Structure analysis of the virtual Compton scattering amplitude at low energies

Abstract

We analyze virtual Compton scattering off the nucleon at low energies in a covariant, model-independent formalism. We define a set of invariant functions which, once the irregular nucleon pole terms have been subtracted in a gauge-invariant fashion, is free of poles and kinematical zeros. The covariant treatment naturally allows one to implement the constraints due to Lorentz and gauge invariance, crossing symmetry, and the discrete symmetries. In particular, when applied to the ep → e ′ p ′ γ reaction, charge-conjugation symmetry in combination with nucleon crossing generates four relations among the ten originally proposed generalized polarizabilities of the nucleon. 13.60.Fz,14.20.Dh Typeset using REVT E X * This work was supported by the Deutsche Forschungsgemeinschaft (SFB 201)

Virtual Compton scattering off the nucleon

“…[Gui95] by the introduction of mixed multipoles which were neither electric nor longitudinal. However the findings of a recent work [Dre98] allow for a much more elegant solution.…”

“…In Ref. [Dre98] it has been shown that P (11,00)1 is not independent and can be eliminated according to …”

Chiral dynamics of rare η decays and virtual Compton scattering off the nucleon

“…That this is not a model-dependent statement could be shown in [14], where the reduction from three to two polarizabilities was traced back to a combination of invariance with respect to charge conjugation and nucleon crossing. A similar reduction from seven to four terms occurs for the spin-dependent polarizabilities.…”

Virtual Compton Scattering—Generalized Polarizabilities of Nucleons and Pions

“…The corresponding ten GPs, P (01,01)0 , ...,P (11,2)1 , are functions of |q| 2 , where mixed-type polarizabilities,P (ρ L ,L)S (|q| 2 ), have been introduced which are neither purely electric nor purely Coulomb type (see [8] for details). Only six of the above ten GPs are independent, if chargeconjugation symmetry is imposed [11,12]. For example, for a charged pion, the constraint for the Compton tensor reads [10,11] M µν π…”

“…Relations between the GPs at |q| = 0 and the four spin-dependent RCS polarizabilities γ i of Ref. [20] were discussed in [12]:…”