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Will Supersymmetry Save or Ruin Physics?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

One of the biggest challenges today lies in the frontiers of particle physics. Despite what many people believe about the Higgs Boson, not only did it resolve a missing part of particle physics, but it also opened the door for other particles to be found. Refinements at the Large Hallidron Collider (LHC) at CERN will be able to test for some of these new particles.

One set of these falls into the domain of supersymmetry (SUSY), a 45-year-old theory that could also be applied to many open-ended ideas in physics, such as dark matter. But if the Raza team at CERN, led by Maurizio Pierini with scientists Joseph Lykken and Maria Spiropulu a part of the team, fails to find these "exotic collisions," then SUSY may be dead—and with it, much of nearly half a century’s worth of work (Lykken 36).

What the Heck Is the Problem?

The Standard Model, which has held up to countless experiments, talks about the world of subatomic physics, which also deals with quantum mechanics and special relativity. This realm is made up of fermions (quarks and leptons that make up protons, neutrons, and electrons) which are held together by forces which also act on bosons, another type of particle. What scientists still don’t understand, despite all the headway the Standard Model has made, is how these forces act, and why they even exist.

Other mysteries include where dark matter arises from, how three of the four forces are united, why there are three leptons (electrons, muons, and taus), and where their mass comes from. Over the years, experimentation has pointed to quarks, gluons, electrons, and bosons as being the basic unit blocks for the world, acting like point objects; but what does that mean in terms of geometry and space time? (Lykken 36, Kane 21-2).

The biggest issue at hand though is known as the hierarchy problem, or why gravity and the weak nuclear force act so differently. The weak force is nearly 10^32 times stronger and works on the atomic scale, on which gravity doesn’t work very well on. W and Z bosons are weak force carriers that move through the Higgs field, an energy layer that gives particles mass. It is unclear, however, why movement through the Higgs field doesn’t give Z or W more mass courtesy of quantum fluctuations and therefore weakens the weak force (Wolchover).

Several theories attempt to address these conundrums. One of which is string theory, an amazing work of mathematics that could describe our entire reality – and beyond. However, a big problem of string theory is that it is nearly impossible to test, and some of the experimental items have come up negative. For example, string theory predicts new particles, which are not only beyond the reach of the LHC, but quantum mechanics predicts that we would have seen them by now anyway courtesy of virtual particles created by them and interacting with normal matter. But SUSY could save the idea of the new particles. And these particles, known as superpartners, would cause the formation of the virtual particles to be difficult if not impossible, thus saving the idea (Lykken 37).

String theory to the rescue?

String theory to the rescue?

Supersymmetry Explained

SUSY can be difficult to explain because it is an accumulation of many theories rolled together. Scientists noticed that nature seems to have lots of symmetry to it, with many known forces and particles exhibiting behavior that can translate mathematically and therefore help explain each other’s properties regardless of the frame of reference. SUSY is what led to conservation laws and special relativity. This idea also applies to quantum mechanics. Paul Dirac predicted antimatter when he extended relativity to quantum mechanics (Ibid).

And even relativity can have an extension known as superspace, which doesn’t relate to up/down/left/right directions ,but instead has “extra fermionic dimensions.” Movement through these dimensions is difficult to describe because of this, with each type of particle requiring a dimensional step. To go to a fermion, you would go a step from a boson, and likewise to go backward. In fact, a net transformation like that would register as a small amount of movement in space-time aka our dimensions.

Normal movement in our dimensional space doesn't transform an object but it's a requirement in superspace as we can get fermion-boson interactions. But superspace also requires 4 extra dimensions unlike our own, with no perceptual size to them, and are quantum mechanical in nature. It is because of this complicated maneuvering through those dimensions that certain particle interactions would be highly unlikely, such as those virtual particles mentioned earlier. So SUSY requires a space, a time, and a force exchange if superspace is to operate. But what is the advantage to gaining such a feature if it's so complicated in its set-up? (Lykken 37; Kane 53-4, 66-7).

Superpartners in superspace

Superpartners in superspace

If superspace exists, then it would help stabilize the Higgs Field, which should be constant; otherwise, any instability would cause the destruction of reality courtesy of a quantum mechanical drop to the lowest energy state. Scientists know for sure that the Higgs Field is metastable and close to 100% stability based on comparative studies of the top quark mass versus the Higgs Boson mass. What SUSY would do is offer superspace as a way to prevent that energy drop from likely happening, lowering the chances significantly to the point of near 100% stability.

It also resolves the hierarchy problem, or the gap from the Planck scale (at 10-35 meters) to the Standard Model scale (at 10-17 meters), by having a superpartner to Z and W. This not only unifies them, but also lowers the energy of the Higgs Field and therefore reduces those fluctuations so that the scales cancel in a meaningful, and so observed, way. Finally, SUSY shows that in the early universe supersymmetry partners were abundant but over time decayed into dark matter, quarks, and leptons, providing an explanation for where the heck all that invisible mass comes from (Lykken 38, Wolchover, Moskvitch, Kane 55-8).

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The LHC has thus far found no evidence.

The LHC has thus far found no evidence.

SUSY As Dark Matter

Based on observations and statistics, the Universe has roughly 400 photons per cubic centimeter. Those photons exert gravitational forces that impact the rate of expansion we see in the Universe. But we also have to consider neutrinos, of which all the residual ones from the formation of the Universe remain MIA.

According to the Standard Model though, there should be roughly equal numbers of photons and neutrinos in the Universe, which presents us with a lot of particles whose gravitational influence is hard to pinpoint, namely because of mass uncertainties. This seemingly trivial problem becomes significant when we take into account that, of all the matter in the Universe, only 1/5 to 1/6 can be attributed to baryonic sources. Known levels of interactions with baryonic matter place a cumulative mass limit for all the neutrinos in the Universe at most 20%, so we still need plenty more to fully account for everything, and we account for this as dark matter. SUSY models offer a possible solution to this, for its lightest possible particles many features of cold dark matter including weak interactions with baryonic matter but also contributes gravitational influences (Kane 100-3).

We can hunt for signatures of this particle via many routes. Their presence would impact nuclei energy levels, so if you could say have a low radioactive decaying superconductor then any changes to it could be backtracked to SUSY particles once the Earth-Sun motion was analyzed over a year (because of background particles contributing to random decays, we would want to remove that noise if possible). We can also look for the decay products of these SUSY particles as they interact with each other. Models show we should see a tau and anti-tau arise from these interactions, which would happen at the center of massive objects like the Earth and Sun (for these particles would interact weakly with normal matter but still be gravitationally influenced, they would fall into the center of objects and thus create a perfect meeting place). Roughly 20% of the time the tau pair decays into a muon neutrino, whose mass is nearly 10 times that of their solar brethren because of the production route taken. We just need to spot this particular particle and we would have indirect evidence for our SUSY particles (103-5).

The Hunt So Far

So SUSY postulates this superspace where SUSY particles exist. And superspace has rough correlations to our spacetime. Thus, each particle has a superpartner that is fermionic in nature and exists in superspace. Quarks have squarks, leptons have sleptons, and force-carrying particles have SUSY counterparts as well. Or so the theory goes, for none have ever been detected. But if superpartners do exist, they would be just slightly heavier than the Higgs Boson and therefore possibly within reach of the LHC. Scientists would look for a deflection of particles from somewhere that was highly unstable (Lykken 38).

Gluino vs. Squark mass possibilities plotted out

Gluino vs. Squark mass possibilities plotted out

Gluino vs. Squark mass possibilities plotted out for natural SUSY.

Gluino vs. Squark mass possibilities plotted out for natural SUSY.

Unfortunately, no evidence has been found to prove that superpartners exist. The expected signal of missing momentum from hadrons arising from a proton-proton collision has not been seen. What is that missing component actually? A supersymmetric neutralino aka dark matter. But so far, no dice.

In fact, the first round at LHC killed off a majority of SUSY theories! Other theories besides SUSY could still help explain these unresolved mysteries. Amongst the heavyweights are a multiverse, other extra dimensions, or dimensional transmutations. What does help SUSY is that it has many variants and over 100 variables, meaning that testing and finding what works and what hasn’t is narrowing the field down and making it easier to refine the theory. Scientists such as John Ellis (from CERN), Ben Allanach (from Cambridge University), and Paris Sphicas (from the University of Athens) remain hopeful but acknowledge the diminishing chances for SUSY (Lykken 36, 39; Wolchover, Moskvitch, Ross).

Works Cited

Kane, Gordon. Supersymmetry. Perseus Publishing, Cambridge, Massachusetts. 1999. Print. 21-2, 53-8, 66-7, 100-5.

Lykken, Joseph and Maria Spiropulu. “Supersymmetry and the Crisis in Physics.” Scientific American May 2014: 36-9. Print.

Moskvitch, Katia. “Supersymmetric Particles May Lurk In Universe, Physicist Says.” Huffington Post, 25 Jan. 2014. Web. 25 Mar. 2016.

Ross, Mike. “Natural SUSY’s Last Stand.” Fermilab/SLAC, 29 Apr. 2015. Web. 25 Mar. 2016.

Wolchover, Natalie. “Physicists Debate Future of Supersymmetry.” Simon Foundation, 20 Nov. 2012. Web. 20 Mar. 2016.

© 2016 Leonard Kelley

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