Interaction of Dirac and Majorana Neutrinos with Weak Gravitational Fields

TL;DR

This paper investigates how high-energy Dirac and Majorana neutrinos interact with weak gravitational fields, analyzing their form factors, differences, and similarities, and estimating their transition mass radius within a quantum field theoretical framework.

Contribution

It provides a detailed theoretical analysis of neutrino-graviton interactions, highlighting the near indistinguishability of Dirac and Majorana neutrinos in weak gravitational fields.

Findings

Neutrino gravitational form factors are associated with specific angular momentum states.

Differences between Dirac and Majorana neutrinos are theoretically established but are experimentally indistinguishable under weak field conditions.

The neutrino transition mass radius is smaller than the charge radius by a few orders of magnitude.

Abstract

In this paper the interaction of high energy neutrinos with weak gravitational fields is briefly explored. The form of the graviton-neutrino vertex is motivated from Lorentz and gauge invariance and the non-relativistic interpretations of the neutrino gravitational form factors are obtained. We comment on the renormalization conditions, the preservation of the weak equivalence principle and the definition of the neutrino mass radius. We associate the neutrino gravitational form factors with specific angular momentum states. Based on Feynman diagrams, spin-statistics, CP invariance and symmetries of the angular momentum states in the neutrino-graviton vertex, we deduce differences between the Majorana and Dirac cases. It is then proved that in spite of the theoretical differences between the two cases, as far as experiments are considered, they would be virtually indistinguishable for any space-time geometry satisfying the weak field condition. We then calculate the transition gravitational form factors for the neutrino by evaluating the relevant Feynman diagrams at 1-loop and estimate a neutrino transition mass radius. The form factor is seen to depend on the momentum transfer very weakly. It is also seen that the neutrino transition mass radius is smaller than the typical neutrino charge radius by a couple of orders of magnitude.