nucl-th digest · Aug 22, 2022

[Submitted on 18 Aug 2022] (cross-list from hep-ph)

Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization

Gilberto Colangelo🇨🇭 · Martin Hoferichter🇨🇭 · Bastian Kubis🇩🇪 · Peter Stoffer🇨🇭

Isospin-breaking (IB) effects in the two-pion contribution to hadronic vacuum polarization (HVP) can be resonantly enhanced, if related to the interference of the $ρ (770)$ and $ω (782)$ resonances. This particular IB contribution to the pion vector form factor and thus the line shape in $e^{+} e^{-} \to π^{+} π^{-}$ can be described by the residue at the $ω$ pole - the $ρ$ - $ω$ mixing parameter $ϵ_{ω}$ . Here, we argue that while in general analyticity requires this parameter to be real, the radiative channels $π^{0} γ$ , $π π γ$ , $η γ$ can induce a small phase, whose size we estimate as $δ_{ϵ} = 3.5 (1.0)^{\circ}$ by using a narrow-width approximation for the intermediate-state vector mesons. We then perform fits to the $e^{+} e^{-} \to π^{+} π^{-}$ data base and study the consequences for the two-pion HVP contribution to the anomalous magnetic moment of the muon, its IB part due to $ρ$ - $ω$ mixing, and the mass of the $ω$ resonance. We find that the global fit does prefer a non-vanishing value of $δ_{ϵ} = 4.5 (1.2)^{\circ}$ , close to the narrow-resonance expectation, but with a large spread among the data sets, indicating systematic differences in the $ρ$ - $ω$ region.

Comments:: 18 pages; journal version
Subjects:: High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Experiment (hep-ex); High Energy Physics — Lattice (hep-lat); Nuclear Theory (nucl-th)
arXiv:: 2208.08993 [pdf]

JHEP(2022)·77 citations

Monday·August 22, 2022

Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization

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