Light-Neutrino Exchange and Long-Distance Contributions to $0\nu2\beta$ Decays: An Exploratory Study on $\pi\pi\to ee$

TL;DR

This study demonstrates the feasibility of calculating neutrinoless double beta decay amplitudes from first principles using lattice QCD, highlighting significant long-distance contributions and providing crucial inputs for effective field theories.

Contribution

First lattice QCD calculation of $eta$ decay amplitude via $ o ee$ with physical and unphysical pion masses, offering new insights into long-distance effects.

Findings

Decay amplitudes are 24% and 9% smaller than chiral perturbation theory predictions.

Lattice methods can compute decay amplitudes from first principles.

Results provide essential inputs for effective field theory modeling.

Abstract

We present an exploratory lattice QCD calculation of the neutrinoless double beta decay $\pi\pi\to ee$. Under the mechanism of light-neutrino exchange, the decay amplitude involves significant long-distance contributions. The calculation reported here, with pion masses $m_\pi=420$ and 140 MeV, demonstrates that the decay amplitude can be computed from first principles using lattice methods. At unphysical and physical pion masses, we obtain that amplitudes are $24\%$ and $9\%$ smaller than the predication from leading order chiral perturbation theory. Our findings provide the lattice QCD inputs and constraints for effective field theory. A follow-on calculation with fully controlled systematic errors will be possible with adequate computational resources.