Electromagnetic $|G_E/G_M|$ ratios of hyperons at large timelike $q^2$

Abstract

In recent years, it has become possible to measure not only the magnitude of the electric ($G_E$) and magnetic ($G_M$) form factors of spin $\frac{1}{2}$ baryons, but also to measure the relative phases of those quantities in the timelike kinematic region. Aiming to interpret present $|G_E/G_M|$ data on hyperons of the baryon octet, as well as to predict future data, we present model calculations of that ratio for large invariant 4-momentum square $q^2$ in the timelike region ($q^2>0$). Without any further parameter fitting,we extend to the timelike region a covariant quark model previously developed to describe the kinematic spacelike region ($q^2 \le 0$) of the baryon octet form factors. The model takes into account both the effects of valence quarks and the excitations of the meson cloud which dresses the baryons. This application to the timelike region assumes an approximation based on unitarity and analyticity that is valid only in the large $q^2$ region. Using the recent data from BESIII we establish the regime of validity of this approximation. We report here that our results for the effective form factor (combination of $|G_E|$ and $|G_M|$) are in good agreement with the data already for $q^2$ values above 15 GeV$^2$. In addition, a more conservative onset of the validity of the approximation is provided by the newly available $|G_E/G_M|$ data which suggest that our predictions may be compared against data for $q^2 \ge $ 20 GeV$^2$. This is expected in the near future, when the range of the present measurements is expanded to the 20--50 GeV$^2$ region.