Results on meson-meson scattering at large $N_\text{c}$

TL;DR

This study investigates how meson-meson scattering amplitudes scale with the number of colors in QCD-like theories, using lattice simulations at various N_c values, and explores potential tetraquark states at large N_c.

Contribution

First lattice study of meson-meson scattering at multiple N_c values with focus on tetraquark candidate channels and large N_c scaling behavior.

Findings

Indications of a virtual bound state at N_c=3 in one scattering channel.

Constraints on scattering amplitudes using Lüscher's method across N_c values.

Evidence of subleading N_c corrections affecting meson interactions.

Abstract

We present results on the large $N_\text{c}$ scaling of meson-meson scattering amplitudes. We work in a theory with $N_\text{f}=4$ degenerate quark flavors and run lattice simulations with $N_\text{c}=3-6$ and pion mass $M_\pi\approx 590$ MeV. We focus on three different scattering channels, two of which have the same quantum numbers as some tetraquark candidates recently found at LHCb. Finite-volume energies are extracted using a large set of operators, containing two-particle operators corresponding to two pions or two vector mesons, and local tetraquark operators. Using L\"uscher's quantization condition, we constrain the infinite-volume scattering amplitudes and investigate subleading $N_\text{c}$ corrections to the large $N_\text{c}$ limit. For one of the channels, we find indications of a virtual bound state at $N_\text{c}=3$, which may be related to one of the aforementioned exotic states.