Study of $\gamma \pi \to \pi \pi$ below 1 GeV using Integral Equation Approach

Abstract

The scattering of $\gamma \pi \to \pi \pi$ is studied using the axial anomaly, elastic unitarity, analyticity and crossing symmetry. Using the technique to derive the Roy's equation, an integral equation for the P-wave amplitude is obtained in terms of the strong P-wave pion pion phase shifts. Its solution is obtained numerically by an iteration procedure using the starting point as the solution of the integral equation of the Muskelshsvilli-Omnes type. It is, however, ambiguous and depends sensitively on the second derivative of the P-wave amplitude at $s=m_{\pi }^2$ which cannot directly be measured.

26 pages, 10 figures

References in corpus (2)

• Electromagnetic corrections to gamma pi(+) -> pi(0) pi(+)
• The anomalous process gamma pi -> pi pi to two loops

Cited by in corpus (15)

• Roy-Steiner-equation analysis of pion-nucleon scattering
• B_l4 decays and the extraction of |V_ub|
• Dispersive analysis of the pion transition form factor
• Extracting the chiral anomaly from gamma pi --> pi pi
• Model-independent approach to eta -> pi+ pi- gamma and eta' -> pi+ pi- gamma
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• The $\pi \gamma \to \pi \pi$ transition and the $\rho$ radiative decay width from lattice QCD
• Exclusive Measurement of the eta --> pi+ pi- gamma Decay
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Pion form factors
• A new determination of the $\gamma \pi \to \pi \pi$ anomalous amplitude via ${\pi }^{-}{e}^{-}\to {\pi }^{-}{e}^{-}{\pi }^0$ data
• Transition form-factor of $\gamma \to 3\pi$ in nonlocal quark model
• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• Account for axial vector mesons in the $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ decays
• Tests of Three-Flavor Chiral Perturbation Theory