Determination of the ${\mathrm{\Sigma }}^{+}$ Timelike Electromagnetic Form Factors

Based on data samples collected with the BESIII detector at the BEPCII collider, the process $e^{+}{e}^{-}\to {\mathrm{\Sigma }}^{+}{\overline{\mathrm{\Sigma }}}^{-}$ is studied at center-of-mass energies $\sqrt{s}=2.3960$, 2.6454, and 2.9000 GeV. Using a fully differential angular description of the final state particles, both the relative magnitude and phase information of the ${\mathrm{\Sigma }}^{+}$ electromagnetic form factors in the timelike region are extracted. The relative phase between the electric and magnetic form factors is determined to be $\sin \mathrm{\Delta }\mathrm{\Phi }=-0.67\pm 0.29(\mathrm{stat})\pm 0.18(\mathrm{syst})$ at $\sqrt{s}=2.3960\mathrm{GeV}$, $\mathrm{\Delta }\mathrm{\Phi }=55°\pm 19°(\mathrm{stat})\pm 14°(\mathrm{syst})$ at $\sqrt{s}=2.6454\mathrm{GeV}$, and $78°\pm 22°(\mathrm{stat})\pm 9°(\mathrm{syst})$ at $\sqrt{s}=2.9000\mathrm{GeV}$. For the first time, the phase of the hyperon electromagnetic form factors is explored in a wide range of four-momentum transfer. The evolution of the phase along with four-momentum transfer is an important input for understanding its asymptotic behavior and the dynamics of baryons.

Figure 1

The distributions of (a) $M_{\mathrm{bc}}$ at 2.3960 GeV, (b) $M_{{\mathrm{\Sigma }}_{\mathrm{rec}}}$ at 2.6454 GeV, and (c) $M_{{\mathrm{\Sigma }}_{\mathrm{rec}}}$ at 2.9000 GeV. The black dots with error bars are data. The histograms filled with green diagonal lines represent the signal MC samples, and the histograms filled with purple shading represent the backgrounds estimated by the sidebands. The purple solid lines are the total fit result. The yellow dash-dotted and magenta dotted lines are the signal and background shapes, respectively. The signal and background regions used for further angular analysis are indicated by purple solid-line arrows and yellow dashed-line arrows, respectively.

Figure 2

The polarization $P_y$ as a function of the scattering angle at 2.3960 GeV (a) and 2.6454 and 2.9000 GeV (b). The open squares, solid squares, and dots are data. The histograms with solid lines (dotted line at 2.6454 GeV) are signal MC samples based on the fit results, and the histograms with the gray dashed lines are the PHSP signal MC samples at each energy point.

Figure 3

Results for $|G_E/G_M|$ (a) and the relative phase $\mathrm{\Delta }\mathrm{\Phi }$ (b) from this work (purple dots). The yellow squares in (a) denote the previous results from BESIII [26]. The open circle in (b) represents the second solution of $\mathrm{\Delta }\mathrm{\Phi }$ at 2.3960 GeV. The vertical dashed lines indicate the production threshold for $e^{+}{e}^{-}\to {\mathrm{\Sigma }}^{+}{\overline{\mathrm{\Sigma }}}^{-}$, where $|G_E/G_M|=1$ and $\mathrm{\Delta }\mathrm{\Phi }=0°$ by definition.