How to build the MSSM Lagrangian

Abstract

A concise overview of the supersymmetry and the MSSM is presented. Supersymmetry is an attempt to unify fermions and bosons into a consistent framework. It is unique in that it is about intrinsic properties of elementary particles, and simultaneously, is connected to spacetime translations. A method for treating supersymmetric theories is the superfield formalism, which deals with fields defined on a superspace. A chiral superfield is an extension of a left-handed chiral fermion field, and a vector superfield is of a gauge field. Using them, a general supersymmetric Lagrangian can be written down systematically. The MSSM is a minimal supersymmetric extension of the standard model. It adds one superpartner to each of the particles already existing in the standard model. The superpotential of the MSSM is fixed by gauge invariance, renormalizability and R-parity conservation. The soft terms, which are needed to break the supersymmetry and get the Lagrangian realistic, include gaugino mass terms, scalar mass terms and scalar trilinear couplings whose coupling constants are of the electroweak scale. Universality and proportionality of the soft parameters are usually assumed to reflect the rareness of flavor changing processes and CP-violation, and there are models such as gravity- or gauge-mediated supersymmetry breaking, which give the appropriate forms of the soft terms in their effective theory. From the Higgs potential dictated by the MSSM, the lightest Higgs mass is predicted to be (≤ 150GeV).