For over 100 y, scientists have investigated the properties of the proton, which is one of the most abundant components of visible matter in the universe. Nevertheless, researchers do not fully understand many details about its internal structure and dynamics. Time-like electromagnetic form factors are some of the observable quantities that can help us achieve a deeper understanding. In this review article, we present an overview of the current experimental status in this field, consisting of measurements of the time-like reactions $e^{+}{e}^{-}\to p\overline{p}$ and $p\overline{p}\to e^{+}{e}^{-}$ and future measurements of $p\overline{p}\to {\mu }^{+}{\mu }^{-}$. The focus is put on recent high-precision results of the reaction $e^{+}{e}^{-}\to p\overline{p}$ that have been obtained after analyzing 688.5 pb${}^{-1}$ of data taken at the BESIII experiment. They are compared to and put into perspective with results from previous measurements in this channel. We discuss the channels $p\overline{p}\to e^{+}{e}^{-}$ and $p\overline{p}\to {\mu }^{+}{\mu }^{-}$ in terms of the few existing, as well as future measurements, which the PANDA experiment will perform. Finally, we review several new theoretical models and phenomenological approaches inspired by the BESIII high-precision results and then discuss their implications for a deeper understanding of the proton’s structure and inner dynamics.

A search for C P violation with an entangled system of Ξ − Ξ ¯ + pairs is performed, using ( 10 , 087 ± 44 ) × 10 6 J / ψ events collected with the BESIII experiment. A nine-dimensional helicity amplitude is used to fit e + e − → J / ψ → Ξ − Ξ ¯ + and its subsequent decays. The Ξ − and Ξ ¯ + decay parameters are determined with higher precision compared to the best results reported so far. Furthermore, the strong phase difference, ( δ P − δ S ) = ( 0.3 ± 1.2 ± 0.2 ) × 10 − 2 rad , and the weak phase difference, ( ξ P − ξ S ) = ( − 0.2 ± 1.2 ± 0.1 ) × 10 − 2 rad , are directly determined. These are the most precise measurements to date. The C P asymmetry observables A C P Ξ = ( − 7.8 ± 4.8 ± 0.8 ) × 10 − 3 and Δ ϕ C P Ξ = ( 0.6 ± 5.1 ± 0.2 ) × 10 − 3 rad are determined, which are consistent with C P conservation. In addition, independent measurements of the Λ decay parameter and C P asymmetry A C P Λ = ( − 2.9 ± 4.3 ± 0.7 ) × 10 − 3 are also obtained, which are in agreement with the previous measurements, but with much improved precision.

We report a direct search for a new gauge boson, X , with a mass of 17 MeV / c 2 , which could explain the anomalous excess of e + e − pairs observed in the Be 8 nuclear transitions. The search is conducted in the charmonium decays χ c J → X J / ψ ( J = 0 , 1 , 2 ) via the radiative transition ψ ( 3686 ) → γ χ c J using ( 2712.4 ± 14.3 ) × 10 6 ψ ( 3686 ) events collected with the BESIII detector at the BEPCII collider. No significant signal is observed, and the updated upper limit on the coupling strength of charm quark and the new gauge boson, ε c , is set to be | ε c | < 1.2 × 10 − 2 at 90% confidence level. We also report new constraints on the mixing strength ε between the Standard Model photon and dark photon γ ′ in the mass range from 5 to 300 MeV / c 2 . The upper limits at 90% confidence level vary within ( 2.5 – 17.5 ) × 10 − 3 depending on the γ ′ mass.

A bstract: Using e ⁺ e ⁻ collision data corresponding to a total integrated luminosity of 20 fb ^{− 1} collected with the BESIII detector at the BEPCII collider, we present a measurement of the Born cross section for the process $$ {e}^{+}{e}^{-}\to p{K}^{-}{K}^{-}{\overline{\Xi}}^{+} $$ e + e − → p K − K − Ξ ¯ + at 39 center-of-mass energies between 3.5 and 4.9 GeV with a partial reconstruction technique. By performing a fit to the dressed cross section of $$ {e}^{+}{e}^{-}\to p{K}^{-}{K}^{-}{\overline{\Xi}}^{+} $$ e + e − → p K − K − Ξ ¯ + with a power law function for continuum production and one resonance at a time for the ψ (3770), ψ (4040), ψ (4160), ψ (4230), ψ (4360), ψ (4415) or ψ (4660), respectively, the upper limits for the product of partial electronic width and branching fraction into the final state $$ p{K}^{-}{K}^{-}{\overline{\Xi}}^{+} $$ p K − K − Ξ ¯ + for these resonances are determined at the 90% confidence level.

A bstract: Based on a sample of (10087 ± 44) × 10 ⁶ J / ψ events collected at the center-of-mass energy $$ \sqrt{s}=3.0969 $$ s = 3.0969 GeV with the BESIII detector, we search for the charmonium rare weak decay $$ J/\psi \to {\overline{D}}^0{\overline{K}}^{\ast 0}+\textrm{c}.\textrm{c}. $$ J / ψ → D ¯ 0 K ¯ ∗ 0 + c . c . . No significant signal is observed, and the upper limit on its decay branching fraction at the 90% confidence level is set as 1.4 × 10 ^{− 7} , improving the sensitivity of the previous best limit by an order of magnitude.

A bstract: Based on (10087 ± 44) × 10 ⁶ J / ψ events recorded with the BESIII detector, we search for the rare charmonium weak decays $$ J/\psi \to {D}_s^{-}{\rho}^{+}+\textrm{c}.\textrm{c}. $$ J / ψ → D s − ρ + + c . c . and $$ J/\psi \to {D}_s^{-}{\pi}^{+}+\textrm{c}.\textrm{c}. $$ J / ψ → D s − π + + c . c . No signal is observed, and upper limits on the branching fractions at the 90% confidence level are set as $$ \mathcal{B}\left(J/\psi \to {D}_s^{-}{\rho}^{+}+\textrm{c}.\textrm{c}.\right)<8.0\times {10}^{-7} $$ B J / ψ → D s − ρ + + c . c . < 8.0 × 10 − 7 and $$ \mathcal{B}\left(J/\psi \to {D}_s^{-}{\pi}^{+}+\textrm{c}.\textrm{c}.\right)<4.1\times {10}^{-7} $$ B J / ψ → D s − π + + c . c . < 4.1 × 10 − 7 . Our results provide the most stringent experimental constraints on these decays.