The one-loop on-shell renormalization of some vertexes in MSSM

Abstract

The on-shell renormalization scheme for the electroweak theory is well studied in the standard model(SM), but a consistent on-shell renormalization scheme for the minimal supersymmetric standard model(MSSM) is still unknown. In MSSM, we study the on-shell scheme for three vertexes$Z\overline{l^I}{l}^I,W^{+}\overline{{\nu }^I}{l}^I$ and ${\tilde{L}}_i^{\ast }\overline{{\chi }_{\alpha }^0}{l}^I$ with virtual SUSY particles (chargino, sneutrino, neutralino and slepton) at one-loop order. Instead of amplitude of a single triangle diagram, the sum of amplitude of triangle diagrams belonging to one suit can be renormalized in the on-shell scheme. One suit points out that the internal virtual particles are consistent. Zero-momentum scheme is also used for the renormalization. The two schemes can make the renormalized results decoupled. In MSSM, some special characters of the on-shell scheme are shown here. This work is propitious to complete the on-shell renormalization scheme in MSSM.