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.

arXiv comment64 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 (48)

• The COMPASS Experiment at CERN
• Dispersion relation for hadronic light-by-light scattering: two-pion contributions
• The Mesonic Chiral Lagrangian of Order $p^6$
• Elastic $\pi \pi$ scattering to two loops
• Dispersion relations in real and virtual Compton scattering
• Mesonic low-energy constants
• Low-Energy Photon-Photon Collisions to Two-Loop Order
• The quark condensate from K_{e_4} decays
• Roy-Steiner equations for gamma gamma -> pi pi
• Low-Energy Compton Scattering of Polarized Photons on Polarized Nucleons
• Charged Pion-Pair Production and Pion Polarizabilities to two Loops
• 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
• Photon-Photon Scattering, Pion Polarizability and Chiral Symmetry
• High-statistics measurement of neutral-pion pair production in two-photon collisions
• Unified dispersive approach to real and virtual photon-photon scattering at low energy
• High-statistics measurement of neutral-pion pair production in two-photon collisions
• Measurement of the pi^+ meson polarizabilities via the gamma p->gamma pi^+ n reaction
• New Precise Measurement of the Pion Weak Form Factors in the Pi+ -> e+ nu gamma Decay
• Dispersive analysis of the $\gamma {\gamma }^{\ast }\to \pi \pi$ process
• Low-energy photon-photon collisions to two loops revisited
• Charged Pion Polarizabilities to two Loops
• 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
• Generalized dipole polarizabilities and the spatial structure of hadrons
• Hadron Polarizabilities
• Determination of ${\pi }^{+}-$ meson polarizabilities from the $\gamma \gamma ->{\pi }^{+}{\pi }^{-}$ process
• Compton Scattering by a Pion and off--Shell Effects
• Compton Scattering on the Charged Pion and the Process γγ\to π^0 π^0
• Dispersion Theory in Electromagnetic Interactions
• ${\pi }^{+}$ and ${\pi }^0$ Polarizabilities from {$\gamma \gamma \to \pi \pi$} Data on the Base of S-Matrix Approach
• Generalized polarizabilities of the proton in a constituent quark model revisited
• Virtual Compton scattering off spin-zero particles at low energies
• The polarizability of the pion: no conflict between dispersion theory and chiral perturbation theory
• The off-shell electromagnetic form factors of pions and kaons in chiral perturbation theory
• Determination of π^0 meson quadrupole polarizabilities from the process γγ-> π^0π^0
• Kaon Polarizabilities in Chiral Perturbation Theory
• Generalized polarizabilities of the pion in chiral perturbation theory
• Pion Polarizabilities from $\gamma \gamma \to \pi \pi$ Analysis
• Radiative corrections to pion-nucleus bremsstrahlung
• Pion Generalized Dipole Polarizabilities by Virtual Compton Scattering $\pi e\to \pi e\gamma$
• Real and Virtual Compton Scattering at Low Energies
• Reply to "Comment on `The polarizability of the pion: no conflict between dispersion theory and chiral perturbation theory'"
• Dipole polarizabilities of charged pions
• Comment on "Polarizability of the pion: No conflict between dispersion theory and chiral perturbation theory"
• First Measurement of pi e -> pi e gamma Pion Virtual Compton Scattering
• Radiative Corrections for Pion Polarizability Experiments

Cited by in corpus (8)

• Pion magnetic polarisability using the background field method
• Towards charged hadron polarizabilities from four-point functions in lattice QCD
• Charged pion electric polarizability from four-point functions in lattice QCD
• Charged pion electric polarizability from lattice QCD
• Polarizabilities from kaon Compton scattering
• Chiral extrapolation of the magnetic polarizability of the neutral pion
• Dipole polarizabilities of light pseudoscalar mesons within the Domain Model of QCD vacuum
• Tests of Three-Flavor Chiral Perturbation Theory