Parity-violating $\pi NN$ coupling constant from the flavor-conserving effective weak chiral Lagrangian

TL;DR

This paper calculates the parity-violating $ ext{pi NN}$ coupling constant using the chiral quark-soliton model, incorporating QCD corrections, and finds a value around 10^{-7} with NLO corrections reducing the LO estimate by 20%.

Contribution

It introduces a calculation of the parity-violating $ ext{pi NN}$ coupling constant including next-to-leading order QCD corrections within the chiral quark-soliton framework.

Findings

The coupling constant is approximately 10^{-7}.

Next-to-leading order corrections reduce the leading order result by about 20%.

The method incorporates effective weak Hamiltonian and gradient expansion.

Abstract

We investigate the parity-violating pion-nucleon-nucleon coupling constant $h^1_{\pi NN}$, based on the chiral quark-soliton model. We employ an effective weak Hamiltonian that takes into account the next-to-leading order corrections from QCD to the weak interactions at the quark level. Using the gradient expansion, we derive the leading-order effective weak chiral Lagrangian with the low-energy constants determined. The effective weak chiral Lagrangian is incorporated in the chiral quark-soliton model to calculate the parity-violating $\pi NN$ constant $h^1_{\pi NN}$. We obtain a value of about $10^{-7}$ at the leading order. The corrections from the next-to-leading order reduce the leading order result by about 20~\%.