Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2001-05-14
Phys.Rev. D65 (2002) 056004
Physics
High Energy Physics
High Energy Physics - Phenomenology
26 pages, 10 figures
Scientific paper
10.1103/PhysRevD.65.056004
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.
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