# Lattice QCD Method To Study Proton Decay

## TL;DR

This paper develops a lattice QCD approach to calculate the non-perturbative proton decay matrix element, a key quantity for understanding proton decay, which has not yet been observed experimentally.

## Contribution

The paper formulates a first-principles lattice QCD method to compute the proton decay matrix element, enabling non-perturbative calculations of this important quantity.

## Key findings

- Derived a non-perturbative formula for proton decay matrix element
- Established a lattice QCD framework for proton decay studies
- Provided a basis for future numerical calculations

## Abstract

The proton decay has not been experimentally observed with the lower limit of the proton lifetime being $\gtrsim 10^{34}$ years which is more than the age of the universe. One of the important quantity that appears in the study of the proton decay is the proton decay matrix element which is a non-perturbative quantity in QCD which cannot be calculated by using the perturbative QCD (pQCD) method but it can be calculated by using the lattice QCD method. In this paper we formulate the lattice QCD method to study the proton decay matrix element. We derive the non-perturbative formula of the proton decay matrix element from the first principle in QCD which can be calculated by using the lattice QCD method.