Quantum Bootstrap Approach to a Non-Relativistic Potential for Quarkonium systems
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866908780258656256 |
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| author | Lopez, Jairo Alexis Sandoval, Carlos |
| author_facet | Lopez, Jairo Alexis Sandoval, Carlos |
| contents | The quantum bootstrap method is applied to determine the bound-state spectrum of Quarkonium systems using a non-relativistic potential approximation. The method translates the Schrödinger equation into a set of algebraic recursion relations for radial moments $\langle r^m \rangle$, which are constrained by the positive semidefiniteness of their corresponding Hankel matrices. The numerical implementation is first validated by calculating the $1S$ and $1P$ mass centroids for both charmonium ($c\bar{c}$) and bottomonium ($b\bar{b}$) systems, finding deviations of less than 0.5\% from experimental data from the Particle Data Group (PDG). This analysis is then extended to the hypothetical toponium ($t\bar{t}$) system, predicting a $1S$ ground state mass of $M \approx 344.3 \text{ GeV}$. This theoretical mass is in agreement with the energy of the recently observed resonance-like enhancement in the $t\bar{t}$ cross-section by the ATLAS and CMS collaborations. This result provides theoretical support for the interpretation of this experimental phenomenon as the formation of a quasi-bound toponium state and highlights the predictive power of the non-relativistic potential approach for systems of two massive quarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02916 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Bootstrap Approach to a Non-Relativistic Potential for Quarkonium systems Lopez, Jairo Alexis Sandoval, Carlos High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics The quantum bootstrap method is applied to determine the bound-state spectrum of Quarkonium systems using a non-relativistic potential approximation. The method translates the Schrödinger equation into a set of algebraic recursion relations for radial moments $\langle r^m \rangle$, which are constrained by the positive semidefiniteness of their corresponding Hankel matrices. The numerical implementation is first validated by calculating the $1S$ and $1P$ mass centroids for both charmonium ($c\bar{c}$) and bottomonium ($b\bar{b}$) systems, finding deviations of less than 0.5\% from experimental data from the Particle Data Group (PDG). This analysis is then extended to the hypothetical toponium ($t\bar{t}$) system, predicting a $1S$ ground state mass of $M \approx 344.3 \text{ GeV}$. This theoretical mass is in agreement with the energy of the recently observed resonance-like enhancement in the $t\bar{t}$ cross-section by the ATLAS and CMS collaborations. This result provides theoretical support for the interpretation of this experimental phenomenon as the formation of a quasi-bound toponium state and highlights the predictive power of the non-relativistic potential approach for systems of two massive quarks. |
| title | Quantum Bootstrap Approach to a Non-Relativistic Potential for Quarkonium systems |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2508.02916 |