Study of pion vector form factor and its contribution to the muon $(g-2)$

Abstract

In the present work, we investigate several phenomenological theoretical models of the pion vector form factor and aim at getting the best fit for the two-pion cross sections to reduce the uncertainties of the calculation of two-pion contribution to the muon anomalous magnetic moment. Combined with a polynomial description to the experimental data up to 1 GeV, we obtain the best fit from the Gournaris-Sakurai (or Kühn-Santamaria) model, where the mass and width of ρ resonance, and the branching ration of ω → ππ can be extracted as m ρ = (774.07 ± 0.14) MeV, Γ ρ = (149.54 ± 0.27) MeV, and Br(ω → ππ) = (1.52 ± 0.09)%, respectively. With the best fit of the data, we obtain the muon anomalous magnetic moment from two-pion contribution as a HVP, LO µ (π + π − ≤ 1 GeV) = (497.76 ± 1.12) × 10 −10 . Our results are consistent with the results of Particle Data Group and the other works.

Two body final states production in electron-positron annihilation and their contributions to (g − 2)μ

“…For recent progress trying to refine HVP contributions, we refer to refs. [22][23][24][25][26]. Furthermore, as has been pointed out by ref.…”