A New Approach to Weak Amplitudes in Large-Nc QCD

TL;DR

This paper advances understanding of weak meson matrix elements in large-Nc QCD by analytically matching short and long-distance effects, and computes specific matrix elements relevant to meson mass differences and decays.

Contribution

It introduces a systematic analytical matching method in large-Nc QCD for weak matrix elements and computes key matrix elements related to meson mass differences and decay processes.

Findings

Analytical matching between short and long distances achieved.

Computed matrix elements of operator Q_7.

Determined chiral counterterms for pseudoscalar decays.

Abstract

We report on some recent progress made in understanding weak matrix elements of mesons in the context of the next-to-leading order of the large-Nc approximation to QCD. Specifically, we first use the example of the weak contributions to the pi^+ - pi^0 mass difference to exhibit how a systematic matching can be achieved analytically between short distances and long distances within our large-Nc framework. We are then also able to compute matrix elements of the operator Q_7, as they turn out to depend on the same QCD correlator as the previous pion mass difference. As a final example we determine the chiral counterterms governing the pseudoscalar decay into a lepton pair, where we briefly comment also on the special case K_L -> mu^+ mu^-.