Momentum-dependence of $\rho -\omega$ mixing in the pion vector form factor and its effect on $(g-2{)}_{\mu }$

Abstract

The inclusion of the $\rho -\omega$ mixing effect is essential for a precise description of the pion electromagnetic form factor in the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ process, which quantifies the two-pion contribution to the anomalous magnetic moment of the muon $a_{\mu }$. In this paper, we analyse the momentum dependence of the $\rho -\omega$ mixing by considering loop contributions at the next-to-leading order in the $1/N_C$ expansion within the framework of resonance chiral theory. We revisit the work [Y. H. Chen, D. L. Yao, and H. Q. Zheng, Commun. Theor. Phys. 69 (2018) 1], considering the contribution arising from the kaon mass splitting in the kaon loops and the latest experimental data. We perform two kinds of fits (with momentum-independent or momentum-dependent $\rho -\omega$ mixing amplitude) to describe the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ and $\tau \to {\nu }_{\tau }2\pi$ data within the energy region of 600$\sim$900 MeV and the decay width of $\omega \to {\pi }^{+}{\pi }^{-}$, and compare their results. Our findings indicate that both the momentum-independent and momentum-dependent $\rho -\omega$ mixing schemes provide appropriate descriptions of the data. However, the momentum-dependent scheme exhibits greater self-consistency, considering the reasonable imaginary part of the mixing matrix element ${\Pi }_{\rho \omega }$ obtained. Regarding the contribution to the anomalous magnetic moment of the muon, $a_{\mu }^{\pi \pi }{|}_{[0.6,0.9]\text{GeV}}$, the results obtained from the fits considering the momentum-dependent $\rho -\omega$ mixing amplitude agree well with those obtained without incorporating the momentum dependence of the $\rho -\omega$ mixing, within the margin of errors. Furthermore, based on the fitted values of the relevant parameters, we observe that the decay width of $\omega \to {\pi }^{+}{\pi }^{-}$ is predominantly influenced by the $\rho -\omega$ mixing effect.

24 pages, 4 figures

References in corpus (19)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• The anomalous magnetic moment of the muon in the Standard Model
• Towards a consistent estimate of the chiral low-energy constants
• Constraints on the two-pion contribution to hadronic vacuum polarization
• Lepton flavour violating semileptonic tau decays in constrained MSSM-seesaw scenarios
• Spectral distribution for the decay tau -> nu_tau K pi
• The Dipion Mass Spectrum In e+e- Annihilation and tau Decay: A Dynamical (rho0, omega, phi) Mixing Approach
• Long-distance radiative corrections to the di-pion tau lepton decay
• 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
• Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ process cross section with the SND detector at the VEPP-2000 collider in the energy region $0.525<\sqrt{s}<0.883$ GeV
• Precise determination of the low-energy hadronic contribution to the muon $g-2$ from analyticity and unitarity: An improved analysis
• 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
• Radiative corrections to $\tau \to \pi (K){\nu }_{\tau }[\gamma ]$: a reliable new physics test
• Unified study of $J/\psi \to PV$, $P{\gamma }^{(\ast )}$ and light hadron radiative processes
• Two and Three Pseudoscalar Production in $e^{+}{e}^{-}$ annihilation and their contributions to $(g-2{)}_{\mu }$
• A study of $\rho -\omega$ mixing in resonance chiral theory
• Weak magnetic field corrections to light vector or axial mesons mixings and vector meson dominance
• Study of pion vector form factor and its contribution to the muon $(g-2)$