Meson spectrum and low-energy constants in large-$N$ QCD

Abstract

We present new non-perturbative results about the meson spectrum and the low-energy constants of QCD in the 't Hooft large-$N$ limit, $N\to\infty$ with $N_{\scriptscriptstyle{\rm f}}/N\to 0$. These are obtained from lattice Monte Carlo simulations of the Twisted Eguchi-Kawai (TEK) model up to $N=841$. More precisely, we will discuss: our findings for the meson mass spectrum; the determination of the radial Regge trajectories in the $π$ and $ρ$ channels; the computation of the coefficients of the $1/N$ expansion of the chiral condensate, of the pion decay constant, and of the next-to-leading-order coupling $\bar{\ell}_4$, up to $\mathcal{O}(1/N^3)$ from the combination of TEK and standard finite-$N$ results.

Figures (3)

• Figure 1: Left panel: extraction of the $\rho$ mass from the exponential decay of the GEVP optimal correlator. Central panel: cross-check of the extraction of the $\rho$ mass from the effective mass plateau. Right panel: chiral-continuum extrapolation of $m_\rho(m_\pi)$ in units of the string tension $\sigma$. The old TEK result, obtained from $N$ values up to $N=361$, comes from Ref. Perez:2020vbn. Figures taken from Ref. Bonanno:2025hzr.
• Figure 2: Left panel: meson spectrum of large-$N$ QCD. Conversion to "physical units" is done for illustrative purposes only. We used $\sqrt{\sigma}=445~\mathrm{ MeV}$Bulava:2024jpj. Right panel: radial Regge trajectories in large-$N$ QCD from the TEK model in the $\pi$ and $\rho$ channels in the chiral limit. Figures taken from Ref. Bonanno:2025hzr.
• Figure 3: The large-$N$$1/N$ expansion of the $\mathcal{O}(N^0)$$\chi$PT low-energy constants $B_{{{\rm R}}}=\Sigma_{{{\rm R}}}/F_\pi^2$, $\Sigma_{{\rm R}}/N$, $F_\pi/\sqrt{N}$ and $\bar{\ell}_4/N$. Figures taken from Ref. Bonanno:2025hzr.