Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization - Hoferichter, Martin; Hoid, Bai-Long; Kubis, Bastian; Schuh, Dominic (The journal of high energy physics, 2023)
A bstract Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e + e − → π + π − channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e + e − → 3 π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ – ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η 3 π that generalizes the analog treatment of virtual and final-state photons in the 2 π case. The global fit to the e + e − → 3 π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives a μ 3 π ≤ 1.8 GeV = 45.91 53 × 10 − 10 for the total 3 π contribution to the anomalous magnetic moment of the muon, of which a μ FSR 3 π = 0.51 1 × 10 − 10 and a μ ρ − ω 3 π = − 2.68 70 × 10 − 10 can be ascribed to IB. We argue that the resulting cancellation with ρ – ω mixing in e + e − → 2 π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters M ω = 782 . 70(3) MeV, M ϕ = 1019 . 21(2) MeV, Γ ω = 8 . 71(3) MeV, and Γ ϕ = 4 . 27(1) MeV.