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
In which sense this is a "approximate" symmetry? How can a symmetry be approximate?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[itex]\rightarrow[/itex]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[itex]\pm[/itex],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 said:In which sense this is a "approximate" symmetry? How can a symmetry be approximate?
Custodial symmetry is a mathematical concept in the Standard Model of particle physics that relates the properties of different types of particles. Specifically, it ensures that the left- and right-handed versions of a particle have the same mass and coupling strength.
Custodial symmetry helps to explain why certain particles, such as the W and Z bosons, have similar properties despite being different types of particles. It also helps to maintain the overall consistency and accuracy of the Standard Model.
The Higgs mechanism, which gives particles their mass, is closely linked to custodial symmetry. In order for the Higgs mechanism to work, custodial symmetry must be present in the equations describing particle interactions.
While custodial symmetry is an important concept in the Standard Model, it is not a fundamental principle and can be broken in certain situations. For example, in theories beyond the Standard Model, custodial symmetry may be violated, leading to different predictions for particle interactions.
Custodial symmetry can be tested by measuring the properties of particles, such as their masses and couplings, and comparing them to the predictions of the Standard Model. If custodial symmetry is broken, these measurements may deviate from the expected values, providing evidence for new physics beyond the Standard Model.