Proton Time-like Form Factors Research Articles

Phenomenological analysis of near-threshold periodic modulations of the proton timelike form factor

We have recently highlighted the presence of a periodically oscillating 10 \% modulation in the BABAR data on the proton timelike form factors, in the reaction $e^++e^-$ $\rightarrow$ $\bar{p}+p$. 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 $F_0$ $+$ $F_{osc}$, where $F_0$ is a parametrization expressing the long-range trend of the form factor (for $q^2$ ranging from the $\bar{p}p$ threshold to 36 GeV$^2$), and $F_{osc}$ is a function of the form $\exp(-Bp)\cos(Cp)$, where $p$ is the relative momentum of the final $\bar{p}p$ pair. Error bars allow for a clean identification of the main features of this modulation for $q^2$ $<$ 10 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 $\bar{p}p$ interaction is due to the annihilation of $\bar{p}p$ pairs into multi-meson 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, including heavy ones, that may exist for a short time. The decay of these large mass states leads to an intermediate stage regeneration of the $\bar{p}p$ channel.

Proton electromagnetic form factors: present status and future perspectives at PANDA

Data and models on electromagnetic proton form factors are reviewed, highlighting the contribution foreseen by the PANDA collaboration. Electromagnetic hadron form factors contain essential information on the internal structure of hadrons. Precise and surprising data have been obtained at electron accelerators, applying the polarization method in electron-proton elastic scattering. At electron-positron colliders, using initial state radiation, BABAR measured proton time-like form factors in a wide time-like kinematical region and the BESIII collaboration will measure very precisely proton and neutron form factors in the threshold region. In the next future an antiproton beam with momentum up to 15 GeV/c will be available at FAIR (Darmstadt). Measurements of the reaction p&#773; + p -> e^+ + e^- by the PANDA collaboration will contribute to the individual determination of electric and magnetic form factors in the time-like region of momentum transfer squared, as well as to their first determination in the unphysical region (below the kinematical threshold), through the reaction p&#773; + p -> e^+ + e^- + pi^0. From the discussion on feasibility studies at PANDA, we focus on the consequences of such measurements in view of an unified description of form factors in the full kinematical region. We present models which have the necessary analytical requirements and apply to the data in the whole kinematical region.

Radiative corrections in nucleon time-like form factors measurements

The completely general radiative corrections to lowest order, including the final- and initial-state radiations, are studied in proton-antiproton annihilation into an electron-positron pair. Numerical estimates have been made in a realistic configuraton of the PANDA detector at FAIR for the proton time-like form factors measurements.

Antiproton-nucleus electromagnetic annihilation as a way to access the proton timelike form factors

Contrary to the reaction \( \bar{{p}}\) p \( \rightarrow\) e + e - with a high-momentum incident antiproton on a free target proton at rest, in which the invariant mass M of the e + e - pair is necessarily much larger than the \( \bar{{p}}\) p mass 2m , in the reaction \( \bar{{p}}\) d \( \rightarrow\) e + e - n the value of M can take values near or below the \( \bar{{p}}\) p mass. In the antiproton-deuteron electromagnetic annihilation, this allows to access the proton electromagnetic form factors in the timelike region of q2 near the \( \bar{{p}}\) p threshold. We estimate the cross-section \( d\sigma _{\bar pd \to e^ + e^ - n} /d\mathcal{M} \) for an antiproton beam momentum of 1.5GeV/c. We find that near the \( \bar{{p}}\) p threshold this cross-section is about 1pb/MeV. The case of heavy-nuclei target is also discussed. Elements of experimental feasibility are presented for the process \( \bar{{p}}\) d \( \rightarrow\) e + e - n in the context of the \( \overline{{{\rm P}}}\) ANDA project.

Proton timelike form factors and recent $$e^ + e^ - \to p\bar p$$ data

We present an analysis of recent\(e^ + e^ - \to p\bar p\) data in an extended vector-dominance model which has usual analyticity properties and a rather weak asymptotic boundedness condition. The model allows the necessary analytic continuation into the annihilation region. The few free parameters are determined by the fit to the world’s data. As expected, the scarce timelike data place a strong constraint on the analysis, causing, in the variants we considered, the timelike form factors to develop a large imaginary part.