Lattice QCD Inputs for nuclear double beta decay

Abstract

Second order β-decay processes with and without neutrinos in the final state are key probes of nuclear physics and of the nature of neutrinos. Neutrinoful double-β decay is the rarest Standard Model process that has been observed and provides a unique test of the understanding of weak nuclear interactions. Observation of neutrinoless double-β decay would reveal that neutrinos are Majorana fermions and that lepton number conservation is violated in nature. While significant progress has been made in phenomenological approaches to understanding these processes, establishing a connection between these processes and the physics of the Standard Model and beyond is a critical task as it will provide input into the design and interpretation of future experiments. The strong-interaction contributions to double-β decay processes are non-perturbative and can only be addressed systematically through a combination of lattice Quantum Chromoodynamics (LQCD) and nuclear many-body calculations. In this review, current efforts to establish the LQCD connection are discussed for both neutrinoful and neutrinoless double-β decay. LQCD calculations of the hadronic contributions to the neutrinoful process nn → ppe − e −ν eνe and to various neutrinoless pionic transitions are reviewed, and the connections of these calculations to the phenomenology of double-β decay through the use of effective field theory (EFTs) is highlighted. At present, LQCD calculations are limited to small nuclear systems, and to pionic subsystems, and require matching to appropriate EFTs to have direct phenomenological impact. However, these calculations have already revealed qualitatively that there are terms in the EFTs that can only be constrained from double-β decay processes themselves or using inputs from LQCD. Future prospects for direct calculations in larger nuclei are also discussed. many-body methods and effective field theory (EFT) analysis of the transition operators, where lattice QCD can provide key input. To improve upon this situation, recent efforts have advocated an "endto-end" EFT analysis of 0νββ to link the scale Λ of LNV to nuclear scales. This multi-prong approach includes various steps:1. The use of the Standard Model EFT to link the scale Λ of LNV to the hadronic scale Λ χ ∼ O(1) GeV, where non-perturbative QCD effects arise. This step is by now mature: the operator basis (to which any underlying model can be matched) is known up to dimension-nine and the renormalization group evolution of these operators under strong interactions is known. Light new degrees of freedom (such as sterile neutrinos) can also be included in this framework.2. The matching of the quark-gluon level EFT to hadronic EFTs such as Chiral Perturbation Theory (χPT) in the meson and single nucleon sector, and chiral EFT and pionless EFT in the multinucleon sector. This step can be performed consistently in the strong and weak sectors of the theory, which in the case of interest here involves ∆L = 2 transition operators. The form of the transition operators is known to...

Determining the leading-order contact term in neutrinoless double β decay

“…Additional experimental input could, in principle, separate C 1 from C 2 , e.g., via CIB in nuclei, but such an extraction also requires the development of a suitable theoretical framework. While our results allow for first phenomenological estimates of the impact of the contact term on 0νββ decay rates, they thus also define a benchmark for future lattice-QCD calculations [46,[52][53][54][55][56][57]. In addition to comparing the final result for A ν , there could also be aspects of the matching strategy and spectral representation, as described in section 2, that might prove synergistic between the two approaches.…”

“…As discussed in greater detail in refs. [43,46], the new coupling encodes a non-factorizable two-nucleon effect, beyond the factorizable one-nucleon corrections captured by the radii of weak form factors, which also give a short-range neutrino potential. Moreover, the new short-range coupling is not JHEP05(2021)289 captured by the so-called short-range correlations [47][48][49][50], as it is needed even when one works with fully correlated wave functions, i.e., exact solutions of the Schrödinger equation with the appropriate strong potential.…”

“…The value of the short-range coupling in the 1 S 0 channel then has to be either extracted from other processes related by chiral symmetry or calculated from first principles in lattice QCD [46,[52][53][54][55][56][57] (see ref. [58] for a large-N c analysis).…”

Electroweak Currents from Chiral Effective Field Theory

“…Therefore, the validity of the theory is confined to kinematic regions where the constraint Q Λ is realized. The coefficients of the chiral expansion, or low-energy constants (LECs), are unknown and need to be fixed by comparison with experimental data or calculated by nonperturbative QCD computational methods such as Lattice QCD [7][8][9][10][11][12][13][14][15][16][17].…”

The path from lattice QCD to the short-distance contribution to $0νββ$ decay with a light Majorana neutrino

“…Lattice QCD, which numerically solves QCD on a finite grid in an Euclidean spacetime, has the promise of reliably constraining the EFTs of 0νββ in the few-nucleon sector [16][17][18], and has already demonstrated its reach and capability in constraining pionic matrix elements for lepton-number violating processes π − → π + (ee) and π − π − → ee within the light-neutrino scenario [19][20][21], the π − → π + (ee) process within a heavy-scale scenario [22], as well as the two-neutrino double-β decay (2νββ) of a two-nucleon state [23,24] (the latter yet at unphysically large quark masses due to the computational cost). Lattice-QCD matrix elements for these processes, however, lack certain complexities compared with the desired nn → pp (ee) process with a light Majorana neutrino, whose determination is the key to matching to the EFT descriptions developed in recent years [9,10,25].…”