We present an ab initio calculation of nuclear $\beta$ decay within the framework of nuclear lattice effective field theory (NLEFT), employing auxiliary-field quantum Monte Carlo methods to solve the nuclear many-body problem. Our approach combines next-to-next-to-leading order two- and three-body chiral interactions with one- and two-body axial current operators, all consistently derived in chiral effective field theory. Low-energy constants are determined exclusively from nucleon-nucleon scattering phase shifts and few-body observables for systems with $A\le 3$. Using these interactions and transition operators, we perform two-channel Monte Carlo simulations to compute the $\beta$-decay matrix element for ${}^6\mathrm{He}$, obtaining results in reasonable agreement with experimental measurements. To address the Monte Carlo sign problem, we implement a perturbative expansion around a leading-order Hamiltonian with approximate Wigner-SU(4) symmetry. This systematic approach provides a foundation for extending NLEFT simulations to precision studies of weak processes in medium-mass nuclei.

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• Beta decay
• Effective field theory
• Few-body systems
• Nuclear forces
• Nuclear structure & decays
• Nucleon-nucleon interactions