$Re(A_0)$, $Re(A_2)$ and RG evolution for $N_f=3$

TL;DR

This paper calculates the real parts of decay amplitudes $A_0$ and $A_2$ using lattice QCD with HYP staggered fermions, addressing RG evolution issues for $N_f=3$ and providing finite solutions.

Contribution

It introduces a finite solution to the RG evolution matrix for $N_f=3$, resolving a singularity in Buras's original formulation, and presents lattice QCD results for decay amplitudes.

Findings

Calculated $Re(A_0)$ and $Re(A_2)$ using lattice QCD.

Resolved RG evolution singularity for $N_f=3$ with a finite solution.

Provided numerical results for decay amplitudes.

Abstract

We present results of $Re (A_0)$ and $Re (A_2)$ calculated using HYP staggered fermions on the lattice of $16^3 \times 64$ at $\beta=6.0$. These results are obtained using leading order chiral perturbation in quenched QCD. Buras's original RG evolution matrix develops a removable singularity for $N_f=3$. This subtlety is resolved by finding a finite solution to RG equation and the results are presented.