Masses and couplings of vector mesonsfrom the pion electromagnetic, weak, and transition form factors

D. Melikhov; O. Nachtmann; V. Nikonov; T. Paulus

doi:10.1140/epjc/s2004-01726-4

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2004) 34: 345-360
https://doi.org/10.1140/epjc/s2004-01726-4

theoretical physics

Masses and couplings of vector mesonsfrom the pion electromagnetic, weak, and $\pi\gamma$ transition form factors

D. Melikhov¹^*, O. Nachtmann¹, V. Nikonov² and T. Paulus¹

¹ Institut für Theoretische Physik, Philosophenweg 16, 69120, Heidelberg, Germany
² Petersburg Nuclear Physics Institute, 188300, Gatchina, St.-Petersburg, Russia

^* e-mail: melikhov@thphys.uni-heidelberg.de

Abstract

We analyze the pion electromagnetic, charged-current, and $\pi\gamma$ transition form factors at timelike momentum transfers q, $q^2 = s\le 1.4$ 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 $e^ + e^-\to \pi^ + \pi^-$ , $\tau^-\to \pi^-\pi^0\nu_\tau$ , and $e^ + e^-\to \pi^0\gamma$ 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 $s\le 1$ GeV. The fit to the form factor data leads to the following values of the Breit-Wigner resonance masses $m_{\rho^-} = 775.3\pm 0.8$ MeV, $m_{\rho^0} = 773.8\pm 0.6$ MeV and $m_\omega = 782.43\pm 0.05$ MeV, where the errors are only statistical.