Electromagnetic form factors of the $Ω^-$ baryon in the spacelike and timelike regions

Abstract

We present complete calculations of the electromagnetic form factors of the Ω − in the spacelike region and in the timelike region. The four elastic form factors: electric charge (GE0), magnetic dipole (GM1), electric quadrupole (GE2) and magnetic dipole (GM3), are estimated within the covariant spectator quark model, in terms of the square momentum transfer q 2 . The free parameters of the Ω − 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 ≤ 0) and with the recent e + e − → Ω − Ω+ data from CLEO in the timelike region (q 2 > 0). The estimates in the timelike region for square momentum transfer q 2 ≥ 4M 2 Ω , are based on large-q 2 asymptotic relations (MΩ is the Ω − 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 Ω − , and the e + e − → Ω − Ω+ integrated cross sections for very large q 2 are estimated based on the model results.

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“…Characterized by three valence strange quarks with aligned spins and the absence of valence up or down quarks, the Ω − is expected to show less relativistic effects in comparison with other octet and decuplet baryons. Yet, even after more than five decades of research, many aspects of its physical properties, apart from its charge and magnetic moment, remain largely uncharted [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. While the decuplet baryon model predicts a spin-3/2 for the Ω − , direct measurements of its spin have been ongoing [25][26][27][28].…”