# The isotensor axial polarisability and lattice QCD input for nuclear double-$\beta$ decay phenomenology

## TL;DR

This paper uses lattice QCD and effective field theory to evaluate short-distance nuclear effects in double-beta decay, highlighting the importance of the isotensor axial polarisability for accurate nuclear modeling.

## Contribution

It introduces the first lattice QCD calculation of the isotensor axial polarisability relevant for double-beta decay, emphasizing its significance in nuclear models.

## Key findings

- Short-distance effects are comparable to axial charge quenching.
- Nuclear models should include isotensor axial polarisability effects.
- Lattice QCD can help constrain nuclear double-beta decay parameters.

## Abstract

The potential importance of short-distance nuclear effects in double-$\beta$ decay is assessed using a lattice QCD calculation of the $nn\rightarrow pp$ transition and effective field theory methods. At the unphysical quark masses used in the numerical computation, these effects, encoded in the isotensor axial polarisability, are found to be of similar magnitude to the nuclear modification of the single axial current, which phenomenologically is the quenching of the axial charge used in nuclear many-body calculations. This finding suggests that nuclear models for neutrinoful and neutrinoless double-$\beta$ decays should incorporate this previously neglected contribution if they are to provide reliable guidance for next-generation neutrinoless double-$\beta$ decay searches. The prospects of constraining the isotensor axial polarisabilities of nuclei using lattice QCD input into nuclear many-body calculations are discussed.