Compton Scattering off Pions and Electromagnetic Polarizabilities

Abstract

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.

64 pages, 13 figures, preprint of a review article submitted for consideration in International Journal of Modern Physics A \c{opyright} [2019] [copyright World Scientific Publishing Company] [https://www.worldscientific.com/worldscinet/ijmpa]

References in corpus (13)

• The COMPASS Experiment at CERN
• Mesonic low-energy constants
• 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
• High-statistics measurement of neutral-pion pair production in two-photon collisions
• High-statistics measurement of neutral-pion pair production in two-photon collisions
• New Precise Measurement of the Pion Weak Form Factors in the Pi+ -> e+ nu gamma Decay
• High-statistics study of neutral-pion pair production in two-photon collisions
• Measurement of the charged-pion polarisability
• Cross sections for low-energy ${\pi }^{-}\gamma$ reactions
• The polarizability of the pion: no conflict between dispersion theory and chiral perturbation theory
• Radiative corrections to pion-nucleus bremsstrahlung
• Dipole polarizabilities of charged pions