Ab initio calculation of the $\beta$ decay spectrum of $^6$He

We calculate the $\beta$ spectrum in the decay of $^6$He using Quantum Monte Carlo methods with nuclear interactions derived from chiral Effective Field Theory and consistent weak vector and axial currents. We work at second order in the multipole expansion, retaining terms suppressed by $\mathcal O(q^2/m_\pi^2)$, where $q$ denotes low-energy scales such as the reaction's $\mathcal Q$-value or the electron energy, and $m_\pi$ the pion mass. We go beyond the impulse approximation by including the effects of two-body vector and axial currents. We estimate the theoretical error on the spectrum by using four potential models in the Norfolk family of local two- and three-nucleon interactions, which have different cut-off, fit two-nucleon data up to different energies and use different observables to determine the couplings in the three-body force. We find the theoretical uncertainty on the $\beta$ spectrum, normalized by the total rate, to be well below the permille level, and to receive contributions of comparable size from first and second order corrections in the multipole expansion. We consider corrections to the $\beta$ decay spectrum induced by beyond-the-Standard Model charged-current interactions in the Standard Model Effective Field Theory, with and without sterile neutrinos, and discuss the sensitivity of the next generation of experiments to these interactions.