Understanding Supersymmetry and Symmetry Breaking in the Higgs Sector

[Safinaz]

Hi guys,

I have a question about symmetry breaking in Susy, I hope it won't be so naive that I just started to study supersymmetry ..

The question is that there are two Higgs doublets in Susy, H_u and H_d, how these two doublets first break supersymmetry at high energy scale and then make electroweak symmetry breaking at MZ scale ? It is not possible to take VeV. twice ..

I think the scale of Susy breakings is higher because Susy particles are heavier than their SM
partner so they have not found yet ..

I saw the equations where H_u and H_d couple to Susy particles like sleptons and squarks and where they couple to SM particles .. so what's happen ?


Bests,
S.S.

 

[ChrisVer]

The reason you need two Higgs doublets in MSSM is to break the electroweak symmetry, and not SuSy. What breaks SuSy is still an unclear topic, and a very complicated one. At first someone, in order to break SuSy, introduces some soft breaking terms in the scalar potential which then lead to SuSy SSB. These soft terms may come from a hidden sector which is somehow mediated to MSSM and causes its breakdown, and the reason it's unclear is because there are many suggestions about this Hidden Sector mediation, for example:
1. gravity (Sugra)
2. Gauge
3. Anomaly
The reason you need a 2nd Higgs doublet is for an anomaly cancelation occurring due to the 1st field's higgsino (fermion with Y=-1/2)
I don't understand the other question about their coupling, what's the point? In general you can allow Yukawa terms in the superpotential, which give those couplings of Higgses and Higgsinos with particles/sparticles.

 

[ofirg]

The second higgs doublet is needed to have a lamda term to your Higgs potential. Your superpotential due to renormalizability cannot accept a term like H_{u,d}^{4} for example

I believe This not true. Event with one doublet, you would get quartic terms in your Lagrangian as in the SM from the D term scalar potential part.

The reason two doublet are needed is twofold.

1) It is not possible to couple a single Higgs doublet to the up and down type quarks in a supersymmetric way, and thus give masses to all quarks. Two doublets are needed.

2) Higgs doublets also have their fermionic partners, which are chiral in this case. They contribute to dangerous gauge anomalies and two are needed with opposite hypercharge for these to cancel.

 

[ChrisVer]

Yes ofirg, that was not true, that's why I corrected it. Fortunately the OP was still offline before the corrections :)