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

Abstract

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−→ 3π 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 η3π that generalizes the analog treatment of virtual and final-state photons in the 2π case. The global fit to the e+e−→ 3π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives {left.{a}_{mu}^{3pi}right|}_{le 1.8 textrm{GeV}}=45.91(53)times {10}^{-10} for the total 3π contribution to the anomalous magnetic moment of the muon, of which {a}_{mu}^{textrm{FSR}}left[3pi right]=0.51(1)times {10}^{-10} and {a}_{mu}^{rho -omega}left[3pi right]=-2.68(70)times {10}^{-10} can be ascribed to IB. We argue that the resulting cancellation with ρ–ω mixing in e+e−→ 2π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters Mω = 782.70(3) MeV, Mϕ = 1019.21(2) MeV, Γω = 8.71(3) MeV, and Γϕ = 4.27(1) MeV.