The $\eta/\eta' \rightarrow \pi^+ \pi^- \gamma$ decays within BHLS$_2$ and the Muon HVP - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue European Physical Journal C: Particles and Fields Année : 2023

The $\eta/\eta' \rightarrow \pi^+ \pi^- \gamma$ decays within BHLS$_2$ and the Muon HVP

Résumé

The departure of the latest FNAL experimental average for the muon anomalous magnetic moment $a_μ=(g_μ−2)/2$ measurements having increased from 4.2σ to 5.0σ, with respect to the White Paper consensus, it may indicate a hint for new physics. As the most delicate piece of aμ is its leading order HVP part $a^{HVP−LO}_μ$, methods to ascertain its theoretical value are crucial to interpret this discrepancy. We propose to examine the dipion spectra from the η/η′→π+π−γ decays in the Hidden Local Symmetry (HLS) context using its BHLS2 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−→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 BHLS2 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−→π+π− annihilation data, allow for a prediction of the pion vector form factor data Fπ(s) which fairly agree with the usual dipion spectra collected in the e+e−→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 $a^{HVP−LO}_μ$, and points towards a common non experiment-dependent origin to this tension with the now well accepted LQCD result.

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Origine : Publication financée par une institution
Licence : CC BY - Paternité

Dates et versions

hal-04234677 , version 1 (10-10-2023)
hal-04234677 , version 2 (27-03-2024)

Identifiants

Citer

M. Benayoun, L. Delbuono, F. Jegerlehner. The $\eta/\eta' \rightarrow \pi^+ \pi^- \gamma$ decays within BHLS$_2$ and the Muon HVP. European Physical Journal C: Particles and Fields, 2023, 84 (3), pp.295. ⟨10.1140/epjc/s10052-024-12608-w⟩. ⟨hal-04234677v2⟩
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