Light-Neutrino Exchange and Long-Distance Contributions to $0\nu 2\beta$ Decays: An Exploratory Study on $\pi \pi \to ee$

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.

Comments: 6 pages, 3 figures. V2: version accepted by PRL; minor changes compared to v1