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

TL;DR

The paper surveys state-of-the-art ab initio calculations of beta-decay corrections that underpin precision tests of the Standard Model, with a focus on radiative and recoil-order effects in light nuclei and their impact on extracting $|V_{ud}|$. It analyzes two complementary theoretical frameworks—current algebra and effective field theory—and demonstrates how they can be combined with multiple many-body methods (NCSM, SA-NCSM, and QMC) to achieve quantified uncertainties. Key results include unprecedented precision for $oxed{\delta_{NS}}$ in ${}^{10}{\rm C}\rightarrow {}^{10}{\rm B}$ and ${}^{14}{\rm O}\rightarrow {}^{14}{\rm N}$, and detailed recoil-order analyses for ${}^6{\rm He}$ and ${}^{8}{\rm Li}/{}^{8}{\rm B}$ decays, collectively tightening constraints on exotic tensor and scalar currents. The work strengthens the synergy between theory and experiment, enabling more sensitive probes of physics beyond the Standard Model and guiding future expansions to heavier systems and unique forbidden decays.

Abstract

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.

Figures (16)

• Figure 2.1: $N_{\rm max}$ = 0 and $N_{\rm max}$ = 4 configurations in $^{10}$B in a standard particle-based NCSM (a single configuration is shown in each case).
• Figure 2.2: Ground-state energies of $^6$Li, $^{12}$C, and $^{16}$N obtained with the NN-N4LO + 3N$_\mathrm{lnl}^*$ interaction Kravvaris:2022eyf with different HO frequencies. Data for the figure is taken from Ref. Jokiniemi:2024zdl.
• Figure 2.3: (a) Convergence of the $^8$Li ground state quadrupole moment vs. $N_{\rm max}$ calculated using SA-NCSM with different HO parameters ($\hbar\Omega$) and compared to the experimental value from BorremansBBG2005Q2. The dashed horizontal line with a band shows the infinite-space extrapolated value. Figure adapted from Ref. Sargsyan_A8 with permission. (b) Quadrupole moments of various nuclei divided by their proton numbers calculated using SA-NCSM and compared to the experimental values from Ref. STONE2016. Uncertainties of some of the experimental values are smaller than the size of the marker.
• Figure 2.4: GFMC propagation of the $^6$He $\to$$^6$Li Gamow-Teller $\beta$ decay transition matrix element for the NV2+3-Ia nuclear Hamiltonian. The one-body matrix element is shown in blue in the top panel, and is compared with the matrix element retaining one- and two-body transition operators shown in green. The two-body contribution is isolated in the bottom panel and plotted in orange. The average GFMC estimate is shown by the green dotted line, with statistical uncertainty represented by the solid green lines. The average is compared to a variational monte carlo calculation with central value represented by the dashed black line, and statistical uncertainties shown with the solid black lines. Figure reprint with permission from Ref. King:2020wmp.
• Figure 3.1: First diagram: A generic $\gamma W$-box diagram for $\beta^\pm$-decay. Second and third diagram: the "traditional" picture for $\delta_\text{NS}$.