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 pola...

Compton scattering off pions and electromagnetic polarizabilities

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.

Compton Scattering off Pions and Electromagnetic Polarizabilities

We report measurements of double radiative capture in pionic hydrogen and pionic deuterium. The measurements were performed with the RMC spectrometer at the TRIUMF cyclotron by recording photon pairs from pion stops in liquid hydrogen and deuterium targets. We obtained absolute branching ratios of [3.02{+-}0.27(stat.){+-}0.31(syst.)]x10{sup -5} for hydrogen and [1.42{+-}{sub 0.12}{sup 0.09}(stat.){+-}0.11(syst.)]x10{sup -5} for deuterium and relative branching ratios of double radiative capture to single radiative capture of [7.68{+-}0.69(stat.){+-}0.79(syst.)]x10{sup -5} for hydrogen and [5.44{+-}{sub 0.46}{sup 0.34}(stat.){+-}0.42(syst.)]x10{sup -5} for deuterium. For hydrogen, the measured branching ratio and photon energy-angle distributions are in fair agreement with a reaction mechanism involving the annihilation of the incident {pi}{sup -} on the {pi}{sup +} cloud of the target proton. For deuterium, the measured branching ratio and energy-angle distributions are qualitatively consistent with simple arguments for the expected role of the spectator neutron. A comparison between our hydrogen and deuterium data and earlier beryllium and carbon data reveals substantial changes in the relative branching ratios and the energy-angle distributions and is in agreement with the expected evolution of the reaction dynamics from an annihilation process in S-state capture to a bremsstrahlung process in P-state capture. Lastly, we comment on the relevance of the double radiative processmore » to the investigation of the charged pion polarizability and the in-medium pion field.« less

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Double radiative pion capture on hydrogen and deuterium and the nucleon's pion cloud

Effective field theories of the strong interactions based on the approximate chiral symmetry of QCD provide a model-independent approach to low-energy hadron physics. We give a brief introduction to mesonic and baryonic chiral perturbation theory and discuss a number of applications. We also consider the effective field theory including vector and axial-vector mesons.

Chiral effective field theories of the strong interactions

The electric α π and magnetic β π charged pion Compton polarizabilities are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). They are directly linked to the phenomenon of spontaneously broken chiral symmetry within QCD and to the chiral QCD lagrangian. They characterize the induced dipole moments of the pion during γπ Compton scattering. Pion polarizabilities affect the shape of the γπ Compton scattering angular distribution. The combination (α π -β π ) was measured by: (1) CERN COMPASS via π - Z → π - Zγ radiative pion Primakoff scattering (Bremsstrahlung) in the nuclear Coulomb field, (2) SLAC PEP Mark-II via two-photon production of pion pairs, γγ→π + π − , and (3) Mainz Microtron MAMI via radiative pion photoproduction from the proton, γp→ γπ + n . Ongoing and planned pion polarizability experiments (COMPASS at CERN, BESIII at Beijing, JLab at Newport News) are also described. The Mark-II pion polarizability 95% confidence interval is approximately 0-11 ×10 −4 fm 3 , based on α π −β π = (4.4±3.2 stat+syst )×10 −4 fm 3 . Mainz’s α π −β π = (11.6 ± 1.5 stat ± 3.0 syst ± 0.5 model ) ×10 −4 fm 3 is excluded on the basis of a dispersion relations calculation which uses the Mainz value as input, and gives significantly too large γγ→π 0 π 0 sections compared to DESY Crystal Ball data. To date, only the COMPASS polarizability measurement has acceptably small uncertainties. Its value 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 , thereby strengthening the identification of the pion with the Goldstone boson of QCD.

Pion Polarizability 2022 Status Report

We analyze the amplitude of radiative charged pion photoproduction within the framework of heavy baryon chiral perturbation theory (HBChPT) and discuss the best experimental setup for the extraction of the charged pion polarizabilities from the differential cross section. We find that the contributions from two unknown low energy constants(LECs) in the $\pi N$ chiral Lagrangian at order $p^{3}$ are comparable with the contributions of the charged pion polarizabilities. As a result, it is necessary to take these two LECs' effects into account. Furthermore, we discuss the applicability of the extrapolation method and conclude that this method is applicable only if the polarization vector of the incoming photon is perpendicular to the scattering plane in the center of mass frame of the final $\gamma-\pi$ system.

Extraction of the charged pion polarizabilities from radiative charged pion photoproduction in Heavy Baryon Chiral Perturbation Theory

/pdf/author-correction-measurement-of-the-generalized-spin-gpjx1rh0.pdf

Author Correction: Measurement of the generalized spin polarizabilities of the neutron in the low-Q2 region

order p 3 are comparable with the contributions of the charged pion polarizabilities. As a result, it is necessary to take these two LECs’ effects into account. Furthermore, we discuss the applicability of the extrapolation method and conclude that this method is applicable only if the polarization vector of the incoming photon is perpendicular to the scattering plane in the center of mass frame of the final γ π system. Electric (α) and magnetic (β) polarizabilities characterize the global responses of a composite system to external electric and magnetic fields. They provide precious information about the inner structure of the composite system. Since the pion is the simplest composite system bound by the strong interaction, its polarizabilities are fundamental benchmark of QCD in the realm of confinement, and an accurate determination of the charged pion polarizabilities is highly desirable. The charged pion polarizabilities have been calculated by chiral perturbation theory(ChPT). The

Extraction of the charged pion polarizabilities from radiative charged pion photoproduction in heavy baryon chiral perturbation theory

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Extraction of the charged pion polarizabilities from radiative charged pion photoproduction in Heavy Baryon Chiral Perturbation Theory

Author Correction: Measurement of the generalized spin polarizabilities of the neutron in the low-Q2 region

Extraction of the charged pion polarizabilities from radiative charged pion photoproduction in heavy baryon chiral perturbation theory