Isotensor Axial Polarizability and Lattice QCD Input for Nuclear Double-$\beta$ Decay Phenomenology

The potential importance of short-distance nuclear effects in double-$\beta$ decay is assessed using a lattice QCD calculation of the $nn\to pp$ transition and effective field theory methods. At the unphysical quark masses used in the numerical computation, these effects, encoded in the isotensor axial polarizability, 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 polarizabilities of nuclei using lattice QCD input into nuclear many-body calculations are discussed.

Figure 1

Ratios from Eqs. (12)–(15) used in the analysis. In each panel, the orange diamonds (blue circles) correspond to the SS (SP) data. The green bands show fits to the SP data in the lower two panels. The SS data are slightly offset in the horizontal direction for clarity. The difference between the SS and SP ratios in the upper two panels is due to contamination that is removed in constructing the subsequent quantities in the lower panels.