The Study Of Effective Potential And Its Applications On The Vacuum Stability Analysis Of The Singlet-doublet Fermion Dark Matter Model

In quantum field theory,the vacuum can be unstable,and the unstable vacuum will decay.An important tool to study the stability of the vacuum is the effective potential.This paper introduces the method of calculating the effective potential and RG improved effective potential.This paper studies the gauge dependent properties of the effective potential.The false vacuum dacay rate can be computed by WKB method or the method of Euclidean field theory.This paper introduces these two methods and mainly studies the application of the method of Euclidean field theory.We study the effective potential and the Renormalization Group(RG)improvement of the effective potential of Higgs boson in a singlet-doublet fermion dark matter extension of the Standard Model and in general singlet-doublet fermion extension models in which several copies of doublet fermions or several copies of singlet fermions are considered.We show that in these models the RG improved effective potential at high energy scale can be quite different from the Higgs potential aided with running quartic self-coupling which is usually considered in literatures,contrary to the case of the SM in which the difference at high energy scale is accidentally small.Then we study the decay of the electroweak vacuum using the RG improved effective action in these model beyond the SM.We find that the decay rate of the false vacuum is slightly changed when calculated using the RG improved effective action in the singlet-doublet fermion dark matter model.In general singlet-doublet fermion extension models,we find that the presence of several copies of doublet can make the electroweak vacuum stable if the new Yukawa couplings are not large.If the new Yukawa couplings are large,the electroweak vacuum can be turned into metastable or unstable again by the presence of extra fermions.