A lattice study of ππ scattering at large N c

Abstract

Abstract We present the first lattice study of pion-pion scattering with varying number of colors, N c. We use lattice simulations with four degenerate quark flavors, N f = 4, and N c = 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 N f ≥ 4. A representative state is D s + π + − D + K + / 2 $$ \left(\left.\left|{D}_s^{+}{\pi}^{+}\right.\right\rangle -\left.\left|{D}^{+}{K}^{+}\right.\right\rangle \right)/\sqrt{2} $$ . Using Lüscher’s formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large N c. For this, we compute the analytical U(N f) ChPT prediction for two-pion scattering, and use the lattice results to constrain the N c scaling of the relevant low-energy couplings.

Keywords

• Hadronic Spectroscopy
• Structure and Interactions
• Lattice QCD
• 1/N Expansion
• Chiral Lagrangian