Electromagnetic form factors of the transition from the spin-3/2 Σ to the Λ hyperon

Abstract

The three electromagnetic form factors for the transition from a $3/{2}^{+}\phantom{\rule{4pt}{0ex}}{\mathrm{\ensuremath{\Sigma}}}^{*}$ hyperon to the ground-state $\mathrm{\ensuremath{\Lambda}}$ hyperon are studied. At low energies, combinations of the transition form factors can be deduced from Dalitz decays of the ${\mathrm{\ensuremath{\Sigma}}}^{*}$ hyperon to $\mathrm{\ensuremath{\Lambda}}$ plus an electron-positron pair. It is pointed out how more information can be obtained with the help of the self-analyzing weak decay of the $\mathrm{\ensuremath{\Lambda}}$. In particular, it is shown that these transition form factors are complex quantities already in this kinematical region. Such measurements are feasible at hyperon factories such as, for instance, the Facility for Antiproton and Ion Research (FAIR). At higher energies, the transition form factors can be measured in electron-positron collisions. The transition form factors are related to decay distributions and differential cross sections. Using dispersion theory, the low-energy electromagnetic form factors for the ${\mathrm{\ensuremath{\Sigma}}}^{*}$-to-$\mathrm{\ensuremath{\Lambda}}$ transition are related to the pion vector form factor. The additionally required input, i.e., the two-pion--${\mathrm{\ensuremath{\Sigma}}}^{*}$--$\mathrm{\ensuremath{\Lambda}}$ amplitudes, is determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory, including the baryons from the octet and the decuplet. A poorly known NLO parameter is fixed to the experimental value of the ${\mathrm{\ensuremath{\Sigma}}}^{*}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\ensuremath{\gamma}$ decay width. Pion rescattering is taken into account by using dispersion theory and solving a Muskhelishvili-Omn\`es equation. Subtracted and unsubtracted dispersion relations are discussed. However, in view of the fact that the transition form factors are complex quantities, the current data situation does not allow for a full determination of the subtraction constants. To reduce the number of free parameters, unsubtracted dispersion relations are used to make predictions for the transition form factors in the low-energy space- and timelike regions.