Electromagnetic form factors of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> baryon in the spacelike and timelike regions
G. Ramalho
Abstract
We present complete calculations of the electromagnetic form factors of the ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}$ 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 ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}$ 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 (${Q}^{2}=\ensuremath{-}{q}^{2}\ensuremath{\le}0$) and with the recent ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}{\overline{\mathrm{\ensuremath{\Omega}}}}^{+}$ data from CLEO in the timelike region (${q}^{2}>0$). The estimates in the timelike region for square momentum transfer ${q}^{2}\ensuremath{\ge}4{M}_{\mathrm{\ensuremath{\Omega}}}^{2}$ are based on large-${q}^{2}$ asymptotic relations (${M}_{\mathrm{\ensuremath{\Omega}}}$ is the ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}$ 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 ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}$ and the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}{\overline{\mathrm{\ensuremath{\Omega}}}}^{+}$ integrated cross sections for very large ${q}^{2}$ are estimated based on the model results.