Improved lattice computation of proton decay matrix elements

In this paper, we present an improved result for the lattice computation of the proton decay matrix elements in N_f = 2 + 1 QCD. In this study, by adopting the error reduction technique of all-mode-averaging, a significant improvement of the statistical accuracy is achieved for the relevant form factor of proton (and also neutron) decay on the gauge ensemble of N_f= 2 + 1 domain-wall fermions with m_π = 0.34 – 0.69 GeV on a 2.7 fm³ lattice, as used in our previous work. We improve the total accuracy of matrix elements to 10–15% from 30–40% for p → πe⁺ or from 20–40% for p → Kν̄. The accuracy of the low-energy constants α and β in the leading-order baryon chiral perturbation theory (BChPT) of proton decay are also improved. The relevant form factors of p → π estimated through the "direct" lattice calculation from the three-point function appear to be 1.4 times smaller than those from the "indirect" method using BChPT with α and β . It turns out that the utilization of our result will provide a factor 2–3 larger proton partial lifetime than that obtained using BChPT. Lastly, we also discuss the use of these parameters in a dark matter model.