Electromagnetic form factors of the ${\Omega }^{-}$ baryon in the spacelike and timelike regions

Abstract

We present complete calculations of the electromagnetic form factors of the ${\Omega }^{-}$ in the spacelike region and in the timelike region. The four elastic form factors: electric charge ($G_{E0}$), magnetic dipole ($G_{M1}$), electric quadrupole ($G_{E2}$) and magnetic octupole ($G_{M3}$), are estimated within the covariant spectator quark model, in terms of the square momentum transfer $q^2$. The free parameters of the ${\Omega }^{-}$ wave function, including a $S$-wave state and two independent $D$-wave states radial wave functions and the admixture coefficients are fixed by the comparison with the lattice QCD data in the spacelike region ($Q^2=-q^2\le 0$) and with the recent $e^{+}{e}^{-}\to {\Omega }^{-}{\bar{\Omega }}^{+}$ data from CLEO in the timelike region ($q^2>0$). The estimates in the timelike region for square momentum transfer $q^2\ge 4M_{\Omega }^2$ are based on large-$q^2$ asymptotic relations ($M_{\Omega }$ is the ${\Omega }^{-}$ mass). We examine also the impact of the large-$Q^2$ correlations between different form factors and analyze the possible solutions. The electric quadrupole and the magnetic octupole moments of the ${\Omega }^{-}$, and the $e^{+}{e}^{-}\to {\Omega }^{-}{\bar{\Omega }}^{+}$ integrated cross sections for very large $q^2$ are estimated based on the model results.

Published version. 22 pages, 5 figures and 6 tables

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• Electromagnetic Transition Form Factors of Baryon Resonances
• Study of $e^{+}{e}^{-}\to {\Omega }^{-}{\bar{\Omega }}^{+}$ at center-of-mass energies from 3.49 to 3.67 GeV
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