Long-range scalar interactions in the effective field theory approach to $0\nu\beta\beta$

Abstract

As a lepton-number-violating process whose observation would establish the Majorana nature of neutrinos, neutrinoless double-beta decay ($0\nu\beta\beta$) is an important low-energy nuclear probe of beyond-the-Standard-Model physics. Effective field theory (EFT) provides a general, model-independent description, and interference among effective mechanisms is essential for disentangling their contributions to the total decay rate. We focus on scalar-type terms of the long-range Lagrangian in the EFT approach to $0\nu\beta\beta$. We simultaneously retain the two scalar interactions involving a common $(S+P)$ leptonic current coupled either to an $(S-P)$ or an $(S+P)$ hadronic current. Their coherent contribution produces mutual interference between the two scalar mechanisms, controlled by the relative complex phase of their couplings, in addition to their separate interference with the standard mass mechanism. We give a compact half-life expression, the explicit scalar--scalar interference coefficient in terms of scalar nuclear-matrix-element ratios and integrated phase-space factors, and a positivity bound on that coefficient. The calculation uses the closure and single-nucleon impulse approximations, retains the dominant scalar recoil subset, and includes the $s_{1/2}$ and $p_{1/2}$ Coulomb waves of the outgoing electrons. The resulting dimensionally explicit formulation provides a basis for correlated analyses of the two scalar coefficients.