Custodial SU(2) approximate symmetry

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Discussion Overview

The discussion revolves around the concept of custodial SU(2) approximate symmetry, particularly in the context of the Higgs mechanism and its implications in particle physics. Participants explore its definition, origins, and relevance in various Higgs models.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant inquires about the meaning of custodial SU(2) approximate symmetry, specifically in relation to its classification as a 5 or a 3, and its connection to Higgs triplet and charged Higgs contexts.
  • Another participant suggests that the concept of custodial symmetry may be linked to 't Hooft's naturalness principle, which posits that an approximate symmetry protects small mass scales, implying that if the symmetry were exact, the mass would be zero.
  • A reference to a paper is provided, indicating that the Higgs field can be classified according to its transformation properties under custodial SU(2) symmetry, but details are lacking.
  • One participant explains that custodial symmetry is a specific global symmetry in the Standard Model, distinguishing it from the gauged SU(2)_L and noting the existence of a global SU(2)_R symmetry that influences electroweak observables.
  • The same participant mentions that the transformation of the Higgs under custodial symmetry varies depending on the specific Higgs model being considered.

Areas of Agreement / Disagreement

Participants express varying levels of certainty regarding the context and implications of custodial symmetry, with some proposing connections to broader principles while others provide specific technical details. No consensus is reached on the exact nature or implications of custodial SU(2) symmetry.

Contextual Notes

Participants acknowledge a lack of detailed information regarding the classification of the Higgs field under custodial symmetry and the implications of hypercharge and fermion masses on electroweak observables.

thoms2543
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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.
 
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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.
 
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.
 
"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.
 
Thanks
 

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