The branching ratio $$\omega \rightarrow \pi ^+\pi ^-$$ ω → π + π - revisited

Abstract

We analyze the most recent data for the pion vector form factor in the timelike region, employing a modelindependent approach based on dispersion theory. We confirm earlier observations about the inconsistency of different modern high-precision data sets. Excluding the BaBar data, we find an updated value for the isospin-violating branching ratio B(ω → π + π − ) = (1.46 ± 0.08) × 10 −2 . As a side result, we also extract an improved value for the pion vector or charge radius, r 2 V = 0.6603 (5)(4) fm, where the first uncertainty is statistical as derived from the fit, while the second estimates the possible size of nonuniversal radiative corrections. In addition, we demonstrate that modern high-quality data for the decay η → π + π − γ will allow for an even improved determination of the transition strength ω → π + π − .

Radiative resonance couplings in γπ→ππ

“…The dispersive formalism for the analytic continuation to s ρ has been studied in detail in the literature, see [25,[41][42][43][44][45][46][47][48][49], and data abound, mostly motivated by the ππ contribution to hadronic vacuum polarization in the anomalous magnetic moment of the muon. In this way, the dominant uncertainties actually arise from the error in g ρππ as well as the systematics of the fit, e.g.…”

Erratum to: The branching ratio $$\omega \rightarrow \pi ^+\pi ^-$$ ω → π + π -

“…In the published paper [1], a data set for the pion vector form factor from the BaBar experiment [2] was used that was not consistent with the ones employed for the other experiments, since it did not include the contributions from the vacuum polarization, while it contained those of the final-state radiation. The use of the official form factor data changes some of the results, as we report in this erratum.…”

Towards a dispersive determination of the η and η′ transition form factors

“…7. The leading left-hand-cut contribution provided by a 2 -exchange gives an estimate of the parameter β = (−1.0 ± 0.1) GeV −4 [30], which yields the correct sign and order of magnitude, but is somewhat larger than what the new data suggest [26]. The combination of the very precise representation of the η ′ → π + π − γ decay amplitude as well as the pion vector form factor then once more yields a dispersive prediction of the isovector part of the η ′ (singly-virtual) transition form factor according to the analogous formula to Eq.…”

“…The preliminary BESIII data [40] demonstrate the need of such a quadratic term to very high significance; moreover, they are so precise that even the isospin-breaking ρ-ω-mixing effect is clearly discernible (see Ref. [26] for details on how to extract the mixing strength and subsequently the partial width Γ(ω → π + π − ) from this decay). The full representation of the η ′ → π + π − γ P-wave amplitude is therefore of the form [26] …”

“…[26] for details on how to extract the mixing strength and subsequently the partial width Γ(ω → π + π − ) from this decay). The full representation of the η ′ → π + π − γ P-wave amplitude is therefore of the form [26] …”