BHLS$_2$ and $\pi^+ \pi^-$ Final State Interaction~: The $\eta/\eta' \rightarrow \pi^+ \pi^- \gamma$ Decays and the Muon HVP

M Benayoun (1) , L Delbuono (1) , F Jegerlehner (2)

1 LPNHE (UMR_7585) - Laboratoire de Physique Nucléaire et de Hautes Énergies
2 HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin

The departure of the latest FNAL experimental average for the muon anomalous mag- netic moment aμ = (gμ − 2)/2 measurements having increased from 4.2σ [1] to 5.0σ [2], with respect to the White Paper (WP) consensus[3], it may indicate a hint for new physics. As the most delicate piece of aμ is its leading order HVP part aHV P −LO μ , meth- ods to ascertain its theoretical value are crucial to interpret appropriately this departure with the measurement. We therefore propose to examine closely 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 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. It is shown that, once the Final State Interaction (FSI) effects are accounted for, the BHLS2 framework provides a fair account of their dipion spectra. More precisely, it is first proven that a single FSI 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 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 may already be considered as supporting the Dispersive Approach results for aHV P −LO μ

Domains: Physics [physics]

M Benayoun, L Delbuono, F Jegerlehner. BHLS$_2$ and $\pi^+ \pi^-$ Final State Interaction~: The $\eta/\eta' \rightarrow \pi^+ \pi^- \gamma$ Decays and the Muon HVP. 2023. ⟨hal-04234677v1⟩