On the vector transition form factors in the Ω- → Ξ0 W- decay

Abstract: To learn more about the structure of hadrons we study form factors. In the semi-leptonic decay Ω- → Ξ0W- two types of form factors arise namely the vector and axial-vector transition form factors. We focus on the vector transition form factors at next-to-next-to-leading order in the power counting of chiral perturbation theory and study their quark mass dependence. They are related to the scattering amplitude for the transition and therefore we have to calculate Feynman diagrams. Next-to-next-to-leading order Feynman diagrams translate to 1-loop diagrams and at this order there is a substantial amount of them. This study is a feasibility study and therefore we limit this study to diagrams containing the low-energy constants HA and hA from the leading order chiral Lagrangian. There are 5 such diagrams, three with two propagators in the loop (bubble diagrams) and two with three propagators in the loop (triangle diagrams). We derive explicit expressions for all 5 diagrams. To calculate these diagrams numerically we use Mathematica and FeynCalc. We provide numerical results for the three bubble diagrams but not the triangle diagrams due to the long computing time for these diagrams. Therefore, we show that performing form factor calculations at NNLO seems feasible but there needs to be more investment into figuring out the coding aspects regarding the triangle diagrams.