# supersymmetry

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## supersymmetry

**supersymmetry,**in physics, theory concerning the relationship of the elementary particles called boson to those known as fermions, and vice versa, and linking the four fundamental forces. In supersymmetry every ordinary elementary particle has as its counterpart a supersymmetric particle, or superparticle, with similar properties except for angular momentum, or “spin,” which differs by a half unit. According to supersymmetry, each ordinary fermion has a superpartner that is a boson, and each ordinary boson has a superpartner that is a fermion. The superpartners of fermions are named by adding the prefix

*s-*to the fermion's name, e.g., the squark is the quark's counterpart, and those of bosons by adding the suffix

*-ino*to the root of the boson's name, e.g., the photino is the photon's counterpart. Proof of the theory—discovery of the predicted particles through their creation and detection in a particle accelerator—requires extremely high energy levels, and it was hoped that the Large Hadron Collider would provide evidence for supersymmetry, but a lack of evidence for the existence of superpartner particles as predicted by the simple version of supersymmetry has called the theory into question. See also string theory.

## Supersymmetry

A conjectured enhanced symmetry of the laws of nature that would relate two fundamental observed classes of particles, bosons and fermions.

All particles can be classified as fermions, such as the electron and quarks, or bosons, such as the photon and graviton. A fundamental characteristic distinguishing these two classes is that they carry different quantum-mechanical spin. If the amount of spin of an elementary particle is measured in terms of the fundamental quantum unit of angular momentum—, equal to Planck's constant divided by 2&pgr;—then bosons always have integer amounts of spin (that is, 0, 1, 2 …), while fermions have odd half-integer amounts of spin (that is, 1/2, 3/2, 5/2, …). *See* Spin (quantum mechanics)

There is seemingly a fundamental distinction between particles with differing amounts of spin. For example, bosons like to act collectively (Bose-Einstein statistics), producing such distinctive behavior as the laser, while, conversely, fermions obey the Pauli exclusion principle (and the Pauli-Dirac statistics), which disallows two identical fermions to be in the same state, and explains the stability of matter. Moreover, all the symmetries that are observed in the world relate different particles of the same spin. *See* Bose-Einstein statistics, Fermi-Dirac statistics, Quantum statistics, Symmetry laws (physics)

In contrast, supersymmetry would relate bosons and fermions. This would be a remarkable step forward in understanding the physical world. However, if supersymmetry were realized as an exact symmetry, the particles so related should have almost all their characteristics, such as mass and charge, preserved. Explicitly, any fermion of spin 1/2 should have a boson superpartner of spin 0, while any gauge boson of spin 1 should have a fermion superpartner of spin 1/2. This is apparently a disaster for the idea of supersymmetry since it predicts, for instance, that there should exist a spin-0 boson partner of the electron, the selectron, with electric charge and mass equal to that of the electron. Such a particle would be easy to detect and is certainly ruled out by very many experiments.

The crucial caveat to this negative result is the condition that supersymmetry be realized as an exact symmetry. A fundamental concept of modern physics is spontaneously broken symmetry. Physics displays many examples of symmetries that are exact symmetries of the fundamental equations describing a system, but not of their solutions. In particle physics the spontaneous breaking of a symmetry usually results in a difference in the masses of the particles related by the symmetry; the amount of breaking can be quantified by this mass difference. *See* Symmetry breaking

If supersymmetry is broken by a large amount, then all the superpartners have masses much greater than the particles that are currently observed, and there is little hope of seeing evidence for supersymmetry. However, evidence that supersymmetry is broken by only a moderate amount comes from examination of the properties of the fundamental forces at high energy.

Of the four fundamental forces, the three excluding gravity are very similar in their basic formulation; they are all described by gauge theories, generalizations of the quantum theory of electromagnetism, and quantum electrodynamics (QED). The strength of electrical interaction between two electrons can be quantified in terms of a number, the coupling constant α_{1}. However, the quantity α_{1} is actually not a constant, but depends on the energies at which the interaction strength is measured. In fact, the interaction strengths, α_{1}, α_{2}, and α_{3}, of the three forces (excluding gravity) all depend on energy, μ. The couplings α_{1,2,3} satisfy differential equations—renormalization group equations—that depend on the types of elementary particles that exist with mass at or below the energy scale μ and that are charged with respect to each of the three interactions. If the fundamental particles include not only the observed particles but also their superpartners, taken to have masses not greater than 1000 GeV heavier than their (observed) partners, then from the renormalization group equations, the couplings α_{i} are predicted to meet (unify) at a huge energy of 2 × 10^{16} GeV. In contrast, if either supersymmetry is not an underlying symmetry of the world, or it is very badly broken so that the superpartners are very massive, the couplings fail to unify at a single point. *See* Fundamental interactions, Quantum electrodynamics, Renormalization

Although the unification of couplings is the most significant indication that supersymmetry is a new law of nature, there are a number of other hints in this same direction. By observing the large-scale motions of the galaxies, the average density of large volumes of the universe can be deduced, resulting in a value that is substantially greater than that directly observed in luminous matter such as stars and hot gas. Therefore, a substantial fraction of the mass of the universe must be composed of some form of nonluminous or dark matter. Remarkably, many attractive models of supersymmetry predict that the lightest of all the superpartners is a weakly interacting massive particle with just the right characteristics to be this dark matter. *See* Weakly interacting massive particle (WIMP)

## supersymmetry

(soo-per-**sim**-ĕ-tree) (SUSY) An extension of the theories (GUTs) seeking to unify the four fundamental forces of nature. It unifies the particles called fermions (with half-integral spin) and the force particles, the bosons (with integral spin). In the simplest SUSY models, this leads to a new family of particles as every fermion has a supersymmetric boson partner and every boson has a supersymmetric fermion partner; for example,

*photinos*and

*gravitinos*are the hypothesized partners of the photon and graviton. Adding supersymmetric particles to the standard model of elementary particles remedies some of its discrepancies, but there is no experimental evidence for them. See also dark matter.