LHC run 2, does Supersymmetry worsen hierarchy fine tuning

[kodama]

post-LHC run 2, does Supersymmetry worsen hierarchy fine tuning?

according to what most theorists argument, the SM has a hierarchy fine tuning in the Higgs sector based on naturalness. The proposed solution to this problem is supersymmetry.

post-LHC run 2, no SUSY partners and no hints of SUSY in decay rates of particles, has falsified the hypothesis of supersymmetry as a solution to the naturalness problem in the Higgs.

one possible answer is that the Higgs sector is simply fine-tuned. however unlikely and unnatural that may be, only 1 higgs boson and field is somehow fine tuned and if it is stable for some reason against quantum correction, its stability is NOT the result of supersymmetry.

given this

I wish to note some details.

The MSSM predicts two even-parity neutral Higgs particles, h and H0, one odd-parity Higgs particle, A, and two charged Higgs particles, H+ and H- (or two variants of one particle). The h and H0 have a 2*2 mass matrix, as one might expect.

If one of the MSSM parameters is high enough, then the H0, A, and H+- have masses close to each other, masses much greater than the h mass.

The MSSM has a "mu problem", from an interaction term (mu) * (Hu.Hd) (Hu and Hd are the two unbroken Higgs doublets in the MSSM). The problem with (mu) is lack of explanation of why it has an electroweak-scale mass rather than a GUT-scale mass. The NMSSM adds an additional Higgs particle, S, a Standard-Model gauge singlet. Electroweak symmetry breaking yields an additional even-parity neutral Higgs particle, an additional odd-party neutral Higgs particle, and an additional Higgsino. This means 3 even-party neutral Higgs particles, 2 odd-parity ones, and 5 neutralinos.

That additional particle S replaces the (mu) in the above mass term, and SUSY breaking makes an effective (mu) value. So in the NMSSM, all the electroweak-scale masses are due to SUSY breaking.

Turning to GUT's, SO(10) puts the Hu and the Hd in a single 10 (vector) multiplet H, and the elementary fermions into three generations of 16 (spinor) multiplets F. The S remains a gauge singlet in it.

However, going to E6, the H, the F, and the S can be part of a single fundamental 27 multiplet. The triplet interaction (27).(27).(27) is a gauge singlet and also symmetric in the fields. Breaking down to SO(10) gives interactions S.H.H and H.F.F -- what the NMSSM needs.

since supersymmetry doesn't solve the higgs fine tuning problem, doesn't adding 4 additional higgs boson and its associated fields, makes the higgs fine tuning problem worse?

in the SM, there is just 1 higgs that is predicted, discovered 1at 126 gev and it is apparently fine-tuned.

in SUSY, there are a total of 5 higgs, the other 4 are evidently higher mass, unknown how high, and they also have a fine-tuning problem, since supersymmetry doesn't predict their masses from quantum corrections, based on LHC results.

in SM the higgs only couples to the known particles of the SM, minus photon and possibly graviton. this results in a fine-tuning problem for 1 higgs.

in SUSY-extensions, the 1 higgs couples to known particles of the SM, minus photon and possibly graviton, plus all the SUSY-partners of them, plus an additional 4 higgs, plus any particles such as x-boson associated with GUT physics, if it exists.

in summary LHC run 2 results implies that if there is a supersymmetry, it doesn't solve the naturalness problem. with just the SM there is only 1 higgs field that needs to be fine-tuned. perhaps that is how nature is.

supersymmetry posits 4 additional higgs, plus many more particles, for a total of 5, all of which have a naturalness problem and fine-tuning problem, that SUSY doesn't solve.

it appears SUSY makes naturalness problem that it was supposed to solve, much worse, as it adds additional particles and higgs that have to be fine-tuned.

SUSY doesn't appear to solve the naturalness problem with 1 higgs we know about in the SM, based on LHC results, so positing 4 additional higgs means more complications ?

in terms of occam's razor, SUSY was posited to solve the fine-tuning naturalness problem of the higgs problem by positing that fermions and bosons contributions cancel each other out.
LHC run 2 results imply SUSY is falsified as an explanation. we are left with 1 higgs boson which may be fine-tuned. since susy doesn't solve the naturalness problem, SUSY posits 4 additional higgs that also have a fine-tuning problem, so a SUSY-SM is more complicated and even more fine-tuned.

occam's razor SM with 1 higgs fine tuned
SUSY - SM with 5 higgs fine tuning + 120+ parameters fine tuned so as to avoid falsification with LHC/tevatron having SUSY partners that tevatron or LHC should have seen, but did not.

occam's razor SM with 1 higgs fine tuned is simpler.
how do SUSY theorists explain the stability of the additional higgs bosons since SUSY doesn't seem to do the job?

 

[lpetrich]

SUSY itself does the stabilizing, with the Higgs particles having fermionic partners, the higgsinos. The problem is if SUSY gets broken at too high energies. There is then a big SUSY-less gap between SUSY breaking and the electroweak energy scale.

 

[kodama]

SUSY itself does the stabilizing, with the Higgs particles having fermionic partners, the higgsinos. The problem is if SUSY gets broken at too high energies. There is then a big SUSY-less gap between SUSY breaking and the electroweak energy scale.

the LHC results imply that SUSY is broken "at too high energies" so it doesn't stablize