Proton lifetime bounds from chirally symmetric lattice QCD

We present results for the matrix elements relevant for proton decay in grand unified theories (GUTs). The calculation is performed at a fixed lattice spacing ${a}^{\ensuremath{-}1}=1.73(3)\text{ }\text{ }\mathrm{GeV}$ using $2+1$ flavors of domain-wall fermions on lattices of size ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ and ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ with a fifth dimension of length 16. We use the indirect method which relies on an effective field theory description of proton decay, where we need to estimate the low-energy constants, $\ensuremath{\alpha}=\ensuremath{-}0.0112(25)\text{ }\text{ }{\mathrm{GeV}}^{3}$ and $\ensuremath{\beta}=0.0120(26)\text{ }\text{ }{\mathrm{GeV}}^{3}$. We relate these low-energy constants to the proton decay matrix elements using leading order chiral perturbation theory. These can then be combined with experimental bounds on the proton lifetime to bound parameters of individual GUTs.