Dispersive analysis of the $\gamma {\gamma }^{\ast }\to \pi \pi$ process

Abstract

We present a theoretical study of the $\gamma {\gamma }^{\ast }\to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ processes from the threshold through the $f_2(1270)$ region in the $\pi \pi$ invariant mass. We adopt the Omnès representation in order to account for rescattering effects in both s- and d-partial waves. For the description of the $f_0(980)$ resonance, we implement a coupled-channel unitarity. The constructed amplitudes serve as an essential framework to interpret the current experimental two-photon fusion program at BESIII. They also provide an important input for the dispersive analyses of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment.

8 pages, 4 figures (journal version)

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• The anomalous magnetic moment of the muon in the Standard Model: an update
• Precision tests of fundamental physics with $\eta$ and ${\eta }^{\prime }$ mesons
• Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Kaon electromagnetic form factors in dispersion theory
• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• A dispersive estimate of scalar contributions to hadronic light-by-light scattering
• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• Hadronic vacuum polarization and vector-meson resonance parameters from $e^{+}{e}^{-}\to {\pi }^0\gamma$
• Asymptotic behavior of meson transition form factors
• Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update
• Coupled-channel approach in hadron-hadron scattering
• Dispersion relations for ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \pi$: helicity amplitudes, subtractions, and anomalous thresholds
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• The hadronic light-by-light contribution to the muon's anomalous magnetic moment
• Radiative corrections to the forward-backward asymmetry in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$
• Determination of the lightest strange resonance $K_0^{\ast }(700)$ or $\kappa$, from a dispersive data analysis
• An optimized basis for hadronic light-by-light scattering
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• Dispersive analysis of the $\gamma \gamma \to D\bar{D}$ data and the confirmation of the $D\bar{D}$ bound state
• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Dispersive analysis of the Primakoff reaction $\gamma K\to K\pi$
• Virtual Compton Scattering and Nucleon Generalized Polarizabilities
• Compton Scattering off Pions and Electromagnetic Polarizabilities
• The role of charged exotic states in $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$
• Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$
• Simultaneous description of the $e^{+}{e}^{-}\to J/\psi \pi \pi (K\bar{K})$ processes
• Two-current transition amplitudes with two-body final states
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• Scalar mesons in the chiral theory with quark degrees of freedom
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Analytical dispersive parameterization for elastic scattering of spinless particles
• Dispersive analysis of low energy ${\gamma }^{\ast }N\to \pi N$ process
• Prospects for ${\gamma }^{\star }{\gamma }^{\star }\to \pi \pi$ via lattice QCD
• Cross sections for 2-to-1 meson-meson scattering
• A study on the correlation between poles and cuts in $\pi \pi$ scattering
• Inelastic Meson-Meson Scattering in Hadronic Matter
• Phenomenological model for the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}{\pi }^0$ reaction
• Gravitational form factors in the perturbative limit
• Cross sections for 2-to-3 meson-meson scattering
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$