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Register a new userAnalytic Model of a Regge Trajectory in the Space-like and Time-like Regions
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A model for a Regge trajectory compatible with the threshold behavior required by unitarity and asymptotics in agreement with Mandelstam analyticity is analyzed and confronted with the experimental data on the spectrum of the $rho$ trajectory as well as those on the $pi^- pto pi^0 n$ charge-exchange reaction. The fitted trajectory deviates considerably from a linear one both in the space-like and time-like regions, matching nicely between the two.
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Some recent advances in the theoretical description of the Nucleon electromagnetic form factors, both in the space- and time-like regions, will be briefly illustrated. In particular, both the present stage of the lattice calculations and updated phenomenological approaches, like the ones based on dispersion relations and on microscopical models, will be reported.
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.
A model for a Regge trajectory compatible with the threshold behavior required by unitarity and asymptotics in agreement with analyticity constraints is given in explicit form. The model is confronted in the time-like region with widths and masses of the mesonic resonances and, in the space-like region, the $rho$ trajectory is compared with predictions derived from $pi-N$ charge-exchange reaction. Breaking of the exchange degeneracy is studied in the model and its effect on both the masses and widths is determined.
The possibility to compute nucleon electromagnetic form factors in the time-like region by analytic continuation of their space-like expressions has been explored in the framework of the Skyrme model. We have developed a procedure to solve analytically Fourier transforms of the nucleon electromagnetic current and hence to obtain form factors defined in all kinematical regions and fulfilling the first-principles requirements. The results are discussed and compared to data, both in space-like and time-like region.
Radial excitations of the quark-antiquark string sweeping the Wilson-loop area are considered in the framework of the effective-action formalism. Identifying these excitations with the daughter Regge trajectories, we find corrections which they produce to the constituent quark mass. The energy of the quark-antiquark pair turns out to be mostly saturated by the constituent quark masses, rather than by the elongation of the quark-antiquark string. Specifically, while the constituent quark mass turns out to increase as the square root of the radial-excitation quantum number, the energy of the string increases only as the fourth root of that number.
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