I 5 Higgs-like bosons -- natural supersymmetry required?

[lpetrich]

Yes they would, if their masses are low enough for them to be produced by the LHC.

They would likely be produced in much the same way that the SM Higgs is produced, and their production cross sections and decays are likely similar. That means that it may be hard to search for them, since they may not have decays that stand up above the background very much.

But that's why the LHC will eventually get its High Luminosity upgrade, to search for particles and decay modes that are less distinguishable from the LHC's background than what it can currently see.

 

[kodama]

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.

Yes they would, if their masses are low enough for them to be produced by the LHC.

They would likely be produced in much the same way that the SM Higgs is produced, and their production cross sections and decays are likely similar. That means that it may be hard to search for them, since they may not have decays that stand up above the background very much.

But that's why the LHC will eventually get its High Luminosity upgrade, to search for particles and decay modes that are less distinguishable from the LHC's background than what it can currently see.

wouldn't a higher energy upgrade to 28-33TEV be even more useful?

 

[lpetrich]

True, but it would be difficult to keep the accelerated protons in the accelerator. The magnets' field strength would have to be over twice as great to steer them in place (Gyroradius - Wikipedia). The Large Hadron Collider has a radius of 4.3 km, and here's what magnetic field is necessary to get up to these energies:

• 6.5 TeV - 5.0 T (LHC now)
• 7 TeV - 5.4 T (LHC design)
• 14 TeV - 10.7 T
• 16.5 TeV - 12.7 T
• 28 TeV - 21 T
• 33 TeV - 25 T

The actual maximum field of the LHC's steering magnets is 7.7 T.

The synchrotron-radiation energy loss is proportional to (E⁴*v²)/(m⁴*r²) (E, v, m = particle energy, velocity, mass, r = radius of particle path). The previous occupant of the LHC's tunnels, the LEP, was an e-e+ collider. It was limited to 104.5 GeV per particle. If the LHC was limited by synchrotron-radiation losses, then it could go up to about 200 TeV.

That's why proposals for more energy involve building larger accelerators.

 

[kodama]

just replace the 5.4 T magnets with 25 T

 

[lpetrich]

just replace the 5.4 T magnets with 25 T

Has anyone ever built 25-tesla electromagnets? Is there any superconductor that won't be quenched by a magnetic field that strong?

 

[Dr.AbeNikIanEdL]

Well, https://en.wikipedia.org/wiki/Superconducting_magnet#History lists 26.8 T as world record. Of course, this does not mean you have this ready to use in an accelerator. Have a look at e.g. these slides https://indico.cern.ch/event/521926/attachments/1310549/1960888/160718_summer-students_II_final.pdf shown at a summer school this year. Anything above ~15 T seems be far in the future with time scales "beyond 2035". I am not in this field, and others might have different opinions on future developments, but I think it is clear that this is not as easy as "just replace the magnets"...

 

[arivero]

MSSM and nMSSM require 5 higgs like bosons

Is 5 the minimum?

From degrees of freedom I would expect some susy theory with only three, consider a neutral higgsino weyl, and a charged one dirac. Only six spartners. Three dof are eaten to give mass to the Z and W and the other three are H0 H+ and H-

Another look: a massive gauge supermultiplet is one spin 1 particle, two Weyl fermions, one scalar. We have three massive particles, so three scalars.

 

[kodama]

do these additional higgs fields also generate mass in elementary particles? and since the LHC hasn't seen them, do they have to have masses higher than energies LHC can probe?

 

[Vanadium 50]

Is 5 the minimum?

Yes. You need different Higgs fields to couple to u-type and d-type quarks. The problem isn't the quarks, strictly speaking: it's the squarks. In supersymmetric theories the scalars belong to chiral multiplets and their complex conjugates belong to multiplets of the opposite chirality; because multiplets of different chiralities cannot couple together in the Lagrangian, a single Higgs doublet is unable to give mass simultaneously to the u-type and d-type quarks. The same argument holds for leptons if the neutrino is Dirac.

 

[kodama]

Yes. You need different Higgs fields to couple to u-type and d-type quarks. The problem isn't the quarks, strictly speaking: it's the squarks. In supersymmetric theories the scalars belong to chiral multiplets and their complex conjugates belong to multiplets of the opposite chirality; because multiplets of different chiralities cannot couple together in the Lagrangian, a single Higgs doublet is unable to give mass simultaneously to the u-type and d-type quarks. The same argument holds for leptons if the neutrino is Dirac.

does this provide any predictions lhc can see with regards to the 1 higgs they see