Compton Scattering off Pions and Electromagnetic Polarizabilities

• Published in: arXiv.org
• Main Authors: Murray Moinester, Scherer, Stefan
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 14.05.2019
• Subjects: Angular distribution; Broken symmetry; CERN; Chiral dynamics; Cross-sections; Elastic scattering; Pair production; Perturbation theory; Photoproduction; Physics - High Energy Physics - Experiment; Physics - High Energy Physics - Phenomenology; Physics - Nuclear Experiment; Physics - Nuclear Theory; Pions; Quantum chromodynamics; Quarks; Scattering angle; Sum rules; Uncertainty
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1905.05640

The electric (\(\alpha_\pi\)) and magnetic (\(\beta_\pi\)) Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the \(\gamma\pi\to\gamma\pi\) Compton scattering angular distribution at back scattering angles and \(\gamma\gamma\to\pi\pi\) absolute cross sections. Theory derivations are given of the \(\gamma\pi\to\gamma\pi\) Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical predictions. The \(\pi^0\) polarizabilities were deduced from DESY Crystal Ball \(\gamma\gamma\to\pi^0\pi^0\) data, but with large uncertainties. The charged pion polarizabilities were deduced most recently from (1) radiative pion Primakoff scattering \(\pi^- Z \to \pi^-Z\gamma\) at CERN COMPASS, (2) two-photon pion pair production \(\gamma\gamma\to\pi^+\pi^-\) at SLAC Mark II, and (3) radiative pion photoproduction \(\gamma p\to\gamma \pi^+ n\) from the proton at MAMI in Mainz. A stringent test of chiral perturbation theory (ChPT) is possible based on comparisons of precision experimental charged pion polarizabilities with ChPT predictions. Only the CERN COMPASS charged pion polarizability measurement has acceptably small uncertainties. Its value \(\alpha_{\pi^\pm}-\beta_{\pi^\pm} = (4.0\pm 1.8)\times 10^{-4}\,\text{fm}^3\) agrees well with the two-loop ChPT prediction \(\alpha_{\pi^\pm}-\beta_{\pi^\pm}=(5.7\pm 1.0)\times 10^{-4}\,\text{fm}^3\), strengthening the identification of the pion with the Goldstone boson of chiral symmetry breaking in QCD.