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