Supersymmetry, "Sparticles," and Grand Unification Theories

A diagram for R-parity violating rapid proton decay described in a supersymmetric theory.

In a recent unit for a class I am currently taking,* known to my peers as “Honors Earth and Space Sciences,” I learned about the different types of minerals and the composition of the atom. While taking a test for the unit, I was asked, “Which of these options is NOT a building block of the atom?” The four possible answers included the electron, the proton, the neutron, and the selectron. Obviously, assuming that we are not considering any superpartner particles, then the selectron is certainly not a building block of the atom. Naturally curious as I was, however, I looked the selectron up; immediately, I fell into the rabbit hole and began learning about selectrons and, more broadly, sfermions, the superpartner particle group of the fermions.

Interested as I was in learning about supersymmetry, I decided to write an entry on it, this one being entry twenty-six. As I assume is known, let us now consider supersymmetry and its roles in physics, astronomy, and quantum mechanics.

A snapshot of supersymmetry’s origins

Although most of the breakthroughs in particle physics occurred during the late nineteenth and early twentieth centuries, the history of supersymmetry is far more recent; even the very hypothesis of supersymmetry is less than sixty years old. Such a young discovery is a demonstration that science is a profound mechanism for instantaneous growth and progression, as even some of the greatest advancements in scientific history are younger than some of us (even the Higgs mechanism, discovered in 2012, is younger than me).

The existence of supersymmetry was first proposed in 1966 by the physicist Hironari Miyazawa, who envisioned unifying mesons–unstable matter composed of an equal number of quarks and antiquarks bound together through the strong interaction–and baryons, which carries an odd number of valence quarks, notably three–such as in protons and neutrons. Miyazawa did not hypothesize in the context of spacetime, but rather in the context of internal symmetry, a major blunder on his part. As such, the paper was initially largely ignored.

In 1971, however, physicists J.L. Gervais and Bunji Sakita rediscovered supersymmetry in what was known as the Gervais-Sakita rediscovery, and extrapolated it to quantum field theory and, therefore, spacetime. They, as well as the many other physicists who discovered supersymmetry independent of them, helped formalize a relationship between bosons–the elementary particles that act as carriers for masses and the fundamental interactions–and fermions, the building blocks of matter. 

Subsequent advances helped justify the theory in the context of particle physics and other core concepts of physics; in 1974, for example, Julius Wess and Bruno Zumino formulated the features of four-dimensional supersymmetric field theories. Subsequently, they and their colleague, Abdus Salam, applied supersymmetry to various particle models.

Supersymmetry, although not readily observable, is fundamental to modern physics. Its mathematical structure–the graded Lie superalgebra–has been applied to numerous fields of study, including nuclear physics, critical phenomena, quantum mechanics, statistical physics, as well as many other fields. As it is accurate and so applicable to other concepts of physics, models of quantum mechanics or particle physics generally must cater to supersymmetry.

The fundamentals of supersymmetry

Before we delve deeper, let us first understand supersymmetry’s most simple definition: that it is a proposed relationship between two classes of particles–bosons and fermions. Bosons are particles with integer valued spins that transfer masses and interactions, and fermions are particles with half-integer valued spins (including, for example, quarks and electrons).

Relating the unification of bosons and fermions to Standard Model particles, a particle in one group, such as an electron–a fermion with spin ½–would have a superpartner particle in the other group, such as a selectron–a boson with spin 0–whose spins differ by ½. Consider further the fermion and the boson: the boson has an integer-valued spin while the fermion has a half-integer valued spin. So, for any boson and fermion pair, the difference between the spin of the fermion and that of the boson would be a half-integer value. In every respect, supersymmetry is not this simple, but the concept of spin is critical to supersymmetry as a whole.

As we now understand the broadest ideas of supersymmetry and superpartner particles, we may be compelled into question: How could supersymmetry exist when all bosons and fermions have a difference of a half integer spin between one another? Or how can fermions have bosonic superpartners and vice versa when they do not have symmetrical spins? 

Supersymmetry involves supersymmetrical versions of each particle (“sparticles”) in the Standard Model: each boson has a bosino superpartner, and each fermion has an sfermionic partner. Sparticles have equal values to their Standard Model counterparts for every physical quantity–excluding spin and, depending on the particle, mass. Although fermions and bosons are reliably different from one another,** they still possess the ability to be symmetrical to their sparticle counterparts.

Supersymmetry, as with many other concepts in particle physics, has yet to be experimentally confirmed. As of yet, the Large Hadron Collider–which is the foremost device for detecting supersymmetric particles–has yet to observe or document any sparticles; as such, supersymmetry remains a purely theoretical concept, which essentially conveys that the idea has yet to be proven in a practical setting.

Applications and solutions

Supersymmetry, although hypothetical, is an important candidate solution for various issues in particle physics and quantum mechanics. In this section, let us consider some of the many questions in physics that supersymmetry could solve.

First and foremost, one of the most significant problems of physics pertains to finding a grand unification theory for three of the fundamental forces–that is, electromagnetism and the strong and weak nuclear forces. If supersymmetry were implemented into the Standard Model, the contributions of the supersymmetric particles would cancel out the contributions of the other particles to the Higgs mass, which solves a quandary over the Higgs boson’s mass (and thereby in supersymmetric particles), perhaps resolving the hierarchy problem–a discrepancy between the relative strength of the weak force and gravitational force. If implemented into the Standard Model, the fundamental forces described in the Standard Model could have the exact same strength at high energy levels, thereby relating them to one another.

Another significant achievement that supersymmetry will foster is the unification of the fermions and the bosons. As was considered earlier in this entry, supersymmetry is defined as a relationship between two particles of different classes, notably bosons and fermions, which results in a half-integer difference between their spins and the similarity of most other quantities (excluding, sometimes, mass).

In addition, it is believed that the lightest supersymmetric particle in the extended Standard Model would be stable, electrically neutral, and weakly interacting–all of which describe current observations of dark matter. Dark matter is believed to be composed of a lighter particle that is stable, “weakly interacting,” and electrically neutral; when the superpartners of Z-bosons, photons, and neutral Higgs bosons mix (that is, become a superposition of quantum states), the result is a neutralino, which fulfills most of these requirements; nevertheless, the neutralino, as with every other candidate particle for dark matter, is hampered by a lack of observational evidence.

As mentioned earlier, supersymmetry is a candidate solution to the hierarchy problem. The hierarchy problem acknowledges the vast discrepancies between aspects of the various forces, most notably the difference in relative strength between the weak nuclear force and the gravitational force (the weak nuclear force is 1024 times stronger than the gravitational force). Consider, for example (see “References” for the full analogy), that there exist four parameters that determine a certain value for any fundamental object in the universe: in one specific characteristic, the four parameters have relative strengths of 1.2, 1.31, .9, and 4x1029. Though the forces in the universe seem so balanced as to not create such a wild discrepancy, the discrepancy does, in fact, exist; in particle physics, some of these discrepancies are even larger than that listed above. We may, as a result, be inclined to ask, how could the universe have arisen to such a stable degree despite the massive discrepancies between characteristics of the fundamental forces? Certain candidate solutions such as the anthropic principle–which attempts to measure the statistical probability or improbability of the rise of our universe–exist, but supersymmetry has the potential to be much more viable. Yet once again, supersymmetric theories are hampered by a complete lack of experimental confirmation.

Supersymmetry today

Supersymmetry, as it has yet to be experimentally observed, is the center of a vigorous fight seeking to prove–or disprove–its existence. As it is so imperative that we resolve the issues with the fundamental forces and dark matter, it is understandable that there is much experimentation in progress.

Most attempts at direct observation of superpartner particles occur at CERN, the home of the Large Hadron Collider (LHC), where hadron collisions near the speed of light can produce the unusual particles necessary for further scientific study and observation. Numerous experiments at CERN have sought to observe such particles, but as of yet, none have proven successful. At the LHC, scientists can generally observe only rapid-decay particles, a property that exists in few superpartner particles; as such, supersymmetric particles, even if produced in the LHC, cannot be readily observed.

Although the mathematical and physical justifications of supersymmetry are relatively solid, direct observation is necessary to demonstrate the viability of supersymmetry as a theory of physics. 

Wrapping it up

Supersymmetry is a relationship between Standard Model fermions and bosons that couples every Standard Model particle with a superpartner particle of equivalent physical quantities other than spin, and in some cases, mass; superpartners have half-integer value spin difference (½, 3/2, 5/2, etc.), which make them bosonic superpartners to fermions, or fermionic superpartners to bosons. The experimental confirmation of supersymmetric particles could lead to an extension of the Standard Model to accommodate supersymmetric particles, such as the selectron and photino, and could even yield a grand unification theory of particle physics, in addition to solving the hierarchy problem; however, the lack of experimental evidence hampers the credibility of the theory. Even so, its formulation and understanding has vast implications on the fields of particle physics and quantum mechanics. Supersymmetry–a small step in physics–represents a giant leap by humanity towards a cohesive understanding of the laws of nature. As always, take care and stay curious, my friends.

* As, when I publish this entry, I shall be a senior in high school, I am not currently taking this course; I took the course as a sophomore.

** Notably because no fermion can be in the same quantum state as another fermion at any particular time, whereas any boson can exist in the same quantum state, and even occupy the same space, as other bosons.

If you have any questions, comments, or corrections, please comment on this post or email with your concerns. Thank you.


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