Determining the leading-order contact term in neutrinoless double \u03b2 decay

Vincenzo Cirigliano,Emanuele Mereghetti,Martin Hoferichter,Jordy De Vries,Wouter Dekens

doi:10.1007/jhep05(2021)289

Abstract

We present a method to determine the leading-order (LO) contact term contributing to the nn → ppe−e− amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude n(p1)n(p2)W+(k) → pleft({p}_1^{prime}right)pleft({p}_2^{prime}right){W}^{-}(k) , in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon (NN) scattering in the 1S0 channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing the analog I = 2 NN contact term and by reproducing, within uncertainties, the charge-independence-breaking contribution to the 1S0NN scattering lengths. While our analysis is performed in the overline{mathrm{MS}} scheme, we express our final result in terms of the scheme-independent renormalized amplitude {mathcal{A}}_{nu}left(left|mathbf{p}right|,left|mathbf{p}^{prime}right|right) at a set of kinematic points near threshold. We illustrate for two cutoff schemes how, using our synthetic data for {mathcal{A}}_{nu } , one can determine the contact-term contribution in any regularization scheme, in particular the ones employed in nuclear-structure calculations for isotopes of experimental interest.

Highlights

Neutrinoless double β decay (0νββ) is the process in which two neutrons in a nucleus convert into two protons by emitting two electrons and no neutrinos [1]
If 0νββ decay is caused by the exchange of light Majorana neutrinos, as we assume throughout this paper, the amplitude is proportional to the effective neutrino mass mββ = i Ue2imi, where the sum runs over light neutrino masses mi and Uei are elements of the neutrino mixing matrix. 0νββ decay is a complicated process encompassing aspects from particle, nuclear, and atomic physics, with the interpretation of current experimental limits [5,6,7,8,9,10] and of potential future discoveries limited by substantial uncertainties in the calculation of hadronic and nuclear matrix elements [11,12,13,14,15,16,17,18,19]
The issue of gA quenching in single β decays has been demonstrated to arise from the combination of two-nucleon weak currents and strong correlations in the nucleus [32,33,34], and the few-nucleon amplitudes used as input in nuclear structure calculations have been scrutinized in chiral effective field theory (EFT) for various sources of lepton number violation (LNV) [35,36,37,38,39,40,41,42,43,44]

Summary

Introduction

Neutrinoless double β decay (0νββ) is the process in which two neutrons in a nucleus convert into two protons by emitting two electrons and no neutrinos [1]. 0νββ decay is a complicated process encompassing aspects from particle, nuclear, and atomic physics, with the interpretation of current experimental limits [5,6,7,8,9,10] and of potential future discoveries limited by substantial uncertainties in the calculation of hadronic and nuclear matrix elements [11,12,13,14,15,16,17,18,19] It has been realized in recent years that chiral effective field theory (EFT) [20,21,22,23,24,25] can play a central role in addressing these uncertainties. The situation is analogous to single β decay, where two-nucleon weak currents and short-range correlations are both present, and the combination of both leads to the apparent quenching of gA [33, 34]

Results

Discussion

Conclusion