Pion generalized dipole polarizabilities by virtual Compton scattering<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>e</mml:mi><mml:mo>→</mml:mo><mml:mi>π</mml:mi><mml:mi>e</mml:mi><mml:mi>γ</mml:mi></mml:math>

Unkmeir, C.; Ocherashvili, A.; Fuchs, T.; Moinester, M. A.; Scherer, Stefan

doi:10.1103/physrevc.65.015206

Cited by 15 publications

(16 citation statements)

References 38 publications

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“…Using our model calculation of the DVCS amplitude in which the final photon is emitted by the pion, one can calculate the differential cross section of the virtual Compton scattering of the pion, i.e. πe → πeγ, by incorporating the Bethe-Heitler(BH) process [34,35] in which the final photon is emitted by either the incoming electron or the outgoing electron. Considerations along this line are in progress.…”

Section: Discussionmentioning

confidence: 99%

Continuity of generalized parton distributions for the pion virtual Compton scattering

Choi

Kisslinger

2002

Phys. Rev. D

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We discuss a consistent treatment of the light-front gauge-boson and meson wave functions in the analyses of the generalized parton distributions(GPDs) and the scattering amplitudes in deeply virtual Compton scattering(DVCS) for the pion. The continuity of the GPDs at the crossover, where the longitudinal momentum fraction of the probed quark is same with the skewedness parameter, and the finiteness of the DVCS amplitude are ensured if the same light-front radial wave function as that of the meson bound state wave function is used for the gauge boson bound state arising from the pair-creation(or nonvalence) diagram. The frame-independence of our model calculation is also guaranteed by the constraint from the sum rule between the GPDs and the form factors.

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Section: Discussionmentioning

confidence: 99%

Continuity of generalized parton distributions for the pion virtual Compton scattering

Choi

Kisslinger

2002

Phys. Rev. D

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“…M A (γ + π + → γ + π + ) stands for the Compton scattering of the virtue incoming pion. If the incoming photon is also virtual, then this sub-diagram also carry the information of so-called generalized polarizability as studied in [16,17]. M B (π → π) represents the renormalization of the pion mass.…”

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confidence: 99%

“…When t is small the pion-pole diagrams is supposed to be dominant. Therefore, in [7] only the diagrams with a pole at t = m 2 π , such as diagrams from (4-1) to (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16), are considered,…”

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confidence: 99%

Radiative charged pion photoproduction and pion polarizabilities: An analysis within heavy baryon chiral perturbation theory

2007

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We analyze the amplitude of radiative charged pion photoproduction in the framework of heavy baron chiral perturbation theory and discuss the best kinematic conditions for the extraction of pion polarizabilities from the total cross section.Electric (α) and magnetic (β) polarizabilities characterize the global deformation response of a composite system in static uniform external electric and magnetic fields. They provide precious information about the underlying dynamics of the composite system. As a result, a precise measurement of the pion polarizabilities is of great importance to understand the inner structure of the pion. Chiral symmetry allows one to predict the electromagnetic polarizabilities of charged pion in terms of the radiative decay π + → e + ν e γ [1] ,where l r 6 − l r 5 is a linear combination of scale-independent parameters of the Gasser and Leutwyler Lagrangian [2].is the axial vector coupling constant. The next-to-leading-order result has been calculated at O(p 6 ) in Chiral Perturbation Theory(ChPT), and the correction to (1) is small: [4,5]:Therefore the measurement of pion polarizabilities becomes an excellent test of chiral dynamics. Compton scattering of real photons(RCS) is one of the simplest reactions to determine the polarizabilities. When expanded in the energy of final photon, the leading order term of the low-energy scattering amplitudes is specified by the Thomson limit in terms of the charge and the mass of the target. Genuine structure effects first appear at second order parametrized as polarizabilities.where ǫ 1 ( ǫ 2 ), ω(ω ′ ) and k( k ′ ) are the polarization vector, energy and momentum of the initial (final) photon, respectively. T B is the Born amplitude. Because pion targets are unavailable, RCS of pions was done by using indirect ways, such as high-energy pion-nucleus bremsstrahlung π − Z → π − Zγ [6] or radiative pion photoproduction off the proton γp → γπ + n [7] and the cross channel two-photon reaction γγ → ππ [8,9]. Recently the new radiative charged pion photoproduction experiment at Mainz Microtron MAMI [10] reported their result which is far away from the prediction of ChPT,In this letter, we investigate the relation between the charged pion polarizabilities and the radiative charged pion photoproduction in the framework of heavy baryon chiral perturbation theory(HBChPT). (see [11] for a review of HBChPT.) So far, the extractions of charged pion polarizabilities α π ± and β π ± from radiative charged pion photoproduction have relied on two different ways. The method of extrapolation [12,13] is similar to the one suggested by Chew and Low [14] in the late fifties. This method has been successfully employed to determine the pion-nucleon coupling constant through γp → π + p. It is also used in the determination of ππ → ππ scattering from πN → ππN reaction. However, in order to do extrapolation, one has to obtain the experimental data with small error over a sufficiently wide region of t, particularly when very close to t=0. The authors of [10] also point out tha...

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“…In terms of the Mandelstam variables defined for the Compton process, Eqs. (113), this corresponds to s = u = M 2 π and t = 0. By crossing symmetry, the γ(q) + π(p i ) → γ(q ) + π(p f ) amplitudes also describe the γ(q 1 ) + γ(q 2 ) → π(p 1 ) + π(p 2 ) process.…”

Section: Present and Future Experimentsmentioning

confidence: 99%

Compton scattering off pions and electromagnetic polarizabilities

Moinester

Scherer

2019

Int. J. Mod. Phys. A

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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...

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Pion generalized dipole polarizabilities by virtual Compton scatteringπe→πeγ

Cited by 15 publications

References 38 publications

Continuity of generalized parton distributions for the pion virtual Compton scattering

Continuity of generalized parton distributions for the pion virtual Compton scattering

Radiative charged pion photoproduction and pion polarizabilities: An analysis within heavy baryon chiral perturbation theory

Compton scattering off pions and electromagnetic polarizabilities

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