Non-perturbative determination of meson masses and low-energy constants in large-$N$ QCD

TL;DR

This paper non-perturbatively calculates meson masses and low-energy constants in large-N QCD using lattice simulations, providing insights into the meson spectrum and QCD parameters in the 't Hooft limit.

Contribution

It presents the first-principles non-perturbative determination of meson masses and low-energy constants in large-N QCD, including continuum and chiral extrapolations.

Findings

Meson mass spectrum and Regge trajectories analyzed.

Quantitative estimates of low-energy constants like $ar{ ext{l}}_4$, $ ext{F}_ ext{pi}$, and $ ext{Sigma}$.

Assessment of sub-leading 1/N corrections.

Abstract

We provide first-principles non-perturbative determinations of the low-lying meson mass spectrum of large-$N$ QCD in the 't Hooft limit $N_{\scriptscriptstyle{\rm f}}/N\to 0$, as well as of three low-energy constants appearing in the QCD chiral expansion: the quark condensate $\Sigma$, the pion decay constant $F_\pi$, and the next-to-leading-order coupling $\bar{\ell}_4$. Using the excited state masses in the $\pi$ and $\rho$ channels, we are able to investigate the behavior of their radial Regge trajectories. Concerning QCD low-energy constants, we are able to assess the magnitude of sub-leading corrections in $1/N$ by combining our $N=\infty$ results with previous finite-$N$ determinations. Our calculation exploits large-$N$ twisted volume reduction to efficiently perform numerical Monte Carlo simulations of the large-$N$ lattice discretized theory. We employ several values of $N$ up to $N=841$, 5 values of the lattice spacing, and several values of the quark mass, to achieve controlled continuum and chiral extrapolations.