Lattice QCD calculation of the electroweak box diagrams for the kaon semileptonic decays

Peng-Xiang Ma,Chien-Yeah Seng,Lu-Chang Jin,Mikhail Gorchtein,Xu Feng

doi:10.1103/physrevd.103.114503

Abstract

We present a lattice QCD calculation of the axial $\gamma W$-box diagrams relevant for the kaon semileptonic decays. We utilize a recently proposed method, which connects the electroweak radiative corrections in Sirlin's representation to that in chiral perturbation theory. It allows us to use the axial $\gamma W$-box correction in the SU(3) limit to obtain the low energy constants for chiral perturbation theory. From first principles our results confirm the previously used low energy constants provided by the minimal resonance model with a significant reduction in uncertainties.

Highlights

In the Standard Model, the Cabibbo-KobayashiMaskawa (CKM) matrix is a three-generation quark mixing matrix which describes how the strength of the flavorchanging weak interaction in the leptonic sector is distributed among the three quark generations
We present a lattice QCD calculation of the axial γW-box diagrams relevant for the kaon semileptonic decays
The precise determination of the CKM matrix elements is of vital importance in the stringent test of CKM unitarity and search of new physics beyond the Standard Model

Summary

Introduction

In the Standard Model, the Cabibbo-KobayashiMaskawa (CKM) matrix is a three-generation quark mixing matrix which describes how the strength of the flavorchanging weak interaction in the leptonic sector is distributed among the three quark generations. The precise determination of the CKM matrix elements is of vital importance in the stringent test of CKM unitarity and search of new physics beyond the Standard Model. As quoted in the 2020 review by the Particle Data Group (PDG) [1], there exists a ∼3 sigma deviation from unitarity in the first row of CKM matrix elements jVudj þ jVusj þ jVubj2 1⁄4 0.9984ð3ÞVud ð4ÞVus : ð1Þ. JVubj2 ≈ 1.5 × 10−5 is negligibly small and only jVudj and jVusj play a role in the unitarity test

Methods

Results

Conclusion