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Register a new userMeasurements of Sigma+ and Sigma- Time-like Electromagnetic Form Factors for center-of-mass energies from 2.3864 to 3.0200 GeV
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The Born cross sections of the $e^{+}e^{-}toSigma^{+}bar{Sigma}^{-}$ and $e^{+}e^{-}toSigma^{-}bar{Sigma}^{+}$ processes are determined with high precision for center-of-mass energy from 2.3864 to 3.0200 GeV with the BESIII detector. Nonzero cross sections near threshold are observed. The resulting ratio of effective form factors for the $Sigma^{+}$ and $Sigma^{-}$ is consistent with 3, agreeing with the ratio of the incoherent sum of the squared charges of the $Sigma^{+}$ and $Sigma^{-}$ valence quarks, but disagreeing with various theoretical predictions. In addition, ratios of the $Sigma^{+}$ electric and magnetic form factors, $|G_{E}/G_{M}|$, are obtained at three center-of-mass energies through an analysis of the angular distributions. These measurements, which are studied for the first time in the off-resonance region, provide precision experimental input for understanding baryonic structure. The observed novel features of the $Sigma^{pm}$ form factors require a new theoretical description for the hyperons.
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Using dispersion theory the low-energy electromagnetic form factors for the transition of a Sigma to a Lambda hyperon are related to the pion vector form factor. The additionally required input, i.e. the two-pion--Sigma--Lambda amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the baryons from the octet and optionally from the decuplet. Pion rescattering is again taken into account by dispersion theory. It turns out that the inclusion of decuplet baryons is not an option but a necessity to obtain reasonable results. The electric transition form factor remains very small in the whole low-energy region. The magnetic transition form factor depends strongly on one not very well determined low-energy constant of the NLO Lagrangian. One obtains reasonable predictive power if this low-energy constant is determined from a measurement of the magnetic transition radius. Such a measurement can be performed at the future Facility for Antiproton and Ion Research (FAIR).
The measurements of the nucleon electromagnetic form factors in the time-like region are reviewed. Several unexpected features deserving new high precision, high statistics measurements are emphasised.
Simulation results for future measurements of electromagnetic proton form factors at PANDA (FAIR) within the PandaRoot software framework are reported. The statistical precision with which the proton form factors can be determined is estimated. The signal channel $bar p p to e^+ e^-$ is studied on the basis of two different but consistent procedures. The suppression of the main background channel, $textit{i.e.}$ $bar p p to pi^+ pi^-$, is studied. Furthermore, the background versus signal efficiency, statistical and systematical uncertainties on the extracted proton form factors are evaluated using two different procedures. The results are consistent with those of a previous simulation study using an older, simplified framework. However, a slightly better precision is achieved in the PandaRoot study in a large range of momentum transfer, assuming the nominal beam conditions and detector performance.
The extended Lomon-Gari-Krumpelmann model of nucleon electromagnetic form factors, which embodies rho, rho, omega, omega and phi vector meson contributions and the perturbative QCD high momentum transfer behavior has been extended to the time-like region. Breit-Wigner formulae with momentum-dependent widths have been considered for broad resonances in order to have a parametrization for the electromagnetic form factors that fulfills, in the time-like region, constraints from causality, analyticity, and unitarity. This analytic extension of the Lomon-Gari-Krumpelmann model has been used to perform a unified fit to all the nucleon electromagnetic form factor data, in the space-like and time-like region (where form factor values are extracted from e+e- <-> nucleon-antinucleon cross sections data). The knowledge of the complete analytic structure of form factors enables predictions at extended momentum transfer, and also of time-like observables such as the ratio between electric and magnetic form factors and their relative phase.
The data on the proton form factors in the time-like region from the BaBar, BESIII and CMD-3 Collaborations are examined to have coherent pieces of information on the proton structure. Oscillations in the annihilation cross section, previously observed, are determined with better precision. The moduli of the individual form factors, determined for the first time, their ratio and the angular asymmetry of the annihilation reaction $e^+e^-tobar p p$ are discussed. Fiits of the available data on the cross section, the effective form factor, and the form factor ratio, allow to propose a description of the electric and magnetic time-like form factors from the threshold up to the highest momenta.
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