We have recently highlighted the presence of a periodically oscillating 10% modulation in the BABAR Collaboration data on the proton timelike form factors, expressing the deviations from the pointlike behavior of the proton-antiproton electromagnetic current in the reaction $e^{+}+e^{-}\to \overline{p}+p$. Here we deepen our previous data analysis and confirm that in the case of several standard parametrizations it is possible to write the form factor in the form $F_0+F_{\mathrm{osc}}$, where $F_0$ is a parametrization expressing the long-range trend of the form factor (for $q^2$ ranging from the $\overline{p}p$ threshold to 36 ${\mathrm{GeV}}^2$), and $F_{\mathrm{osc}}$ is a function of the form $exp(-Bp)cos\left(Cp\right)$, where $p$ is the relative momentum of the final $\overline{p}p$ pair. Error bars allow for a clean identification of the main features of this modulation for $q^2<10{\mathrm{GeV}}^2$. Assuming this oscillatory modulation to be an effect of final-state interactions between the forming proton and the antiproton, we propose a phenomenological model based on a double-layer imaginary optical potential. This potential is flux absorbing when the distance between the proton and antiproton centers of mass is $\gtrsim 1.7–1.8$ fm and flux generating when it is $\lesssim 1.7–1.8$ fm. The main features of the oscillations may be reproduced with some freedom in the potential parameters, but the transition between the two layers must be sudden (0–0.2 fm) to get the correct oscillation period. The flux-absorbing part of the $\overline{p}p$ interaction is well known in the phenomenology of small-energy antiproton interactions and is due to the annihilation of $\overline{p}p$ pairs into multimeson states. We interpret the flux-creating part of the potential as due to the creation of a $1/q$-ranged state when the virtual photon decays into a set of current quarks and antiquarks. This short-lived compact state may be expressed as a sum of several hadronic states including the ones with large mass $Q_n\gg q$, that may exist for a time $t\sim 1/(Q_n-q)$. The decay of these large-mass states leads to an intermediate-stage regeneration of the $\overline{p}p$ channel.

The data on the proton form factors in the timelike 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 ratios, and the angular asymmetry of the annihilation reaction $e^{+}{e}^{-}\to \overline{p}p$ are discussed. Fits 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 timelike form factors from the threshold up to the highest momenta.

We calculate, in a systematic way, the enhancement effect on p¯p and p¯A annihilation cross sections at low energy due to the initial state electrostatic interaction between the projectile and the target nucleus. This calculation is aimed at future comparisons between n̄ and p¯ annihilation rates on different targets for the extraction of pure isospin channels.

Data on hyperon form factors recently obtained from annihilation reactions are compared to each other and to proton and neutron form factors, in terms of two kinematical variables: the transferred momentum square, $q^2$, and the modulus $P$ of the relative momentum between the outgoing baryons. They are critically discussed in terms of possible correlated structures. The present status of the time-like form factor data for baryons is described and suggestions are given on the reactions and the kinematical range where data are desirable in order to clarify the arisen questions.

The internal structure of composite particles is conveniently described in terms of form factors (FFs)—these are experimentally accessible in annihilation and scattering of elementary reactions, and are theoretically calculable by all models that describe the properties of particles. FFs depend only on one kinematical variable, $q^2$. This is the four-momentum transferred by the virtual photon that carries the interaction. Important developments in accelerator and detector techniques have brought impressive advances, both by extending the kinematical region and by reaching a higher precision. A critical review on the underlying methods and findings in polarized and unpolarized experiments is presented. The unique role played by polarization in determining the ratio of electric to magnetic form factors in the space-like region, and the extraction of individual form factors in the whole kinematical region, are described. Recent results at electron accelerators and electron–positron colliders confirm the existence of periodical structure in the annihilation cross section. We suggest a global framework which describes the dynamical structure of charge distribution in baryons, in order to build a coherent view of the creation and annihilation of baryonic matter.