Friday, May 21, 2010

Assuming Survival principle was not a very good idea

I was doing some calculations regarding renormalization group evolutions of masses, couplings etc within the framework of a model. For simplicity I took the mass of various Higgs fields same as their mass terms appearing in the superpotential. After doing all the analysis, I came to know that the physical masses of the Higgs fields need not always be same as the bare mass terms in the superpotential or the Lagrangian. In fact the assumption I took was quite ad hoc. Before calculating the physical masses of all the Higgs fields, I can not assume their masses, but that's also one way to study the RG running, but it might not give the correct result always. In some cases the physical masses comes out to be very different from the bare mass terms and hence will affect the RG substantially. What happens is that when we write the F-term scalar potential of a model, sometimes the quartic term of a scalar field remains absent because the corresponding trilinear term was not there in the superpotential so as to obey the internal gauge symmetries. Thus the mass terms remain arbitrary at the renormalizable level and higher dimensional terms have to be considered. This leads to lighter Higgs masses than the bare mass terms. And even if the quartic terms are there in the superpotential, it is not to straightforward to say that the mass will be same as the bare mass terms, because the various Higgs fields mix with each other, and it's not unusual that the diagonalization of their mass matrix will give a small eigenvalue. So better calculate the physical masses of all the particles (not just fermions ) and then proceed with the RG evolutions.

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