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 analytical
ly 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.
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 re
gion. 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.
Analyticity of nucleon form factors allows to derive sum rules which, using space-like and time-like data as input, can give unique information about behaviors in energy regions not experimentally accessible. Taking advantage from new time-like data
on proton-antiproton differential cross section and hence the possibility to separate electric and magnetic form factors also in the time-like region, we verify the consistency of the asymptotic behavior predicted by the perturbative QCD for the proton magnetic form factor.
The Sommerfeld rescattering formula is compared to the e+e- -> ppbar BaBar data at threshold and above. While there is the expected Coulomb enhancement at threshold, two unexpected outcomes have been found: |G^p (4M_p^2)|= 1, like for a pointlike fer
mion, and moreover data show that the resummation factor in the Sommerfeld formula is not needed. Other e+e- -> baryon-antibaryon cross sections show a similar behavior near threshold.
Recently the BaBar Collaboration published new data on the cross section for the annihilation e+e- -> phi pi0, obtained using the initial state radiation technique at a center of mass energy of 10.6 GeV. Such a process represents an interesting test
bed for the quark model. Indeed, since the phi-pi0 production via e+e- annihilation proceeds through a mechanism which violates the Okubo-Zweig-Iizuka rule, the corresponding cross section could be characterized by contributions from non-qqbar bound states, like hybrids or tetraquarks. The phi-pi0 cross section is analyzed in connection with other data coming from different processes, that involve the same mesons, using a method which implements the analyticity in the phi-pi0 transition form factor by means of a dispersion relation procedure.
A peculiar feature, observed in the BaBar data on e+e- -> baryon-antibaryon cross sections, is the non-vanishing cross section at threshold for all these processes. This is the expectation due to the Coulomb enhancement factor acting on a charged fer
mion pair. Remarkably, in the case of e+e- -> p-pbar it is found that Coulomb final state interactions largely dominate the cross section at threshold and it turns out a form factor |G(4Mp^2)|~1, as a point-like fermion. Also in the case of e+e- -> Lambda_c-antiLambda_c, as recently measured by Belle for the first time, a point-like behavior is suggested for the charmed charged baryon, being the Lambda_c form factor at threshold |G|~1, even if within a large error. In the case of neutral strange baryons the non-vanishing cross section at threshold is interpreted as a remnant of quark pair Coulomb interaction before the hadronization, taking into account the asymmetry between attractive and repulsive Coulomb factors. Besides strange baryon cross sections are successfully compared to U-spin invariance relationships.
A method to determine masses, widths and coupling constants of vector mesons, like phi(1020), omega(782) and rho0(770) recurrences is defined. Starting from data on decay rates and cross sections for the processes: phi -> M_I gamma, phi -> M_I e+e- a
nd e+e- -> M_I phi, where M_I is a pseudoscalar or scalar meson with isospin I=0,1, the time-like transition form factors, which describe the vertex phi-gamma-M_I, are parametrized using a vector meson-propagators description in the low energy region <3-4 GeV, the quark-counting rule prescription for the high energy behavior, and the analyticity imposed by means of the dispersion relations.
Unexpected features of the BaBar data on e+e- in baryon-antibaryon cross sections are discussed. These data have been collected, with unprecedented accuracy, by means of the initial state radiation technique, which is particularly suitable in giving
good acceptance and energy resolution at threshold. A striking feature observed in the BaBar data is the non-vanishing cross section at threshold for all these processes. This is the expectation due to the Coulomb enhancement factor acting on a charged fermion pair. In the case of e+e- in proton-antiproton it is found that Coulomb final state interactions largely dominate the cross section and the form factor is |G^p(4M^2_p)|~1, which could be a general feature for baryons. In the case of neutral baryons an interpretation of the non-vanishing cross section at threshold is suggested, based on quark electromagnetic interaction and taking into account the asymmetry between attractive and repulsive Coulomb factors. Besides strange baryon cross sections are compared to U-spin invariance predictions.
