Meson interactions at large $N_c$ from Lattice QCD

TL;DR

This paper investigates how QCD observables scale with the number of colours using lattice simulations for N_c=3 to 6, focusing on meson properties, low energy constants, and weak decay processes.

Contribution

It provides new lattice QCD results on meson interactions and decay constants across different N_c values, enhancing understanding of large N_c QCD behavior.

Findings

Meson masses and decay constants scale with N_c as predicted.

Leading and subleading contributions to Low Energy Constants are quantified.

Results offer insights into weak decay matrix elements and the $ riangle I=1/2$ rule.

Abstract

We report on the computation of the scaling of QCD observables with the number of colours, $N_c$. For this, we use dynamical configurations with four active flavours, $N_f=4$, and values of $N_c=3-6$. We study the meson masses and decay constants, and compute the leading and subleading contributions to the Low Energy Constants (LECs) of the chiral Lagrangian. We also explore $\pi \pi$ scattering in the $I=2$ channel, and compute the $K \to \pi $ weak decay matrix elements. We comment on the relation of the latter to $K \to \pi\pi$ processes and the $\Delta I=1/2$ rule.