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

We provide first-principles non-perturbative determinations of the low-lying meson mass spectrum of large-$N$ QCD in the 't Hooft limit $N_{\mathrm{f}}\mathrm{/}N\to 0$, as well as of three low-energy constants appearing in the QCD chiral expansion: the quark condensate $\mathrm{\Sigma }$, the pion decay constant $F_{\pi }$, and the next-to-leading-order coupling ${\bar{\mathrm{\ell }}}_4$. 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 $1\mathrm{/}N$ by combining our $N=\mathrm{\infty }$ 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.