Quenched mesonic spectrum at large N

Abstract

We compute the masses of the $\pi$ and of the $\rho$ mesons in the quenched approximation on a lattice with fixed lattice spacing $a\simeq 0.145\mathrm{fm}$ for SU($N$) gauge theory with $N=2,3,4,6$. We find that a simple linear expression in $1/N^2$ correctly captures the features of the lowest-lying meson states at those values of $N$. This enables us to extrapolate to $N=\infty$ the behaviour of $m_{\pi }$ as a function of the quark mass and of $m_{\rho }$ as a function of $m_{\pi }$. Our results for the latter agree within 5% with recent predictions obtained in the AdS/CFT framework.

Comments: Reference added; typos corrected; version to appear on JHEP