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)

We present the achievements of the last years of the experimental and theoretical groups working on hadronic cross section measurements at the low-energy e + e − colliders in Beijing, Frascati, Ithaca, Novosibirsk, Stanford and Tsukuba and on τ decays. We sketch the prospects in these fields for the years to come. We emphasise the status and the precision of the Monte Carlo generators used to analyse the hadronic cross section measurements obtained as well with energy scans as with radiative return, to determine luminosities and τ decays. The radiative corrections fully or approximately implemented in the various codes and the contribution of the vacuum polarisation are discussed.

High precision measurements of the differential cross sections for π0 photoproduction at forward angles for two nuclei, 12C and 208Pb, have been performed for incident photon energies of 4.9-5.5 GeV to extract the π0→γγ decay width. The experiment was done at Jefferson Lab using the Hall B photon tagger and a high-resolution multichannel calorimeter. The π0→γγ decay width was extracted by fitting the measured cross sections using recently updated theoretical models for the process. The resulting value for the decay width is Γ(π0→γγ)=7.82±0.14(stat)±0.17(syst)  eV. With the 2.8% total uncertainty, this result is a factor of 2.5 more precise than the current Particle Data Group average of this fundamental quantity, and it is consistent with current theoretical predictions.

We investigate the low-energy behavior of the four-point Green's function ⌫ describing virtual Compton scattering off the nucleon. Using Lorentz invariance, gauge invariance, and crossing symmetry, we derive the leading terms of an expansion of the operator in the four-momenta q and qЈ of the initial and final photon, respectively. The model-independent result is expressed in terms of the electromagnetic form factors of the free nucleon, i.e., on-shell information which one obtains from electron-nucleon scattering experiments. Modeldependent terms appear in the operator at O(q ␣ q ␤ Ј ), whereas the orders O(q ␣ q ␤ ) and O(q ␣ Ј q ␤ Ј ) are contained in the low-energy theorem for ⌫ , i.e., no new parameters appear. We discuss the leading terms of the matrix element and comment on the use of on-shell equivalent electromagnetic vertices in the calculation of ''Born terms'' for virtual Compton scattering. ͓S0556-2813͑96͒02108-5͔