Path from Lattice QCD to the Short-Distance Contribution to 0νββ Decay with a Light Majorana Neutrino.

Zohreh Davoudi,Saurabh V Kadam

doi:10.1103/physrevlett.126.152003

Abstract

Neutrinoless double-β (0νββ) decay of certain atomic isotopes, if observed, will have significant implications for physics of neutrinos and models of physics beyond the standard model. In the simplest scenario, if the mass of the light neutrino of the standard model has a Majorana component, it can mediate the decay. Systematic theoretical studies of the decay rate in this scenario, through effective field theories matched to abinitio nuclear many-body calculations, are needed to draw conclusions about the hierarchy of neutrino masses, and to plan the design of future experiments. However, a recently identified short-distance contribution at leading order in the effective field theory amplitude of the subprocess nn→pp(ee) remains unknown, and only lattice quantum chromodynamics (QCD) can directly and reliably determine the associated low-energy constant. While the numerical computations of the correlation function for this process are underway with lattice QCD, the connection to the physical amplitude, and hence this short-distance contribution, is missing. A complete framework that enables this complex matching is developed in this Letter. The complications arising from the Euclidean and finite-volume nature of the corresponding correlation function are fully resolved, and the value of the formalism is demonstrated through a simple example. The result of this work, therefore, fills the gap between first-principles studies of the nn→pp(ee) amplitude from lattice QCD and those from effective field theory, and can be readily employed in the ongoing lattice-QCD studies of this process.

Highlights

Introduction.—The lepton-number violating process ðA; ZÞ → ðA; Z þ 2Þ þ ee, with A and Z being, respectively, the atomic and proton numbers of a parent nucleus, if observed, will mark a major discovery
While the numerical computations of the correlation function for this process are underway with lattice quantum chromodynamics (QCD), the connection to the physical amplitude, and this shortdistance contribution, is missing
Despite the long-range nature of the process, recent nuclear effective field theory (EFT) analyses of the elementary subprocess nn → ppðeeÞ have revealed a short-distance contribution to the amplitude at leading order (LO), with a low-energy constant (LEC) of the corresponding isotensor contact operator that absorbs the ultraviolet (UV) scale dependence of the amplitude through renormalization group (RG) [8,9,10]. As such a subprocess cannot be observed in free space, and given the program that has been formed around the use of nuclear EFTs to systematically improve the ab initio nuclear structure calculations of the nuclear matrix elements [11,12,13,14,15] toward experimentally relevant isotopes, the unknown value of such a short-distance contribution appears to impede progress, and has promoted several estimations based on the connection to charge-invariance breaking contribution to two-nucleon scattering [10], the use of Cottingham formula in the NN sector [16], and large-Nc considerations [17], with varying uncertainties

Summary

Introduction

Introduction.—The lepton-number violating process ðA; ZÞ → ðA; Z þ 2Þ þ ee, with A and Z being, respectively, the atomic and proton numbers of a parent nucleus, if observed, will mark a major discovery. This matching framework builds upon major developments in recent years in accessing local and nonlocal transition amplitudes in hadronic physics from the corresponding finite-volume matrix elements in Euclidean spacetime obtained with

Results

Conclusion