The ππ scattering amplitude at large Nc

Abstract

We study the scaling of meson-meson scattering amplitudes with the number of colors, Nc. We use lattice calculations in a theory with Nf = 4 degenerate flavors, with Nc = 3 – 6 and pion mass Mπ ≈ 560 MeV. We focus on three different scattering channels, two of which have the same quantum numbers as some tetraquark candidates recently found at LHCb: the T cs 0 0 2900 , T c s ¯ 0 + + 2900 , T c s ¯ 0 0 2900 and T cs 1 0 2900 states. Finite-volume energies are extracted using a large set of operators, containing two-particle operators with the form of two pions or two vector mesons, and local tetraquark operators. The resulting energy spectra is used to constrain the infinite-volume scattering amplitude by means of Lüscher’s quantization condition. We consider polynomial parametrizations of the phase shift, as well as one-loop chiral perturbation theory (ChPT) predictions. We find that our lattice results follow the expected Nc scaling and are sensitive to subleading Nc corrections. In addition, we constrain the scaling of different combinations of low-energy constants from matching to large Nc ChPT. The results for the channel corresponding to a π + D s + − K + D + state show evidence of a virtual bound state with energy Evirtual = 1.63(10)Mπ for Nc = 3, while this pole disappears at Nc > 3. This may be connected to the exotic states found in experiment.