The ππ scattering amplitude at large N c

Abstract

Abstract 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 T cs 0 0 2900 $$ {T}_{cs0}^0(2900) $$ , T c s ¯ 0 + + 2900 $$ {T}_{c\overline{s}0}^{++}(2900) $$ , T c s ¯ 0 0 2900 $$ {T}_{c\overline{s}0}^0(2900) $$ and T cs 1 0 2900 $$ {T}_{cs1}^0(2900) $$ 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 + D s + − K + D + $$ \left({\pi}^{+}{D}_s^{+}-{K}^{+}{D}^{+}\right) $$ 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.

Keywords

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