Abstract
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 \( \left(\left.\left|{D}_s^{+}{\pi}^{+}\right.\right\rangle -\left.\left|{D}^{+}{K}^{+}\right.\right\rangle \right)/\sqrt{2} \). Using Lüscher’s formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large 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.
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Baeza-Ballesteros, J., Hernández, P. & Romero-López, F. A lattice study of ππ scattering at large Nc. J. High Energ. Phys. 2022, 49 (2022). https://doi.org/10.1007/JHEP06(2022)049
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DOI: https://doi.org/10.1007/JHEP06(2022)049