Custodial symmetry

In particle physics, a symmetry that remains after spontaneous symmetry breaking that can prevent higher-order radiative corrections from spoiling some property of a theory is called a custodial symmetry. In the Standard Model of particle physics, the custodial symmetry is a residual global SU(2) symmetry of the Higgs potential beyond the basic SU(2)×U(1) gauge symmetry of the Weak Interaction that prevents higher-order radiative-corrections from driving the Standard Model parameter away from ≈ 1 after spontaneous symmetry breaking. (Note: is a ratio involving the masses of the weak bosons and the Weinberg angle). With one or more electroweak Higgs doublets in the Higgs sector, the effective action term which generically arises with physics beyond the Standard Model at the scale Λ contributes to the Peskin–Takeuchi parameter T. Current precision electroweak measurements restrict Λ to more than a few TeV. Attempts to solve the gauge hierarchy problem generically require the addition of new particles below that scale, however. Before electroweak symmetry breaking there was a global SU(2)xSU(2) symmetry in the Higgs potential, which is broken to just SU(2) after electroweak symmetry breaking. This remnant symmetry is called custodial symmetry. The total standard model lagrangian would be custodial symmetric if the yukawa couplings are the same, i.e. Yu=Yd and hypercharge coupling is zero. It is very important to see beyond the standard model effect by including new terms which violate custodial symmetry. The preferred way of preventing the term from being generated is to introduce an approximate symmetry which acts upon the Higgs sector. In addition to the gauged SU(2)W which acts exactly upon the Higgs doublets, we will also introduce another approximate global SU(2)R symmetry which also acts upon the Higgs doublet. The Higgs doublet is now a real representation (2,2) of SU(2)L × SU(2)R with four real components. Here, we have relabeled W as L following the standard convention.