More About Supersymmetry

 

First of all, is a photo of Peter Higgs as a young man in 1954, about the time that he developed the Higgs theory.

Next, in the discussion of SUSY, I didn’t include a diagram showing the SUSY particles in the simplest theory called the Minimal Supersymmetric Standard Model or MSSM.  For this I have to explain that the spin 1/2 (fermions) quarks and leptons have by quantum mechanics only two possible spin alignments:  one along the direction of motion, called left handed, with angular momentum +1/2 along that direction (in units of h/(2 pi) (where h is Planck’s constant); and the other called right handed, with angular momentum of -1/2 along the direction of motion.  It turns out that only the left handed quarks and leptons (labeled by subscript L in the figure below) participate in the weak interaction, and are the weak isospin doublet.  The right handed quarks and leptons (labeled by R) do not participate and are weak isospin singlets.  I also forgot to mention that there are five spinless higgs states that aren’t supersymmetric in the MSSM: neutral ones called called h, H, A; and positive and negative H states.  The figure is courtesy of the Japanese high energy physics lab called KEK.

The neutralino that could be the dark matter is the lightest combination of the supersymmetric Z (Zino), photon (photino), and superpartners h and H (higgsinos).

I also wanted to add a graph showing that in the MSSM model of Supersymmetry, the couplings of the three standard model forces: electromagnetism, the weak interactions, and the gluonic strong interactions all come together at a “unification scale” of about 10^16 GeV.  Dynamics have shown that couplings and masses are dependent on the distance or energy scale at which they are measured.  In field theory, the particles surround themselves with clouds of virtual particles that they can couple to.  At shorter distances one gets closer to their “bare”coupling strength.  It is these bare coupling strengths that come together.  Since the reciprocals of the couplings move linearly with the log of the energy, it is convenient to show the graph of the reciprocals of the couplings with energy.

The curves labeled SU(3) are for the gluonic strong interactions with the three “colors” of quarks.  The curves labeled SU(2) are for the weak interactions with the two up and down possibilities for quarks and leptons.  The curves labeled U(1) are for the single photon of electromagnetic interactions.  The green lines show that with only the standard model, as the energy scale increases, the inverse of the three different force coupling miss each other and do not unify.  On the other hand, with the introduction of SUSY superpartners at around the 1 TeV or 1,000 GeV scale denoted by the vertical yellow line, the SUSY lines have kinks, and then the lines of couplings do meet at 10^16 GeV at the GUT or Grand Unified Theory point.  This evidence for Supersymmetry has been known for a few decades.

 

About Dennis SILVERMAN

I am a retired Professor of Physics and Astronomy at U C Irvine. For a decade I have been active in learning about energy and the environment, and in lecturing and attending classes at the Osher Lifelong Learning Institute (OLLI) at UC Irvine.
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