# A Custodial Symmetry in the Standard Model

1. Aug 22, 2016

### Luca_Mantani

Hi,
I am reading about this symmetry but i'm struggling to have a deep understanding of it. Would somebody please explain this symmetry to me from a conceptual point of view?

Luca

2. Aug 24, 2016

### ofirg

The question seems to me to general. Due you have a more specific question?
A few basics:

Custodial symmetry is a symmetry that is respected by the SU(2) gauge interactions and the higgs self potential. It is not respected by the U(1) hypercharge interactions and yukawa terms for the fermions.
It extends the SU(2)L in the standard model to SU(2)LxSU(2)R (global symmetry only). After electroweak symmetry breaking(EWSB) ,
SU(2)LxSU(2)R$\rightarrow$SU(2)L+R. This residual symmetry after EWSB is usually referred to as the "custodial" symmetry.

The three SU(2)L Gauge bosons (W$\pm$,W3) form a triplet under this symmetry, and thus their masses are equal in the approximation that the symmetry is valid. The deviation from that is due to hypercharge and yukawa terms.

3. Aug 24, 2016

### Luca_Mantani

In which sense this is a "approximate" symmetry? How can a symmetry be approximate?

4. Aug 24, 2016

### ofirg

In the sense that it is not respected by some terms in the Lagrangian. The symmetry is only present when those terms are neglected.