# Geometrical contribution to neutrino mass matrix

## TL;DR

This paper explores how the geometrical properties of curved spacetime, specifically the spin connection and contorsion, can induce effective neutrino masses and flavor mixing, potentially affecting neutrino oscillations without extending the Standard Model.

## Contribution

It demonstrates that fermions in curved spacetime with contorsion can acquire effective masses and flavor mixing, offering a novel geometrical mechanism for neutrino oscillations.

## Key findings

- Fermions gain effective mass in fermionic matter due to spacetime geometry.
- Different neutrino flavors can mix without intrinsic mass in vacuum.
- The mechanism operates within the Standard Model framework, without new fields.

## Abstract

The dynamics of fermions on curved spacetime requires a spin connection, which contains a part called contorsion, an auxiliary field without dynamics but fully expressible in terms of the axial current density of fermions. Its effect is the appearance of a quartic interaction of all fermions in the action, leading to a nonlinear Dirac equation involving all fermions present. Noting that left and right-chiral fermions may couple to contorsion by different strengths, we show that all fermions gain an effective mass when propagating through fermionic matter. This may have an observable effect on neutrino oscillations. In particular we find that different neutrino flavors can mix even if they have zero rest mass in vacuum, without requiring fields beyond the Standard Model.