A lattice study of ππ scattering at large Nc

We present the first lattice study of pion-pion scattering with varying number of colors, Nc. We use lattice simulations with four degenerate quark flavors, Nf = 4, and Nc = 3 − 6. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, SS, and the fully antisymmetric one, AA. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for Nf≥ 4. A representative state is Ds+π+−D+K+/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(\left.\left|{D}_s^{+}{\pi}^{+}\right.\right\rangle -\left.\left|{D}^{+}{K}^{+}\right.\right\rangle \right)/\sqrt{2} $$\end{document}. Using Lüscher’s formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large Nc. For this, we compute the analytical U(Nf) ChPT prediction for two-pion scattering, and use the lattice results to constrain the Nc scaling of the relevant low-energy couplings.