Tetraquarks at large $M$ and large $N$
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909269025095680 |
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| author | Allaman, Héloïse Ekhterachian, Majid Nardi, Filippo Rattazzi, Riccardo Stelzl, Stefan |
| author_facet | Allaman, Héloïse Ekhterachian, Majid Nardi, Filippo Rattazzi, Riccardo Stelzl, Stefan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_18298 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tetraquarks at large $M$ and large $N$ Allaman, Héloïse Ekhterachian, Majid Nardi, Filippo Rattazzi, Riccardo Stelzl, Stefan High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory 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. |
| title | Tetraquarks at large $M$ and large $N$ |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2407.18298 |