Timelike electromagnetic form factors of hyperons at large $q^2$

TL;DR

The paper addresses timelike electromagnetic form factors of spin-1/2 hyperons at large $q^2$, where experimental data from BaBar, CLEO, Belle, and BESIII provide $|G(q^2)|$ and $|G_E/G_M|$ but little direct timelike insight. It extends a covariant spectator quark framework, originally calibrated in the spacelike region, to the timelike domain using asymptotic relations grounded in analyticity and unitarity, with a finite correction $G_\,ell(q^2)=G_\,ell^{SL}(q^2-2 M_B^2)$. The study computes the effective form factor $|G(q^2)|$ and the ratio $|G_E/G_M|$ for octet spin-1/2 hyperons at large $q^2$, finding good agreement with $\, extLambda$, $\, extSigma^+$, and $\, extXi^-$ data above $15$ GeV$^2$ and offering predictions for $\, extSigma^0$, $\, extSigma^-$ and $\, extXi^0$. It also analyzes the real part of $G_E/G_M$ through $|{ m Re}(G_E/G_M)|=R(q^2)|\, m cos \, riangle\

Abstract

In the last few years there has been considerable progress in the study of the electromagnetic form factors of baryons in the timelike region, through electron-positron scattering, with increasing squared transfer momentum $q^2$. The modulus of the electric ($G_E$) and magnetic ($G_M$) form factors has been measured for nucleons, hyperons and other baryons at BaBar, CLEO, Belle and BESIII. The novel measurements motivated the extension of a covariant quark model, developed to the spacelike region ($q^2 \le 0$), to the timelike region, without any further parameter fitting. The extension is based on asymptotic relations derived from analyticity and unitarity, valid for the large-$q^2$ region. We use the model to make predictions for the effective form factor $|G|$ (combination of $G_E$ and $G_M$) and the ratio $|G_E/G_M|$ for spin 1/2 hyperons at large $q^2$ (above 10 GeV$^2$). Our calculations are in good agreement with the data from CLEO and BESIII for $Λ$, $Σ^+$ and $Ξ^-$ above $q^2=15$ GeV$^2$. Upcoming data for $Σ^0$, $Σ^-$ and $Ξ^-$ at large $q^2$ may be used to further test our predictions. We also compare our model calculations with the scarce available data for $|G_E/G_M|$. We conclude that the present $q^2$ range is not large enough to test our calculations, but that a more definitive test can be made by experiments above $q^2=20$ GeV$^2$.

Figures (2)

• Figure 1: Effective form factors $|G(q^2)|$ in the large-$q^2$ region ($q^2 > 10$ GeV$^2$) Hyperons12. The data are from BESIII Lambda1 ($\Lambda$), SigmaP1 ($\Sigma^+$), XiM1 ($\Xi^-$) and CLEO Dobbs17a. The colored band indicates the theoretical deviations from the asymptotic relations.
• Figure 2: Real part of the ratio $G_E/G_M$ for the $\Lambda$ and $\Sigma^+$ hyperons. Data from Refs. BESIII19aBESIII22-25 ($\Lambda$) and BESIII23a ($\Sigma^+$). The colored band indicates the theoretical deviations from the asymptotic relations. The uncertainties associated with the phase $\Delta \Phi$ are not included in the data points.