Electric and magnetic timelike form factors of hyperons at large transfer momentum

TL;DR

The paper addresses the timelike electromagnetic structure of hyperons probed by electron-positron annihilation into hyperon–antihyperon pairs, where $G_E(q^2)$ and $G_M(q^2)$ are complex for $q^2>0$. It extends the covariant spectator quark model, including meson-cloud dressing, to timelike kinematics using asymptotic, unitarity-based relations with $G_ extell(q^2) = G_ extell^{\rm SL}(q^2-2 M_B^2)$ for $\ell \in \{E,M\}$, and quantifies deviations. The results show good agreement with BESIII and CLEO data for the timelike effective form factor $|G|$ of $\Lambda$, $\Sigma^+$, $\Sigma^0$, $\Xi^-$ and $\Xi^0$ above $q^2 > 15$ GeV$^2$, while $\Sigma^-$ awaits data and $|G_E/G_M|$ remains only partially constrained. The approach also describes the $\Omega^-$ form factor within uncertainties and points to future tests at higher $q^2$, as well as extensions to inelastic transitions and heavy-quark baryons.

Abstract

There has been considerable progress in the study of the electromagnetic form factors of baryons in the timelike region, through electron-positron scattering reactions ($e^+ e^- \to B \bar B$), in the last two decades. Timelike experiments reveal information about the distribution of charge and magnetism inside the hyperons that cannot be obtained in spacelike experiments (electron scattering on baryons). Motivated by the novel data, we extend to the timelike region, without any further parameter fitting, a covariant quark model developed for the spacelike region that takes into account the meson cloud excitations of the baryon cores. We use the formalism to calculate the electric ($G_E$) and magnetic ($G_M$) form factors of spin 1/2 baryons in the large square transfer momentum $q^2$ region. Our calculations are compared with the available data from CLEO and BESIII above $q^2=10$ GeV$^2$. We conclude that our predictions for the effective form factors (combination between $G_E$ and $G_M$) are in good agreement with the $q^2 > 15$ GeV$^2$ data for $Λ$, $Σ^+$, $Σ^0$, $Ξ^-$ and $Ξ^0$. Upcoming data for $Σ^-$ can be used to further test our predictions. We also compare our model calculations with the available data for ratio $|G_E/G_M|$. We conclude that the present $q^2$ data range is not large enough to test our calculations, but that a more definitive test can be performed by upcoming data above $q^2=20$ GeV$^2$.

Figures (2)

• Figure 1: Effective form factors $|G(q^2)|$ of the hyperons for $q^2 > 10$ GeV$^2$ (solid line) Hyperons12. The dashed lines represent the limits of deviations from the asymptotic relations. The data are from CLEO Dobbs17a and BESIII BESIII-Data1BESIII-Data2. For $\Sigma^-$ we include also BESIII data below $q^2=10$ GeV$^2$.
• Figure 2: At the left: Real part of the ratio $G_E/G_M$ for the $\Lambda$ with theoretical uncertainties. Data from Refs. BESIII22-25. At the right: Effective form factor of the $\Omega^-$Omega3. The data are from BESIII BESIII-Omega and CLEO Dobbs17a. The blue lines indicate the upper limit of the measurements $|G|=0$.