Quantum Bootstrap Approach to a Non-Relativistic Potential for Quarkonium systems

• URL: http://arxiv.org/abs/2508.02916v1
• Date: Mon, 04 Aug 2025 21:40:10 GMT
• Title: Quantum Bootstrap Approach to a Non-Relativistic Potential for Quarkonium systems
• Authors: Jairo Alexis Lopez, Carlos Sandoval,
• Abstract summary: We use a non-relativistic potential approximation to determine the bound-state spectrum of Quarkonium systems.<n>This result provides theoretical support for the interpretation of this experimental phenomenon as the formation of a quasi-bound toponium state.
• Score: 1.0214800410255813
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 Schr\"odinger 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.

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