Three-nucleon lepton-number-violating potentials in chiral EFT and their matrix elements in light nuclei

TL;DR

This work derives three-nucleon lepton-number-violating neutrino potentials within Δ-full chiral EFT up to N$^3$LO and computes their matrix elements in light nuclei using Variational Monte Carlo with Norfolk NV2+3 interactions. The results show modest quenching from three-nucleon contributions in isospin-conserving transitions, but more pronounced effects in $\Delta T=2$ transitions due to nodal densities that suppress two-nucleon NMEs. The study also assesses model dependencies, notably from the LEC $c_D$, and evaluates short-range counterterms such as $g_\nu^{\mathrm{NN}}$, finding them generally subleading but non-negligible in certain cases. These findings provide benchmarks for ab initio many-body methods and inform the interpretation of upcoming $0\nu\beta\beta$ experiments, highlighting the need to extend three-nucleon analyses to heavier nuclei and to refine LECs and renormalization schemes in the chiral EFT framework.

Abstract

We derive the three-nucleon neutrinoless double beta decay potential in $Δ$-full chiral effective field theory through next-to-next-to-next-to leading order in Weinberg's power counting. The matrix elements of the resulting operators are computed in light nuclei using Variational Monte Carlo with wave functions constructed from the Norfolk family of nuclear interactions. We find that three-nucleon corrections induce a modest quenching of the total nuclear matrix elements. We discuss model dependencies and the potential impact of these corrections on the sensitivity of experimental programs to probe lepton number violating parameters. These results provide a benchmark of many-body methods capable of reaching heavier nuclei of experimental interest.

Figures (14)

• Figure 1: Examples of pion-neutrino loops contributing to the two-body neutrino potential $V_{\nu,\, 2}$. Plain and double lines denotes nucleons and $\Delta$ baryons, respectively. Dashes denote pions. Plain lines with arrows denote electron and neutrinos, and a square denotes an insertion of the neutrino Majorana mass. Dots and circled dots indicate LO and NLO interactions from the pion and nucleon Lagrangians, respectively. The diagrams in the first row contribute at N$^2$LO. The diagrams in the second row indicate N$^2$LO corrections arising in a theory with explicit $\Delta$ degrees of freedom. Diagrams in the third row would contribute at N$^3$LO.
• Figure 2: (2a)
• Figure 3: (3a)
• Figure 4: (4a)
• Figure 5: Ratios of three- and two-nucleon matrix elements with respect to the two-nucleon matrix elements. $M_{\nu, 2}$ includes LO long-range neutrino exchange diagrams and single nucleon form-factor corrections. The top panels denote the N$^3$LO contributions grouped by LEC. The bottom two panels are the full three-nucleon matrix element contributions up to either N$^2$LO or N$^3$LO.