The ππ scattering amplitude at large Nc

A bstract We study the scaling of meson-meson scattering amplitudes with the number of colors, N c . We use lattice calculations in a theory with N f = 4 degenerate flavors, with N c = 3 – 6 and pion mass M π ≈ 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 Tcs0⁰(2900) T cs 0 0 2900 , Tcs̄0⁺⁺(2900) T c s ¯ 0 + + 2900 , Tcs̄0⁰(2900) T c s ¯ 0 0 2900 and Tcs1⁰(2900) 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 N c scaling and are sensitive to subleading N c corrections. In addition, we constrain the scaling of different combinations of low-energy constants from matching to large N c ChPT. The results for the channel corresponding to a (π⁺Dₛ⁺-K⁺D⁺) π + D s + − K + D + state show evidence of a virtual bound state with energy E virtual = 1.63(10) M π for N c = 3, while this pole disappears at N c > 3. This may be connected to the exotic states found in experiment.