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arXiv · 2407.18298

Tetraquarks at large $M$ and large $N$

Héloïse Allaman·Majid Ekhterachian·Filippo Nardi·Riccardo Rattazzi·Stefan Stelzl
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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.

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Héloïse Allaman, Majid Ekhterachian, Filippo Nardi, Riccardo Rattazzi, Stefan Stelzl. 2024-07-25. Tetraquarks at large $M$ and large $N$. https://arxiv.org/abs/2407.18298

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