same momentum.
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