Benchmark calculations of fully heavy compact and molecular tetraquark states

Benchmark calculations of fully heavy compact and molecular tetraquark states

26 Mar 2024 | Wei-Lin Wu, Yan-Ke Chen, Lu Meng, Shi-Lin Zhu
This paper presents benchmark calculations of the mass spectra of S-wave fully heavy tetraquark systems $ QQ\bar{Q}\bar{Q} $ (with $ Q = c, b $) using three quark potential models: AL1, AP1, and BGS. The calculations consider both normal and exotic C-parities, where exotic C-parity systems cannot be composed of two S-wave ground heavy quarkonia. The Gaussian expansion method is used to solve the four-body Schrödinger equation, and the complex scaling method is used to identify resonant states. The results show qualitative agreement among the three models. Resonant states with $ J^{PC} = 0^{++}, 1^{+-}, 2^{++}, 1^{++} $ are found in the mass region (6.92, 7.30) GeV, with some being candidates for the experimentally observed $ X(6900) $ and $ X(7200) $. Exotic C-parity zero-width states with $ J^{PC} = 0^{+-}, 2^{+-} $ are also identified. These states cannot decay via S-wave diquarkonium thresholds and instead decay via P-wave quarkonia. The study also explores the spatial configurations of the states, distinguishing between compact and molecular configurations. The results suggest that while most states are compact, the $ X(7200) $ candidates may have molecular configurations. The paper also discusses the decay modes of the states and the suppression of two-body decay widths due to color mixing and other factors. The findings provide insights into the nature of fully heavy tetraquark states and their potential experimental observations.This paper presents benchmark calculations of the mass spectra of S-wave fully heavy tetraquark systems $ QQ\bar{Q}\bar{Q} $ (with $ Q = c, b $) using three quark potential models: AL1, AP1, and BGS. The calculations consider both normal and exotic C-parities, where exotic C-parity systems cannot be composed of two S-wave ground heavy quarkonia. The Gaussian expansion method is used to solve the four-body Schrödinger equation, and the complex scaling method is used to identify resonant states. The results show qualitative agreement among the three models. Resonant states with $ J^{PC} = 0^{++}, 1^{+-}, 2^{++}, 1^{++} $ are found in the mass region (6.92, 7.30) GeV, with some being candidates for the experimentally observed $ X(6900) $ and $ X(7200) $. Exotic C-parity zero-width states with $ J^{PC} = 0^{+-}, 2^{+-} $ are also identified. These states cannot decay via S-wave diquarkonium thresholds and instead decay via P-wave quarkonia. The study also explores the spatial configurations of the states, distinguishing between compact and molecular configurations. The results suggest that while most states are compact, the $ X(7200) $ candidates may have molecular configurations. The paper also discusses the decay modes of the states and the suppression of two-body decay widths due to color mixing and other factors. The findings provide insights into the nature of fully heavy tetraquark states and their potential experimental observations.
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