Complete measurement of $\Lambda$ electromagnetic form factors

Abstract

The exclusive process $e^{+}{e}^{-}\to \Lambda \bar{\Lambda }$, with $\Lambda \to p{\pi }^{-}$ and $\bar{\Lambda }\to \bar{p}{\pi }^{+}$, has been studied at $\sqrt{s}=$ 2.396 GeV for measurement of the $\Lambda$ electric and magnetic form factors, $G_E$ and $G_M$. A data sample, corresponding to an integrated luminosity of 66.9 pb${}^{-1}$, was collected with the BESIII detector for this purpose. A multi-dimensional analysis with a complete decomposition of the spin structure of the reaction enables a determination of the modulus of the ratio $R=|G_E/G_M|$ and, for the first time for any baryon, the relative phase $\Delta \Phi ={\Phi }_E-{\Phi }_M$. The resulting values are obtained using the recent and most precise measured value of the asymmetry parameter ${\alpha }_{\Lambda }$ = $0.750\pm 0.010$ to be $R=0.96\pm 0.14(stat.)\pm 0.02(sys.)$ and $\Delta \Phi =37^{\mathrm{o}}\pm 12^{\mathrm{o}}(stat.)\pm 6^{\mathrm{o}}(sys.)$, respectively. In addition, the cross section is measured with unprecedented precision to be $\sigma =118.7\pm 5.3(stat.)\pm 5.1(sys.)$ pb, which corresponds to an effective form factor of $|G|=0.123\pm 0.003(stat.)\pm 0.003(sys.)$. The contribution from two-photon exchange is found to be negligible. Our result enables the first complete determination of baryon time-like electromagnetic form factors.

7 pages, 3 figures, Submitted to Phys. Rev. Lett

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