A Custodial Symmetry in the Standard Model

[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?

Thanks in advance,
Luca

 

[ofirg]

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?

Thanks in advance,
Luca

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\rightarrowSU(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.

 

[Luca_Mantani]

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\rightarrowSU(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.

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

 

[ofirg]

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

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