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A model-independent analysis of the isospin breaking in the $X(3872)~\to~J/\psi \pi^+\pi^-$ and $X(3872)~\to~J/\psi \pi^+\pi^0\pi^-$ decays
- Publication Year :
- 2024
-
Abstract
- We analyze the latest LHCb data on the $\pi^+\pi^-$ spectrum in the isospin-violating $X(3872)~\to~J/\psi \pi^+\pi^-$ decay, employing a model-independent approach based on dispersion theory to deal with the $\pi\pi$ final state interactions. Additionally, the isospin breaking effects are properly introduced, allowing for reliable and accurate extraction of the ratio, $R_X$, between the $X(3872)$ couplings to the $J/\psi \rho$ and $J/\psi \omega$ channels from the data. We find very good agreement with the LHCb data for the whole range of the $\pi^+\pi^-$ invariant mass, and $R_X$ is determined to be $0.19\pm 0.02$, significantly smaller than what was determined earlier. Using this value, we make predictions for the $\pi^+\pi^0\pi^-$ mass distribution in the $X(3872)~\to~J/\psi \pi^+\pi^0\pi^-$ process, which is currently accessible by the BESIII Collaboration, and update a prediction for the pole positions of the isovector partner states of the $X(3872)$, $W_{c1}$, with $I(J^{PC})=1(1^{++})$.<br />Comment: 9 pages, 1 table and 2 figures
- Subjects :
- High Energy Physics - Phenomenology
High Energy Physics - Experiment
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.13245
- Document Type :
- Working Paper