Tetraquarks at large $M$ and large $N$

TL;DR

This paper investigates the formation and properties of tetraquarks in large N QCD with heavy quarks, employing non-relativistic quantum mechanics and the Born-Oppenheimer approximation to identify conditions under which tetraquarks are stable.

Contribution

It systematically constructs tetraquark states in large N QCD with heavy quarks and identifies two distinct types of tetraquarks arising from a specific mass hierarchy.

Findings

At leading order, the spectrum consists of free mesons.

1/N corrections generate a potential binding mesons into tetraquarks.

Only a specific mass hierarchy favors a tetraquark ground state.

Abstract

We study tetraquarks in large $N$ QCD with heavy quarks, in the domain where non-relativistic quantum mechanics offers an adequate approximation. Within the regime of validity of the Born-Oppenheimer approximation, we systematically study and explicitly construct tetraquark states. At leading order in the $1/N$ expansion, the bound spectrum consists of free mesons, while the $1/N$ corrections give rise to a Born-Oppenheimer potential that can bind the mesons into tetraquarks. We find two different types of tetraquarks, each endowed with distinct color-spatial wavefunctions. These states arise in the presence of an $\mathcal{O}(N)$ mass hierarchy between the quarks and the antiquarks. We provide a quantitative argument indicating that only for such a hierarchy is the ground state of the system a tetraquark. We discuss what the extrapolation of our results to realistic values of the parameters may imply for the QCD tetraquark states.