Generalized polarizabilities of the pion in chiral perturbation theory

Unkmeir, C.; Scherer, Stefan; L’vov, A. I.; Drechsel, D.

doi:10.1103/physrevd.61.034002

Cited by 22 publications

(41 citation statements)

References 38 publications

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“…In this context, the VCS amplitude is divided into generalized Born terms M Born , containing ground-state properties in terms of the electromagnetic form factor, and a residual non-Born contribution M NB , describing model-dependent internal structure (see Refs. [16,17,28]). In particular, the separation is performed such that both pieces are separately gauge invariant and the generalized Born terms contain all soft-photon singularities.…”

Section: Calculation Of the Squared Invariant Amplitudementioning

confidence: 99%

“…In Sec. II, we briefly discuss the predictions for the generalized dipole polarizabilities as obtained in the framework of ChPT at O(p 4 ) [16]. We provide a physical interpretation of the longitudinal generalized electric dipole polarizability in terms of the induced polarization charge [17].…”

Section: Introductionmentioning

confidence: 99%

“…For the numerical analysis of the above reaction, we make use of the results obtained in the framework of chiral perturbation theory at O(p 4 ) [16]. At this order in the momentum expansion, the generalized dipole polarizabilities display a degeneracy, β(q 2 ) = −α L (q 2 ) = −α T (q 2 ) which will be lifted at O(p 6 ) and O(p 8 ), respectively.…”

Section: Introductionmentioning

confidence: 99%

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Pion generalized dipole polarizabilities by virtual Compton scatteringπe→πeγ

et al. 2001

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We present a calculation of the cross section and the event generator of the reaction πe → πeγ. This reaction is sensitive to the pion generalized dipole polarizabilities, namely, the longitudinal electric α L (q 2 ), the transverse electric α T (q 2 ), and the magnetic β(q 2 ) which, in the real-photon limit, reduce to the ordinary electric and magnetic polarizabilitiesᾱ andβ, respectively. The calculation of the cross section is done in the framework of chiral perturbation theory at O(p 4 ). A pion VCS event generator has been written which is ready for implementation in GEANT simulation codes or for independent use. 13.60.Fz,14.40.Aq

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Section: Calculation Of the Squared Invariant Amplitudementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pion generalized dipole polarizabilities by virtual Compton scatteringπe→πeγ

et al. 2001

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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%

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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“…Generalized polarizability α of the charged pion as function of |q| 2 [23]. Note that α(|q| 2 ) = −β(|q| 2 ) at O(p 4 ).…”

Section: Generalized Polarizabilities Of Pionsmentioning

confidence: 99%