Nuclear matrix elements for neutrinoless double beta decay

4 problems

• Short-range contact coupling in neutrinoless double beta decay

  Partially resolved

  Effective field theory showed in 2018 that the leading neutrinoless double beta decay operator needs a short-range two-nucleon term whose strength is not fixed by symmetry. Its value changes the matrix elements by tens of percent.

• Can double Gamow-Teller transitions calibrate the matrix elements?

  Open

  A related measurable process, the double Gamow-Teller transition (flipping the spin and charge of two nucleons), correlates strongly with the neutrinoless matrix element in calculations. If the correlation holds in all models, measuring it would calibrate the matrix elements.

• Does axial-coupling quenching persist at neutrinoless decay momentum transfers?

  Partially resolved

  Simple nuclear models overpredict ordinary beta-decay rates unless the weak axial coupling $g_{\mathrm{A}}$ is reduced by about 25 percent, a correction called quenching. First-principles work explains this with two-nucleon currents and correlations, but whether the same reduction applies to neutrinoless decay, where momenta are about $100\ \mathrm{MeV}/c$, is unknown.

• Neutrinoless double beta matrix elements to 30 percent uncertainty

  Open

  Different nuclear models give matrix elements differing by factors of two to three for the same nucleus. Pinning them down for the isotopes used in experiments is the central task.