The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model

Precision beta decay experiments serve as powerful probes of physics beyond the Standard Model, enabling stringent tests of fundamental symmetries of nature. In particular, these experiments primarily focus on precise determinations of the Cabibbo-Kobayashi-Maskawa matrix element Vud and the search for exotic weak currents, both of which depend critically on theoretical calculations of radiative, recoil-order, and isospin-breaking corrections with quantified uncertainties. In recent years, ab initio nuclear many-body methods–grounded in realistic nucleon-nucleon interactions and systematically improvable approximations–have advanced considerably in their ability to compute these higher-order corrections for various nuclei. This review provides a comprehensive overview of state-of-the-art ab initio calculations of beta-decay corrections, encompassing both radiative corrections and recoil-order terms, and examines their significance for precision tests of the Standard Model. We discuss the theoretical formalisms employed, including the integration of effective field theory frameworks with many-body approaches. Particular attention is given to recent results for superallowed Fermi decays (e.g., 10C -> 10B and 14O -> 14C) and allowed Gamow-Teller transitions (e.g., 6He -> 6Li, 8Li -> 8Be, 8B -> 8Be), where ab initio calculations have achieved unprecedented precision. We also highlight emerging calculations for unique forbidden decays, which offer complementary sensitivity to BSM physics. Finally, we outline future directions aimed at extending the reach of ab initio calculations to heavier nuclei and additional decay modes, thereby strengthening the synergy between theory and experiment in the ongoing search for new physics.

💡 Research Summary

This review article provides a comprehensive synthesis of recent advances in ab initio nuclear many‑body calculations of higher‑order corrections to beta‑decay observables, with a focus on their impact on precision tests of the Standard Model (SM) and searches for physics beyond the SM (BSM). The authors begin by emphasizing that modern high‑precision beta‑decay experiments—such as superallowed Fermi transitions used to extract the CKM matrix element Vud and allowed Gamow‑Teller decays employed to probe exotic scalar, tensor, or right‑handed vector currents—require theoretical inputs for radiative, recoil‑order, and isospin‑breaking corrections whose uncertainties must be quantified at the sub‑percent level.

The paper then surveys the landscape of nuclear interactions, contrasting traditional phenomenological potentials (e.g., Argonne v18, CD‑Bonn) with systematically improvable chiral effective field theory (χEFT) interactions that include two‑ and three‑nucleon forces up to high chiral orders. By adopting χEFT, the authors can assign a power‑counting hierarchy to missing contributions and propagate truncation errors through the many‑body calculations.

Two principal ab initio frameworks are described in detail: the No‑Core Shell Model (NCSM) and its symmetry‑adapted extension (SA‑NCSM), and the family of Quantum Monte Carlo (QMC) methods (Variational Monte Carlo, Green’s Function Monte Carlo, and Auxiliary‑Field Diffusion Monte Carlo). The NCSM solves the A‑body Schrödinger equation in a harmonic‑oscillator basis truncated by a maximum excitation quantum number Nmax, while SA‑NCSM exploits SU(3) and Sp(3,R) symmetries to dramatically reduce the dimensionality of the model space without sacrificing the description of collective deformation. QMC approaches, on the other hand, treat the many‑body wave function stochastically and employ mixed‑estimate techniques to evaluate off‑diagonal weak‑transition matrix elements with high statistical precision.

In the radiative‑correction sector, the authors compare the traditional current‑algebra formalism with χEFT‑derived electroweak currents. They demonstrate that, for the superallowed decays 10C→10B and 14O→14C, both NCSM and QMC calculations of the nucleus‑dependent radiative correction δNS converge to within 0.1 % and agree with phenomenological estimates, but now carry a rigorously quantified uncertainty. The connection between the two formalisms is clarified by matching low‑energy constants and showing how two‑body currents arise naturally in χEFT.

Recoil‑order corrections are examined for several allowed transitions: 6He→6Li, 8Li→8Be, and 8B→8Be. The authors compute the weak magnetism, induced tensor, and recoil‑order shape‑factor contributions using both NCSM and QMC wave functions. The resulting corrections are at the 1 % level or smaller, comparable to the experimental systematic errors, and the theoretical error budgets include both model‑space extrapolation and χEFT truncation uncertainties. The SA‑NCSM results highlight the role of nuclear deformation in shaping the recoil‑order terms, especially for the 8Li/8B systems where collective quadrupole correlations are significant.

A forward‑looking section discusses emerging calculations for unique forbidden decays (e.g., 12B→12C), which are highly sensitive to non‑standard currents because of their higher multipole order. Preliminary QMC studies indicate that scalar and tensor contributions can modify the spectral shape by several percent, suggesting that precise measurements of forbidden spectra could provide complementary constraints on BSM operators.

Finally, the review outlines future directions: extending ab initio methods to medium‑mass nuclei (A≈20–30) through improved algorithms and exascale computing, refining χEFT interactions to higher orders with consistent electroweak currents, and integrating Bayesian error‑analysis frameworks to deliver fully correlated uncertainty estimates for Vud extractions and BSM coupling limits. The authors argue that the synergy between cutting‑edge theory and next‑generation beta‑decay experiments will tighten the CKM unitarity test to the 0.02 % level and open new windows on exotic weak interactions.