Custodial SU(2) approximate symmetry

[thoms2543]

what is meant by the custodial SU(2) approximate symmetry as a 5, a 3? it is always mentioned in the Higgs triplet, charged higgs context.

 

[arivero]

I think that the concept of protection originates from 't Hooft "naturalness principle", that if in some context a mass is smaller than the natural mass scale, we should be able to found some approximate symmetry "protecting the mass", in the sense that if the symmetry were exact, the mass should be zero. It is a kind of generalization of the physical joke "if its value is not infinity, then it is zero"...

We can call "custodial symmetry" to this symmetry. But I am not 100% sure if this is the context in Higgs theories.

 

[thoms2543]

http://prd.aps.org/abstract/PRD/v42/i5/p1673_1

I read it from this paper. and

Nucl. Phys. B262 463 (1985).

They mention that the Higgs field can be classified according to their transformation properties under the the custodial SU(2) approximate symmetry as a 5, a 3...but i can't found more detail about what they mention.

 

[blechman]

"Custodial symmetry" is a specific (global) symmetry in the Standard Model. The SM has a gauged SU(2)_L, but if we ignore hypercharge and fermion masses, there is also an SU(2)_R symmetry which is global (no gauge bosons). This symmetry forces certain electroweak observables (like the rho parameter) to vanish. The fact that hypercharge and fermion masses are there means that these quantities do NOT vanish, but are proportional to these parameters (g', m_f).

As to the Higgs transforming under custodial symmetry: in each Higgs model (SM, 2Higgs doublets, Higgs triplet, etc) the Higgs transforms under that custodial symmetry (global SU(2)) in a certain way that is model dependent. That is probably what this paper is referring to.

Hope that helps.

 

[thoms2543]

Thanks