The SM as the Quantum Low Energy Effective Theory of the MSSM

Abstract

In the framework of the Minimal Supersymmetric Standard Model we compute the one-loop effective action for the electroweak bosons obtained after integrating out the different sleptons, squarks, neutralinos and charginos, and present the result in terms of the physical sparticle masses. In addition we study the asymptotic behaviour of the two, three and four point Green's functions with external electroweak bosons in the limit where the physical sparticle masses are very large in comparison with the electroweak scale. We find that in this limit all the effects produced by the supersymmetric particles can be, either absorbed in the Standard Model parameters and gauge bosons wave functions, or else they are supressed by inverse powers of the supersymmetric particle masses. This work, therefore, completes the proof of decoupling of the heavy supersymmetric particles from the standard ones in the electroweak bosons effective action and in the sense of the Appelquist-Carazzone Theorem that we started in a previous work. From the point of view of effective field theories this work can be seen as a (partial) proof that the SM can be obtained indeed from the MSSM as the quantum low energy effective theory of this latter when the SUSY spectra is much heavier than the electroweak scale.