Monday·July 29, 2024

[Submitted on 25 Jul 2024] (cross-list from hep-ph)

Tetraquarks at large $M$ and large $N$

Héloïse Allaman🇨🇭 · Majid Ekhterachian🇨🇭 · Filippo Nardi🇨🇭 · Riccardo Rattazzi🇨🇭 · Stefan Stelzl🇨🇭

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.