Large-N π⁺π⁺ scattering from twisted Eguchi--Kawai reduction

We present the first computation of the π⁺π⁺ scattering length in large-N QCD in the 't Hooft limit, N_ f/N→ 0, using the twisted Eguchi--Kawai formulation of the lattice theory. We employ values of N up to 1156 and consider several quark masses and lattice spacings to achieve controlled large-N, continuum, and chiral limits. The chiral behavior of the scattering length is compared with next-to-leading-order Chiral Perturbation Theory predictions. Our result for the low-energy coupling describing the sub-leading quark-mass dependence is consistent with existing S-matrix bootstrap bounds. Combining TEK results with previous lattice QCD data obtained using standard methods for 3≤ N≤ 6, we are also able to extract sub-leading O(1/N) corrections to the large-N scattering length.