Supersymmetric theories predicted that the elementary particles of the standard theory of particle physics (leptons, quarks, photon, gluons, W- and Z-boson, Higgs boson) have supersymmetric partners. This supersymmetric particles (called neutralinos, photino, gluinos, Winos, Zinos, squarks, and sleptons) were all predicted to have rest masses between 50 and 300 GeV (billion electron volts).

Now the ATLAS Collaboration of the LHC (Large Hadron Collider) presented data (arXiv: 1102.2357) which do not confirm the gluino. It would have been detected if its rest mass were less than 700 GeV.

I am not so surprised that signs of light supersymmetric particles have not been detected. I predict that supersymmetry will not be confirmed. My arguments are the following.

(1) The main reason for supersymmetry is that it can explain some shortcomings of minimal Grand Unified Theories, i. e. the mass-hierarchy problem (i. e. the fact that W- and Z-boson do not have rest masses of 10^15 GeV, although they should have “eaten” (coupled to) the Higgs bosons of Grand Unification) and the non-observation of the proton decay (lower limit: mean proton lifetime of 10^33 years).

But this argument requires that there is Grand Unification.

In 1997 I suggested (Modern Physics Letters A 12, 3153 – 3159 = hep-ph/9708394) a generalization of quantum electrodynamics, called quantum electromagnetodynamics. This theory is based on the gauge group U(1) x U’(1). In contrast to QED it describes electricity and magnetism as symmetrical as possible. Moreover it explains the quantization of electric charge. It includes electric and magnetic charges (Dirac magnetic monopoles) and two kinds of photon, the conventional Einstein electric photon and the hypothetical Salam magnetic photon. The electric-magnetic duality of this theory reads:

electric charge — magnetic charge
electric current — magnetic current
electric conductivity — magnetic conductivity
electric field strength — magnetic field strength
electric four-potential — magnetic four-potential
electric photon — magnetic photon
electric field constant — magnetic field constant
dielectricity number — magnetic permeability

Because of the U(1) x U’(1) group structure and the Dirac quantization condition e * g = h (unit electric charge times unit magnetic charge is equal to the Planck constant), this theory is hard to agree with Grand Unification. Although a group such as SU(5) x SU’(5) is in principle not impossible.

(2) Another reason for supersymmetry is that it can explain the existence of (anti-symmetrical) fermions in an otherwise symmetrical theory (such as Special Relativity and General Relativity).

However, it has long been known that a generalization of General Relativity which includes anti-symmetry is Einstein-Cartan theory. The affine connection of this theory includes not only the non-Lorentz invariant symmetrical Christoffel symbol but also the Lorentz invariant anti-symmetrical Torsion tensor.

Within the framework of a quantum field theory, the Torsion tensor corresponds to a spin-three boson called tordion, which was introduced in 1976 by F. W. Hehl et al.: Reviews of Modern Physics 48 (1976) 393 – 416.

In 1999 I discussed (International Journal of Modern Physics A 14, 2531-2535 = arXiv: gr-qc/9806026) the properties of the tordion. Moreover I sugested that the electric-magnetic duality is analogous to the mass-spin duality. This analogy reads:

electric charge — magnetic charge – mass — spin

electric field constant — magnetic field constant — gravitational constant — reduced Planck constant

electric four-potential — magnetic four-potential — metric tensor — torsion tensor

electric photon — magnetic photon — graviton — tordion

(3) Supersymmetric theories including superstring and M theory have not much predictive power. For example, so far no one has shown that these theories predict the empirically obvious Naturkonstanten-Gleichung (fundamental equation of unified field theory, Modern Physics Letters A 14, 1917-1922 = arXiv: astro-ph/9908356):

ln (kappa * c * H * M) = −1 / alpha

where kappa is the Einstein field constant, c is the speed of light, H is the Hubble constant, M is the Planck mass, and alpha is the fine-structure constant. By using the WMAP−5 value

H = (70.5 +/- 1.3) km / (s * Mpc)

(E. Komatsu et al.: Astrophys. J. Suppl. Series 180 (2009) 330 – 376) the left-hand side yields

ln (kappa * c * H * M) = – 137.025(19)

which is within the error bars equal to

- 1 / alpha = – 137.035 999 679(94)

The Naturkonstanten-Gleichung predicts the Hubble constant to be

H = 69.734(4) km / (s * Mpc)

I must be in a dreadful mood as I’m picking on all of Sean’s posts tonight (sorry!). You say “One new thing we would like to see is supersymmetry.” Like? I think it is dangerous when we attach good/bad terms to finding or excluding a result or theory. The conclusion of the post is far better.

I’m rather grateful that as a chemist I only have to deal with electrons.

Good questions. I think the gluinos and squarks have the best chance of being detected early, simply because they are coloured, and therefore should be produced relatively copiously in the LHC collisions. Other superpartners have to be produced via weak or electromagnetic interactions, and therefore require more data to be taken.

In simple models of SUSY breaking, there are some rules about what happens to the masses, a bit like you suggest. However, ‘realistic’ models of SUSY breaking have a hidden sector which actually does the breaking, and this is then communicated to the standard model fields via ‘messengers’. Quite generically, the result is that the coloured superpartners tend to be heavier, with the sleptons, charginos and neutralinos lighter. This is roughly because gauge interactions drive the masses up, so stronger gauge interactions lead to larger masses.

It’s a Frank Sinatra universe, folks. Do not deny.

Is like the splitting of identical energylevels in molecular quantum chemistry, where one goes up as much (or a bit more) than the other goes down? That is to say, will the lightest SUSY ‘thingie’ be the twin of the heaviest normal stuff, which I guess in the top, or is it not as simple as that?

See slides 12, 21 and 23 of

http://indico.cern.ch/contributionDisplay.py?sessionId=31&contribId=44&confId=103979