# What does radiatively stable mean?

In the wiki page for MSSM(Minimal Supersymmetric Standard Model) there is "The Higgs boson mass of the Standard Model is unstable to quantum corrections and the theory predicts that weak scale should be much weaker than what is observed to be. In the MSSM, the Higgs boson has a fermionic superpartner, the Higgsino, that has the same mass as it would if supersymmetry were an exact symmetry. Because fermion masses are radiatively stable, the Higgs mass inherits this stability.". What does radiatively stable mean?

• I think you can obtain the answer yourself by looking up "radiative." I am sure you already know what "stable" means. – Guill Aug 2 '17 at 7:45
• @Guill - I don't mean to be rude, but if somebody asks "What is Supersymmetry", you can't just say look up for "symmetry" and you already know what "super" means. I think QFT is much more intricate that the nomenclature is not usually straightforward. – Invariance Aug 2 '17 at 11:39
• @Invariance: It was not my intention to answer the question, but only to give the OP a "hint." If it is not enough of a hint, I expect the OP to say so. – Guill Aug 3 '17 at 7:26
• @Guill Invariance is the OP. – pfnuesel Aug 3 '17 at 15:02

## 1 Answer

Fermion masses are radiatively stable because they are protected by a symmetry.

Massless fermions enjoy a chiral symmetry which separately rotates their left and right components. This symmetry ensures that there can be no radiative corrections which cause the massless fermions to become massive.

But let's imagine our fermions are not massless, that they have a tiny mass, $\delta m$. Let's treat this term as a perturbation to the theory with massless fermions. If we take the limit as $\delta m\rightarrow 0$, we must find that all the corrections to the masses of the fermions go to 0 as well. This can only be true if corrections to the mass of the fermions are proportional to $\delta m$ itself. This ensures that if $\delta m$ is small, corrections will be small as well.

This is what we mean by "Radiatively Stable", this Higgs mass in the Standard Model is NOT protected by such a symmetry, so there is nothing protecting it from receving large corrections to its mass. Supersymmetry protects this Higgs because it gives the Higgs a parter fermion, the Higgsino. The Higgsino is a fermion, so its mass IS protected by chiral symmetry just like in our example above. But the Higgs and the Higgsino are related by supersymmetry, so the Higgs inherits this protection.