# Improved lattice computation of proton decay matrix elements

## TL;DR

This paper reports an improved lattice QCD calculation of proton decay matrix elements, achieving higher statistical accuracy and refining key constants, which impacts predictions of proton lifetime and dark matter models.

## Contribution

The study introduces an error reduction technique in lattice computations, significantly improving the precision of proton decay matrix elements and related low energy constants.

## Key findings

- Matrix element accuracy improved to 10-15% from 30-40%.
- Form factors are 1.4 times smaller than previous estimates using BChPT.
- Proton lifetime estimates increase by a factor of 2-3.

## Abstract

We present an improved result of lattice computation of the proton decay matrix elements in $N_f=2+1$ QCD. In this study, the significant improvement of statistical accuracy by adopting the error reduction technique of All-mode-averaging, is achieved for relevant form factor to proton (and also neutron) decay on the gauge ensemble of $N_f=2+1$ domain-wall fermions in $m_\pi=0.34$--0.69 GeV on 2.7~fm$^3$ lattice as used in our previous work \cite{Aoki:2013yxa}. We improve total accuracy of matrix elements to 10--15\% from 30--40\% for $p\rightarrow\pi e^+$ or from 20--40\% for $p\rightarrow K \bar\nu$. The accuracy of the low energy constants $\alpha$ and $\beta$ in the leading-order baryon chiral perturbation theory (BChPT) of proton decay are also improved. The relevant form factors of $p\rightarrow \pi$ estimated through the "direct" lattice calculation from three-point function appear to be 1.4 times smaller than those from the "indirect" method using BChPT with $\alpha$ and $\beta$. It turns out that the utilization of our result will provide a factor 2--3 larger proton partial lifetime than that obtained using BChPT. We also discuss the use of these parameters in a dark matter model.