$\mathbf{\beta}$-delayed proton emission from $\mathbf{^{11}}$Be in effective field theory

We calculate the rate of the rare decay $^{11}\text{Be}$ into $^{10}\text{Be} + p +e^- + \bar{\nu}_e$ using Halo effective field theory, thereby describing the process of beta-delayed proton emission. We assume a shallow $1/2^+$ resonance in the $^{10}\text{Be}-p$ system with an energy consistent with a recent experiment by Ayyad et al. and obtain $b_p = 4.9_{-2.9}^{+5.6}\text{(exp.)}_{-0.8}^{+4.0}\text{(theo.)} \times 10^{-6}$ for the branching ratio of this decay, predicting a resonance width of $\Gamma_R = (9.0^{+4.8}_{-3.3}\text{(exp.)}^{+5.3}_{-2.2}\text{(theo.)})~\text{keV}$. Our calculation shows that the experimental branching ratio and resonance parameters of Ayyad et al. are consistent with each other. Moreover, we analyze the general impact of a resonance on the branching ratio and demonstrate that a wide range of combinations of resonance energies and widths can reproduce branching ratios of the correct order. Thus, no exotic mechanism (such as beyond the standard model physics) is needed to explain the experimental decay rate.