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From the Theory Group: Could Quarks and Leptons be Supersymmetric Bound States?

(Image - preons)
 (Image courtesy Gonzalo Torroba.)

The Standard Model of particle physics has been extremely successful in describing the interactions and behaviors of subatomic particles, but many important puzzles remain. One mystery is the origin of the masses for particles called quarks, which make up protons and neutrons, and leptons, of which the best known is the electron. These masses vary widely; for example, the lightest quark, the "up" quark, is lighter than the heaviest quark, the "top" quark, by a factor of 100,000. The Standard Model does not explain the mass ratios between quarks and leptons. Leading theories of physics beyond the Standard Model, such as the popular theory of supersymmetry, also do not address this question.

In the weak interactions of the Standard Model, also called the weak nuclear force, interrelationships between the various quarks have been found to correspond to entries in a model called the Cabbibo-Kobayashi-Maskawa matrix. These matrix entries follow an intricate pattern related to the quark masses. However, the Standard Model does not explain the origin of this matrix, and so does not explain the mass ratios between the quarks or why they show the decay patterns observed in particle experiments. Leading theories of physics beyond the Standard Model, such as the popular theory of supersymmetry, also do not address these questions.

Supersymmetry is the idea that every particle in nature has an associated particle of opposite characteristics—for every elementary particle of matter, or fermion, there is a force-carrying particle called a boson, and vice versa. This theory is interesting to particle physicists because it addresses another question: why all known fundamental particles that have mass are so much smaller than the so-called Planck mass, which arises naturally from fundamental values such as the speed of light and the strength of gravity.

Particle theory indicates that the masses of quarks, leptons and weak bosons are related to the mass of the Higgs boson. In the Standard Model, a mass for the Higgs that results in the correct masses for quarks, leptons, and weak bosons can be reached only by making extremely precise adjustments to the model that are not required by the theory. In contrast, in models with supersymmetry, those adjustments automatically take place—if the supersymmetric partners of quarks and leptons have masses of less than about 1 TeV. Hopefully, such particles will be within the range of the Large Hadron Collider, so answers could be right around the corner.

This explanation raises another question, however: Where did the masses of the supersymmetric partner particles come from? There is no definite answer to that question.

Particle theorists have speculated for a long time that quarks and leptons could be composites of more fundamental particles called preons, which could address the questions of quark and lepton masses and decay characteristics. If the lightest quarks and leptons—the up and down quarks and the electron—are not fundamental particles but are actually composites of preons in what is called a "bound state" (in the same way three quarks make up a proton or neutron), the Higgs field might have less of an effect on them. This could lead to the smaller masses we observe for these particles.

The problem with this idea is that the light quarks and the electron seem to behave as elementary particles in high-energy collisions; that is, they don't seem to break up into smaller constituents. If these particles are composed of preons, the preons must interact through very massive particles and the binding energies required must be more than a million times greater than the actual masses of the quarks and leptons. (Here, it's important to remember that mass and energy are equivalent—at these quantum scales, mass is energy, and energy is mass.)

Surprisingly, supersymmetry can explain how this could be, that preons could form bound states with masses much less than their binding energy. Nathan Seiberg, at the Institute for Advanced Study, showed that these supersymmetric theories can even have bound states with zero mass. These theories have a remarkable feature, now called "Seiberg duality," in which the strongly interacting model of preons can look like a model of elementary particles with simpler interactions—like the quarks and electrons observed in particle experiments.

In the past year, I have been working with colleagues at Stanford, SLAC and the Kavli Institute for Theoretical Physics at Santa Barbara to turn these ideas into a complete theory of quark and lepton masses. The key to our approach is to use supersymmetry and the idea of composite light quarks and leptons together in the same package. We have been able to construct models in which bound states appear with different numbers of preons. The one-preon states are the heavy fermions—top, bottom, and tau—and their supersymmetric partners. The quarks and leptons with more preons have successively smaller masses. These models naturally give a hierarchical pattern of quark and lepton masses.

Our models share the beautiful feature of more typical supersymmetric models in which the electromagnetic force, the strong force and the weak force all come together at high energies to form a simple "grand unified" theory. However, other features of our models differ from the usual cases. In most models of supersymmetry, the masses of superparticles are generated by a set of interactions that have no relation to the properties of Standard Model particles and are very difficult to observe. In our models, a single new set of interactions creates the binding of preons into quarks and leptons and also generates the masses of the supersymmetry partners of these particles. In the currently popular supersymmetric models, the partners of all quarks and leptons have masses of roughly the same size. Our models have a different structure in which the partners of the heavy quarks and leptons have masses near 1 TeV, while the partners of the lighter quarks and leptons are much heavier. This feature allows our type of model to be distinguished from other models experimentally.

Though much work remains to be done, we are very excited with the prospects offered by these models, in which supersymmetry and preon bound states are built around a single new interaction. It amazes us to think that our new approach could finally lead to the correct fundamental theory of particles.

—Gonzalo Torroba
SLAC Today, November 11, 2010