Journal Article

A lattice study of ππ scattering at large N c

Jorge Baeza-Ballesteros, Fernando Romero-López, Pilar Hernández

2022

Overview

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.

• Publisher: SpringerOpen
• Subject: 1/N Expansion / Chiral Lagrangian / Hadronic Spectroscopy / Lattice QCD / Structure and Interactions