Custodial Symmetry in the Standard Model

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Discussion Overview

The discussion centers around custodial symmetry within the context of the Standard Model of particle physics. Participants seek to understand its conceptual framework, implications, and the conditions under which it is considered approximate.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants describe custodial symmetry as a symmetry respected by SU(2) gauge interactions and the Higgs self-potential, but not by U(1) hypercharge interactions and Yukawa terms for fermions.
  • It is noted that custodial symmetry extends SU(2)L to SU(2)LxSU(2)R, and after electroweak symmetry breaking (EWSB), it reduces to a residual symmetry referred to as "custodial" symmetry.
  • There is a claim that the three SU(2)L gauge bosons (W±, W3) form a triplet under this symmetry, leading to equal masses in the approximation that the symmetry holds.
  • One participant questions the nature of custodial symmetry as "approximate," asking how a symmetry can be considered approximate.
  • Another participant responds that custodial symmetry is approximate because it is not respected by certain terms in the Lagrangian, indicating that the symmetry is only valid when those terms are neglected.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding custodial symmetry, with some seeking clarification while others provide foundational explanations. The discussion does not reach a consensus on the implications of the symmetry being approximate.

Contextual Notes

The discussion highlights the dependence on specific terms in the Lagrangian for the validity of custodial symmetry, suggesting limitations in the understanding of its implications when those terms are included.

Luca_Mantani
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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
 
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Luca_Mantani said:
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.
 
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ofirg said:
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?
 
Luca_Mantani said:
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.
 
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