Short-range contact coupling in neutrinoless double beta decay
In plain words
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.
Precise statement
Determine the leading-order low-energy constant $g_{\nu}^{NN}$ of the $\mathrm{nn} \to \mathrm{pp}\,\mathrm{e}\,\mathrm{e}$ contact operator in chiral EFT (Cirigliano et al., PRL 120, 202001, 2018), from a lattice QCD calculation of the $\mathrm{nn} \to \mathrm{pp}$ amplitude or from the dispersive estimate (Cirigliano et al., PRL 126, 172002, 2021). Answer: $g_{\nu}^{NN}$ with 20 percent uncertainty in a stated regulator scheme, and its effect on $M^{0\nu}$ for 76Ge and 136Xe.
What would settle it
A lattice QCD calculation of the two-nucleon $\mathrm{nn} \to \mathrm{pp}\, e\, e$ amplitude at physical quark masses matched to chiral EFT.
Status in the literature
Unverified note
The 2021 dispersive estimate fixed $g_{\nu}^{\mathrm{NN}}$ to about 30 percent and ab initio studies found the term changes $M^{0\nu}$ by tens of percent; no physical-point lattice QCD determination existed as of 2026.