Amplitude determination for $MM\to MM$, $M=\pi ,K$ and cross-sections for $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0,{\pi }^0\eta$ in a chiral model

Abstract

Dai and Pennington have performed a comprehensive analysis of essentially all pion and kaon pair production data from two-photon collisions below 1.5 GeV, including all high statistics results from Belle, as well as the older data from Mark II at SLAC, CELLO at DESY, and Crystal Ball at SLAC. Imposing the basic constraints required by analyticity, unitarity, and crossing symmetry and making use of Low's low-energy theorem for QED, they were able to extract the final-state, strong-interaction scattering amplitudes for the intermediate $\pi \pi \to \pi \pi$ and $\pi \pi \to K\overline{K}$ reactions in a model-independent fashion. In addition, they provided good fits to the respective $\gamma \gamma \to \pi \pi$ cross-sections that are known in the low-energy sector in the restricted angular range, $|\cos \theta |<0.6-0.8$. Using the parameters obtained in this fashion, these authors constructed the $\gamma \gamma \to \pi \pi$ cross-sections integrated over the full angular range. In the present work, we use a version of chiral perturbation theory developed by Oller and Oset to evaluate the final-state, strong-interaction amplitudes theoretically, and we compare our low-energy QCD-based results with the amplitudes extracted by Dai and Pennington. We also calculate the $\gamma \gamma \to \pi \pi$ cross-sections (integrated over the full angular range) and compare them with those obtained by Dai and Pennington. These calculations give a more detailed insight into the fit of chiral perturbation theory, not just to the measured $\gamma \gamma \to \pi \pi$ cross-sections, as is usually presented, but rather to a higher level of detail through the available analysis of the experimental data for the underlying final-state, strong-interaction, meson-meson scattering amplitudes $\pi \pi \to \pi \pi$ and $\pi \pi \to K\overline{K}$ themselves. The fits appear to be sensible.

25 pages, 10 figures

References in corpus (20)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Revisiting γγ->π^+π^- at low energies
• MO analysis of the high statistics Belle results on $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ with chiral constraints
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• Comprehensive Amplitude Analysis of $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ and $\overline{K}K$ below 1.5 GeV
• Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semilocal duality
• Coupled-channel approach in hadron-hadron scattering
• Amplitude Analysis of High Statistics Results on $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ and the Two Photon Width of Isoscalar States
• Improved dispersion relations for γγ\to π^0π^0
• f0(980) meson as a K bar K molecule in a phenomenological Lagrangian approach
• Two photons into π^0π^0
• Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons
• Theoretical analysis of the $\gamma \gamma \to {\pi }^0\eta$ process
• Analysis on the composite nature of the light scalar mesons $f_0(980)$ and $a_0(980)$
• Note on the definitions of branching ratios of overlapping resonances
• Decay of kaonium in a chiral approach
• KKbar molecules with momentum-dependent interactions
• Manifestation of kaonium in the $e^{+}{e}^{-}\to K^{+}{K}^{-}$ process
• The reactions $\pi \pi \to \pi \pi$ and $\gamma \gamma \to \pi \pi$ in $\chi$PT with an isosinglet scalar resonance
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$

Cited by in corpus (1)

• Emergence of kaonium as a sharp resonance in photon-photon to meson-meson cross-sections