The electromagnetic form factors of the transition from the spin-3/2 Sigma to the Lambda hyperon

TL;DR

This paper investigates the electromagnetic form factors for the transition from a spin-3/2 Sigma* hyperon to a Lambda hyperon, combining experimental data and theoretical models to predict their behavior at low energies.

Contribution

It introduces a comprehensive approach using dispersion theory and chiral perturbation theory to relate transition form factors to experimental observables and pion form factors.

Findings

Transition form factors are complex quantities even at low energies.

Predictions for form factors in low-energy regions are made using dispersion relations.

The study connects form factors to pion vector form factors and decay widths.

Abstract

The three electromagnetic form factors for the transition from a 3/2+ Sigma* hyperon to the ground-state Lambda hyperon are studied. At low energies, combinations of the transition form factors can be deduced from Dalitz decays of the Sigma* hyperon to 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 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 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 pertinent relations between the transition form factors and the decay distributions and differential cross sections are presented. Using dispersion theory, the low-energy electromagnetic form factors for the Sigma*-to-Lambda transition are related to the pion vector form factor. The additionally required input, i.e. the two-pion - Sigma* - Lambda amplitudes are 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 Sigma* to Lambda-gamma decay width. Pion rescattering is taken into account by dispersion theory solving a Muskhelishvili-Omnes 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.