Sizing the double pole resonant enhancement in $e^{+}{e}^{-}\to {\pi }^0{\pi }^0\gamma$ cross section and ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }\gamma$ decay

Abstract

The enhancement mechanism due to the resonant properties of the $\rho$ and $\omega$ mesons, which are close in mass, are analysed when such resonances carry different momenta. Considerations from the particular process where they appear to the individual resonant features are at play for the appearance of the global resonant manifestation. In this work, we first consider the $e^{+}{e}^{-}\to {\pi }^0{\pi }^0\gamma$ process. We use the differential cross section at a given angle of emission of one of the pions, to tune the individual features of the two resonances and exhibit how both resonances combine to produce the enhancement. Then, we incorporate the ${\rho }^{\prime }$ using the information obtained from the $e^{+}{e}^{-}\to {\pi }^0{\pi }^0\gamma$ total scattering process and show that, it becomes important thanks to the same enhancement mechanism between the $\rho$ and the $\omega$. In a second step, we use a similar approach to describe a model dependent contribution to the ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }\gamma$ decay, the so-called $\omega$ channel. We show that the dipion invariant mass distribution at particular angles is sensitive to the individual resonant states. We compute the interference of this channel with the known dominant model independent contribution, and show how a better knowledge of the $e^{+}{e}^{-}\to {\pi }^0{\pi }^0\gamma$ process can help to properly account for such model dependent effects. The implication on the isospin symmetry breaking correction to tau-based estimates of the muon magnetic dipole moment is assessed.

arXiv comment23 pages, 11 figures. Text revisited and discussion extended. Format for figures and tables adjusted. Accepted and published in PRD

References in corpus (30)

• The anomalous magnetic moment of the muon in the Standard Model
• Reevaluation of the Hadronic Contributions to the Muon g-2 and to alpha(MZ)
• The Belle II Physics Book
• A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to $\mathbf{\alpha }({\mathbf{m}}_{\mathbf{Z}}^2)$
• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm
• High-Statistics Study of the tau^- -> pi^- pi^0 nu_tau Decay
• Radiative Semileptonic Kaon Decays
• The Discrepancy Between tau and e+e- Spectral Functions Revisited and the Consequences for the Muon Magnetic Anomaly
• An Update of the HLS Estimate of the Muon g-2
• Isospin Violation and the Magnetic Moment of the Muon
• Radiative tau decay and the magnetic moment of the muon
• Unified dispersive approach to real and virtual photon-photon scattering at low energy
• Upgraded Breaking Of The HLS Model: A Full Solution to the tau-e+e- and phi Decay Issues And Its Consequences On g-2 VMD Estimates
• The process $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ up to 1.4 GeV
• Long-distance radiative corrections to the di-pion tau lepton decay
• Study of the Process e+ e- --> omega pi0 --> pi0 pi0 gamma in c.m. Energy Range 920--1380 MeV at CMD-2
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• New $\tau$-based evaluation of the hadronic contribution to the vacuum polarization piece of the muon anomalous magnetic moment
• Updated measurement of the $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ cross section with the SND detector
• Study of e+e- --> omega pi0 --> pi0 pi0 gamma in the energy range 1.05--2.00 GeV with SND
• Consequences of the BaBar e^+e^- --> pi^+pi^- Measurement for the Determination of Model-Dependent rho-omega Mixing Effects in Pi_{ρω}(m_ρ^2) and (g-2)_mu
• Models of Isospin Breaking in the Pion Form Factor: Consequences for the Determination of Pi_{ρω}(m_rho^2) and (g-2)_mu/2
• Radiative two-pion decay of the tau lepton
• Model-dependent radiative corrections to tau- -> pi- pi0 nu revisited
• BHLS${}_2$ Upgrade : $\tau$ spectra, muon HVP and the [${\pi }^0,\eta ,{\eta }^{\prime }$] System
• Vector-meson magnetic dipole moment effects in radiative tau decays
• The omega rho pi coupling in the VMD model revisited
• Triple-product asymmetry in the radiative two-pion tau decay
• Role of the $\rho (1450)$ in low-energy observables from an analysis in the meson dominance approach
• Contribution of exclusive $({\pi }^0{\pi }^0,{\pi }^0\eta ,\eta \eta )\gamma$ channels to the leading order HVP of the muon $g-2$

Cited by in corpus (2)

• Isospin breaking corrections in $2\pi$ production in tau decays and $e^{+}{e}^{-}$ annihilation: consequences for the muon $g-2$ and CVC tests
• Tau Data-Based Evaluations of the hadronic vacuum polarization contribution to the muon $g-2$