Masses and couplings of vector mesonsfrom the pion electromagnetic, weak, and πγ transition form factors - Melikhov, Dmitri; Nachtmann, Otto; Paulus, Timo (The European physical journal. C, Particles and fields, 2004)
We analyze the pion electromagnetic, charged-current, and πγπγπγ transition form factors at timelike momentum transfers q, q2=s≤1.4q2=s≤1.4q^2 = s\le 1.4 GeV2, using a dispersion approach. We discuss in detail the propagator matrix of the photon-vector meson system and define certain reduced amplitudes, or vertex functions, describing the coupling of this system to final states. We then apply the derived analytic expressions to the analysis of the recent e+e−→π+π−e+e−→π+π−e^ + e^-→ π^ + π^-, τ−→π−π0νττ−→π−π0νττ^-→ π^-π^0ν_τ, and e+e−→π0γe+e−→π0γe^ + e^-→ π^0γ data. We find the reduced amplitudes for the coupling of the photon and vector mesons to two pseudoscalars to be constant, independent of s, in the range considered, indicating a “freezing” of the amplitudes for s≤1s≤1s\le 1 GeV. The fit to the form factor data leads to the following values of the Breit-Wigner resonance masses mρ−=775.3±0.8mρ−=775.3±0.8m_{ρ^-} = 775.3± 0.8 MeV, mρ0=773.8±0.6mρ0=773.8±0.6m_{ρ^0} = 773.8± 0.6 MeV and mω=782.43±0.05mω=782.43±0.05m_ω = 782.43± 0.05 MeV, where the errors are only statistical.