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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2309.15050 |
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| _version_ | 1866909072616325120 |
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| author | Benayoun, Maurice DelBuono, Luigi Jegerlehner, Fred |
| author_facet | Benayoun, Maurice DelBuono, Luigi Jegerlehner, Fred |
| contents | The departure of the latest FNAL experimental average for the muon anomalous magnetic moment $a_μ=(g_μ-2)/2$ measurements having increased from $4.2 σ$ to $5.0 σ$, with respect to the White Paper consensus, it may indicate a hint for new physics. As the most delicate piece of $a_μ$ is its leading order HVP part $a_μ^{HVP-LO}$, methods to ascertain its theoretical value are crucial to interpret this discrepancy. We propose to examine the dipion spectra from the $η/η' \rightarrow π^+ π^- γ$ decays in the Hidden Local Symmetry (HLS) context using its BHLS$_2$ broken variant. We thus have at our disposal a framework where the close relationship of the dipion spectra from the $η/η'$ and $τ$ decays and of the $e^+e^- \to π^+π^-$ annihilation can be simultaneously considered. A special focus is put to the high statistic dipion spectra from the $η$ decay collected by the KLOE/KLOE2 Collaboration and $η'$ decay collected by the BESIII Collaboration, and it is shown that the BHLS$_2$ framework provides a fair account of their dipion spectra. More precisely, it is first proven that a single Omnès representation real polynomial is requested, common to both the $η$ and $η'$ dipion spectra. Moreover, it is shown that fits involving the $η/η'/τ$ dipion spectra, and excluding the $e^+e^- \to π^+π^-$ annihilation data, allow for a prediction of the pion vector form factor data $F_π(s)$ which fairly agree with the usual dipion spectra collected in the $e^+e^- \to π^+π^-$ annihilation channel. Even if more precise $η/η'/τ$ dipion spectra would help to be fully conclusive, this confirms the Dispersive Approach results for $a_μ^{HVP-LO}$ and points towards a common non experiment-dependent origin to this tension with the now well accepted LQCD result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15050 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The $η/η' \rightarrow π^+ π^- γ$ Decays within BHLS$_2$ and the Muon HVP Benayoun, Maurice DelBuono, Luigi Jegerlehner, Fred High Energy Physics - Phenomenology The departure of the latest FNAL experimental average for the muon anomalous magnetic moment $a_μ=(g_μ-2)/2$ measurements having increased from $4.2 σ$ to $5.0 σ$, with respect to the White Paper consensus, it may indicate a hint for new physics. As the most delicate piece of $a_μ$ is its leading order HVP part $a_μ^{HVP-LO}$, methods to ascertain its theoretical value are crucial to interpret this discrepancy. We propose to examine the dipion spectra from the $η/η' \rightarrow π^+ π^- γ$ decays in the Hidden Local Symmetry (HLS) context using its BHLS$_2$ broken variant. We thus have at our disposal a framework where the close relationship of the dipion spectra from the $η/η'$ and $τ$ decays and of the $e^+e^- \to π^+π^-$ annihilation can be simultaneously considered. A special focus is put to the high statistic dipion spectra from the $η$ decay collected by the KLOE/KLOE2 Collaboration and $η'$ decay collected by the BESIII Collaboration, and it is shown that the BHLS$_2$ framework provides a fair account of their dipion spectra. More precisely, it is first proven that a single Omnès representation real polynomial is requested, common to both the $η$ and $η'$ dipion spectra. Moreover, it is shown that fits involving the $η/η'/τ$ dipion spectra, and excluding the $e^+e^- \to π^+π^-$ annihilation data, allow for a prediction of the pion vector form factor data $F_π(s)$ which fairly agree with the usual dipion spectra collected in the $e^+e^- \to π^+π^-$ annihilation channel. Even if more precise $η/η'/τ$ dipion spectra would help to be fully conclusive, this confirms the Dispersive Approach results for $a_μ^{HVP-LO}$ and points towards a common non experiment-dependent origin to this tension with the now well accepted LQCD result. |
| title | The $η/η' \rightarrow π^+ π^- γ$ Decays within BHLS$_2$ and the Muon HVP |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2309.15050 |