Towards a non-perturbative calculation of Weak Hamiltonian Wilson coefficients

TL;DR

This paper introduces a lattice QCD-based method to compute weak Hamiltonian Wilson coefficients non-perturbatively at all orders, using an unphysical weak boson mass to control systematic errors and pave the way for precise future calculations.

Contribution

It presents a novel approach to calculate Wilson coefficients non-perturbatively with lattice QCD, including systematic error control, at an unphysical weak boson mass.

Findings

Systematic errors for coefficients C_1 and C_2 are controllable.

Demonstrated feasibility of non-perturbative calculation of Wilson coefficients.

Path established for more precise future determinations.

Abstract

We propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around $2~\mathrm{GeV}$. We demonstrate that systematic errors for the Wilson coefficients $C_1$ and $C_2$, related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.