Near threshold radiative 3$\pi$ production in $e^{+}{e}^{-}$ annihilation

Abstract

We consider the ${\pi }^{+}{\pi }^{-}{\pi }_0\gamma$ final state in electron-positron annihilation at cms energies not far from the threshold. Both initial and final state radiations of the hard photon is considered but without interference between them. The amplitude for the final state radiation is obtained by using the effective Wess-Zumino-Witten Lagrangian for pion-photon interactions valid for low energies. In real experiments energies are never such small that $\rho$ and $\omega$ mesons would have negligible effect. So a phenomenological Breit-Wigner factor is introduced in the final state radiation amplitude to account for the vector mesons influence. Using radiative 3$\pi$ production amplitudes, a Monte Carlo event generator was developed which could be useful in experimental studies.

15 pages, Latex, 6 figures. Misprints corrected. Version to be published in JHEP

References in corpus (5)

• Precise Measurement of the Positive Muon Anomalous Magnetic Moment
• The Muon Anomalous Magnetic Moment: A Harbinger For "New Physics"
• Hadronic light-by-light corrections to the muon g-2: the pion-pole contribution
• Precision Determination of the Pion Form Factor and Calculation of the Muon $g-2$
• On the theoretical uncertainties in the muon anomalous magnetic moment

Cited by in corpus (8)

• The anomalous magnetic moment of the muon in the Standard Model
• Two-pion contribution to hadronic vacuum polarization
• Three-pion contribution to hadronic vacuum polarization
• Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data
• Predictions for g-2 of the muon and alpha_QED(M_Z^2)
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions