Radiative corrections to the forward-backward asymmetry in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$

Abstract

We present a calculation of the $C$-odd radiative corrections to $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ in a dispersive formalism, concentrating on the leading pion-pole contribution in the virtual box diagrams. In particular, we show how the effect of a general pion vector form factor in the loop integral can be incorporated in a model-independent way and how the cancellation of infrared singularities proceeds in this case. The numerical results, dominated by the infrared enhanced contributions, indicate significant corrections beyond scalar QED, essentially confirming recent findings in generalized vector-meson-dominance models.

arXiv comment16 pages, 3 figures; numerical results for the corrections included as supplemental material; corrected treatment of endpoint singularity, including mixed term in real part

References in corpus (49)

• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• Complete Tenth-Order QED Contribution to the Muon g-2
• Refinements in electroweak contributions to the muon anomalous magnetic moment
• Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon g-2 and alpha(mZ) using newest hadronic cross-section data
• Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
• Two-pion contribution to hadronic vacuum polarization
• The electroweak contributions to (g-2)_μ after the Higgs boson mass measurement
• Remarks on higher-order hadronic corrections to the muon g-2
• Dispersion relation for hadronic light-by-light scattering: two-pion contributions
• The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• Three-pion contribution to hadronic vacuum polarization
• Dispersion relation for hadronic light-by-light scattering: pion pole
• Pseudoscalar-pole contribution to the $(g_{\mu }-2)$: a rational approach
• Short-distance constraints for the HLbL contribution to the muon anomalous magnetic moment
• Lattice calculation of the pion transition form factor with $N_f=2+1$ Wilson quarks
• Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
• Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data
• Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2{)}_{\mu }$ with large-$N_c$ Regge models
• Dispersion relation for hadronic light-by-light scattering: theoretical foundations
• Hadronic vacuum polarization: $(g-2{)}_{\mu }$ versus global electroweak fits
• The muon $g$-2 and $\Delta \alpha$ connection
• Update of the e^+e^-\toπ^+π^- cross section measured by SND detector in the energy region 400<\sqrt{s}<1000 MeV
• Measuring sigma(e^+e^- \to hadrons) using tagged photon
• Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Constraints on the two-pion contribution to hadronic vacuum polarization
• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• omega --> pi0 gamma* and phi --> pi0 gamma* Transition form factors in dispersion theory
• Roy-Steiner equations for gamma gamma -> pi pi
• Data-driven evaluations of Euclidean windows to scrutinize hadronic vacuum polarization
• MO analysis of the high statistics Belle results on $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ with chiral constraints
• Unified dispersive approach to real and virtual photon-photon scattering at low energy
• Study of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ in the energy region 400<\sqrt[]{s}<1000 MeV
• The radiative return at phi- and B-factories: FSR for muon pair production at next-to-leading order
• Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Pion Pair Production with Higher Order Radiative Corrections in Low Energy e+e- Collisions
• Impact of correlations between $a_{\mu }$ and ${\alpha }_{QED}$ on the EW fit
• Kaon electromagnetic form factors in dispersion theory
• Dispersive analysis of the $\gamma {\gamma }^{\ast }\to \pi \pi$ process
• Standard Model radiative corrections in the pion form factor measurements do not explain the $a_{\mu }$ anomaly
• Hadronic vacuum polarization and vector-meson resonance parameters from $e^{+}{e}^{-}\to {\pi }^0\gamma$
• Dispersion relations for ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \pi$: helicity amplitudes, subtractions, and anomalous thresholds
• Charge asymmetry and radiative phi decays
• Measuring the FSR--inclusive pi+pi- cross section
• The cross sections of the muons and charged pions pairs production at electron-positron annihilation near the threshold
• Precision Measurement of the Hadronic Contribution to the Muon Anomalous Magnetic Moment
• Charge asymmetry in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ process

Cited by in corpus (21)

• The anomalous magnetic moment of the muon in the Standard Model: an update
• Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross section from threshold to 1.2 GeV with the CMD-3 detector
• Measurement of the pion form factor with CMD-3 detector and its implication to the hadronic contribution to muon (g-2)
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• Tensions in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ measurements: the new landscape of data-driven hadronic vacuum polarization predictions for the muon $g-2$
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• An optimized basis for hadronic light-by-light scattering
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• Width effects of broad new resonances in loop observables and application to $(g-2{)}_{\mu }$
• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Improved evaluation of the electroweak contribution to muon $g-2$
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• Pion pair production in $e^{+}{e}^{-}$ annihilation at next-to-leading order matched to Parton Shower
• Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II
• Disperon QED
• Radiative return at NLOPS accuracy
• Towards a Fully Automated Differential ${\text{NNLO}}_{\text{EW}}$ Generator for Lepton Colliders
• Structure-dependent radiative corrections to $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma$ in the GVMD approach