Custodial Symmetry in the Standard Model

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SUMMARY

Custodial symmetry is a crucial concept in the Standard Model of particle physics, specifically related to the SU(2) gauge interactions and the Higgs self-potential. It extends the SU(2)L symmetry to SU(2)LxSU(2)R, which is a global symmetry that remains after electroweak symmetry breaking (EWSB), resulting in the residual symmetry SU(2)L+R. This symmetry ensures that the three SU(2)L gauge bosons (W±, W3) have equal masses under the approximation of custodial symmetry, although deviations arise due to U(1) hypercharge interactions and Yukawa terms for fermions.

PREREQUISITES
  • Understanding of SU(2) gauge theory
  • Familiarity with electroweak symmetry breaking (EWSB)
  • Knowledge of Higgs self-potential
  • Basic concepts of Lagrangian mechanics in particle physics
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  • Study the implications of electroweak symmetry breaking on particle masses
  • Explore the role of Yukawa interactions in the Standard Model
  • Investigate the relationship between custodial symmetry and precision electroweak measurements
  • Learn about the mathematical formulation of global symmetries in quantum field theory
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Particle physicists, theoretical physicists, and advanced students seeking to deepen their understanding of symmetries in the Standard Model and their implications for particle interactions.

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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