Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
Gilberto Colangelo, Martin Hoferichter, Bastian Kubis, Peter Stoffer
Abstract
A bstract 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 − → 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 , ππγ , ηγ can induce a small phase, whose size we estimate as δ ϵ = 3 . 5(1 . 0) ° by using a narrow-width approximation for the intermediate-state vector mesons. We then perform fits to the e + e − → 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) ° , close to the narrow-resonance expectation, but with a large spread among the data sets, indicating systematic differences in the ρ - ω region.