Compton scattering off pions and electromagnetic polarizabilities

Abstract

The electric (απ) and magnetic (βπ) 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 γπ → γπ Compton scattering angular distribution at back scattering angles and γγ → ππ absolute cross sections. Theory derivations are given of the γπ → γπ 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 π 0 polarizabilities were deduced from DESY Crystal Ball γγ → π 0 π 0 data, but with large uncertainties. The charged pion polarizabilities were deduced most recently from (1) radiative pion Primakoff scattering π − Z → π − Zγ at CERN COMPASS, (2) two-photon pion pair production γγ → π + π − at SLAC Mark II, and (3) radiative pion photoproduction γp → γπ + 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 α π ± − β π ± = (4.0 ± 1.8) × 10 −4 fm 3 agrees well with the two-loop ChPT prediction α π ± − β π ± = (5.7 ± 1.0) × 10 −4 fm 3 , strengthening the identification of the pion with the Goldstone boson of chiral symmetry breaking in QCD. May 15, 2019 0:36 WSPC/INSTRUCTION FILE review˙pion˙polarizabilities 2 M. Moinester and S. Scherer May 15, 2019 0:36 WSPC/INSTRUCTION FILE review˙pion˙polarizabilities Electromagnetic Polarizabilies of Pions 3 experiment via Primakoff scattering of high-energy γ's in the nuclear Coulomb field leading to two-photon fusion production of pion pairs, γγ → ππ [12]. The COM-PASS data are equivalent to γπ → γπ Compton scattering for laboratory γ's having momenta of order 1 GeV/c incident on a target pion at rest. In the reference frame of this target pion, the cross section is sensitive to α π ± − β π ± at backward angles of the scattered γ's. To date, only the COMPASS polarizability measurement has acceptably small uncertainties. Its value α π ± −β π ± = (4.0±1.8)×10 −4 fm 3 agrees well with the two-loop ChPT prediction α π ± − β π ± = (5.7 ± 1.0) × 10 −4 fm 3 , strengthening the identification of the pion with the Goldstone boson of QCD. Finally, in the appendix, we also give an outlook to the concept of generalized polarizabilities. Classical DescriptionCompton scattering at low energies provides a tool for extracting the electromagnetic polarizabilities of particles. These quantities provide information on the structure of composite particles beyond their static properties, such as mass, charge, and magnetic moment [2][3][4][5][6][7]. Before addressing the quantum-mechanical description of the scattering process, we will have a look at the scattering off free charged particles in the framework of classical electrodynamics [13]. Any con...

Pion electric polarizabilities from lattice QCD

“…(115) in Ref. [1]. For the Compton scattering processes, in case where the photons are on-shell, the Born term is equal to the scalar QED contribution.…”

“…Polarizabilities describe the leading energy shift for a neutral particle in a constant electric and magnetic field. In Minkowski space-time convention, we have [1]:…”

Towards charged hadron polarizabilities from four-point functions in lattice QCD

“…The form in Eq. ( 4) can be entirely motivated by general principles of Lorentz invariance, gauge invariance, current conservation, time-reversal symmetry, and crossing symmetry [3]. In fact, current conservation (k µ 1 T µν = k ν 2 T µν = 0) immediately leads to A being related to charge radius by A = r 2 /3.…”

“…Experimentally, polarizabilities are primarily studied by low-energy Compton scattering. On the theoretical side, a variety of methods have been employed to describe the physics involved, from phenomenological models [1,2], to chiral perturbation theory (ChPT) [3][4][5] or chiral effective field theory (EFT) [6,7], to lattice QCD. Reviews of the experimental status can be also found in Refs.…”

Pion Polarizability Review

“…This review focuses on concisely comparing the most recent pion polarizability experiments with ChPT. A more detailed review [17] is available, and a comprehensive pion polarizability review article is also in preparation [18]. The pion polarizability combination απ…”