The differential cross sections \sigma_0=\sigma_T+\epsilon \sigma_L, \sigma_{LT}, and \sigma_{TT} of \pi^0 electroproduction from the proton were measured from threshold up to an additional center of mass energy of 40 MeV, at a value of the photon four-momentum transfer of Q^2= 0.05 GeV^2/c^2 and a center of mass angle of \theta=90^\circ. By an additional out-of-plane measurement with polarized electrons \sigma_{LT'} was determined. This showed for the first time the cusp effect above the \pi^+ threshold in the imaginary part of the s-wave. The predictions of Heavy Baryon Chiral Perturbation Theory are in disagreement with these data. On the other hand, the data are somewhat better predicted by the MAID phenomenological model and are in good agreement with the dynamical model DMT.
The separated cross section SIG(0), SIG(LT) and SIG(TT).
Beam helicity asymmetry.
To determine nonspherical angular momentum amplitudes in hadrons at long ranges (low Q^2), data were taken for the p(\vec{e},e'p)\pi^0 reaction in the Delta region at Q^2=0.060 (GeV/c)^2 utilizing the magnetic spectrometers of the A1 Collaboration at MAMI. The results for the dominant transition magnetic dipole amplitude and the quadrupole to dipole ratios at W=1232 MeV are: M_{1+}^{3/2} = (40.33 +/- 0.63_{stat+syst} +/- 0.61_{model}) (10^{-3}/m_{\pi^+}),Re(E_{1+}^{3/2}/M_{1+}^{3/2}) = (-2.28 +/- 0.29_{stat+syst} +/- 0.20_{model})%, and Re(S_{1+}^{3/2}/M_{1+}^{3/2}) = (-4.81 +/- 0.27_{stat+syst} +/- 0.26_{model})%. These disagree with predictions of constituent quark models but are in reasonable agreement with lattice calculations with non-linear (chiral) pion mass extrapolations, with chiral effective field theory, and with dynamical models with pion cloud effects. These results confirm the dominance, and general Q^2 variation, of the pionic contribution at large distances.
Measured value of SIG(C=T) + EPS*SIG(C=L) as a function of the pion angle relative to the virtual photon direction.
Measured value of SIG(C=TT) as a function of the pion angle relative to thevirtual photon direction.
Measured value of SIG(C=LT) as a function of the pion angle relative to thevirtual photon direction.
The polarized longitudinal-transverse structure function $\sigma_{LT^\prime}$ measures the interference between real and imaginary amplitudes in pion electroproduction and can be used to probe the coupling between resonant and non-resonant processes. We report new measurements of $\sigma_{LT^\prime}$ in the $N(1440){1/2}^+$ (Roper) resonance region at $Q^2=0.40$ and 0.65 GeV$^2$ for both the $\pi^0 p$ and $\pi^+ n$ channels. The experiment was performed at Jefferson Lab with the CEBAF Large Acceptance Spectrometer (CLAS) using longitudinally polarized electrons at a beam energy of 1.515 GeV. Complete angular distributions were obtained and are compared to recent phenomenological models. The $\sigma_{LT^\prime}(\pi^+ n)$ channel shows a large sensitivity to the Roper resonance multipoles $M_{1-}$ and $S_{1-}$ and provides new constraints on models of resonance formation.
Polarized structure function of the reaction E- P --> E- PI0 P for Q**2 = 0.40 and W = 1.1 GeV.
Polarized structure function of the reaction E- P --> E- PI0 P for Q**2 = 0.40 and W = 1.14 GeV.
Polarized structure function of the reaction E- P --> E- PI0 P for Q**2 = 0.40 and W = 1.18 GeV.
The reaction e − + p → e − + p + π 0 has been studied in the region of the Δ (1236) resonance at a four-momentum transfer of the virtual photon of 0.3 (GeV/ c ) 2 . Angles and momenta of the secondary electron and of the outgoing proton were measured in coincidence to obtain the angular dependence of the differential cross section. The angular distribution for s- and p-waves of the pion in the πN cm-system was fitted to the cross section for three W -bins around the maximum of the resonance. The contribution of the resonant multipoles M 1+ , E 1+ and S 1+ to the cross section as well as the contribution of the background amplitudes M 1− , E 0+ and S 0+ are given.
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