Supersymmetry: A Love Story

An exploration of the “WIMP miracle” and why it may not pan out.

Matthew Forman
The Startup

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“ It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are, If it doesn’t agree with experiment, it’s wrong” — Richard Feynman

7 TeV proton-proton collision in the CMS detector of the Large Hadron Collider at CERN in Switzerland. Image by the CMS collaboration.

I started this piece off with one of my favorite Feynman quotes. I include this particular quote because it encapsulates the hard truths of not just physics, but all of evidence-based science as well as the indifference of nature and how she chooses to express herself to us humans. If the data suggest something other than your model or “guess”, it behooves the reasonably minded scientist to consider alternate theories to explain the phenomena being observed. In the lecture where Feynman spoke those famous words, he goes on to explain what he means:

“in that simple statement is the key to science”

This is the essence of scientific progress. Contemporary physics is at a crossroads where some of the brightest minds on the planet are hard at work finding ways to explain some truly striking problems in physics. One of the main efforts of physicists today is to complete the Standard Model (SM) of particle physics, our best theoretical framework that describes everything we can see with light and charge, which is about.. 5% of the universe’s mass-energy. The other 95% is made up of dark matter and dark energy, evading our understanding of matter, energy, and how gravity really works. This isn’t to say we haven’t tried to piece together a coherent theory of nature. Far from it.

Our familiar Standard Model friends admire their supposed Supersymmetric counterparts.

Supersymmetry

Supersymmetry or SUSY is a clever and convenient extension of our current understanding of the nature of matter and energy through the Standard Model of Particle Physics which beautifully explains the phenomena we can detect and observe. Physicists are god-awful at nomenclature. The names of the SUSY partners include higgsinos, squarks, gluinos, and neutralinos(essentially just adding “-ino” on the end of the normal name on an or adding an “s-” to the front). SUSY is particularly attractive to physicists because of the cascade of issues in physics it seems to account for. These issues include the nature of Dark Matter, The Hierarchy Problem, Gauge Unification and other juicy topics that physicists drool over. This is why SUSY is so sought after in physics.

The Atlas detector at CERN, the European Organization for Nuclear Research. The circular accelerator is the largest on the planet with a circumference of 26.7 km or about 17 miles, nestled underneath Geneva, Switzerland. Source: CERN

Before we dive into why SUSY may or may not be the correct description of nature, we must reiterate Feynman’s point: “If it doesn’t agree with experiment, it’s wrong”. SUSY and the consequences it points to such as WIMPs are hotly debated in contemporary physics. The lack of experimental evidence for them is not to be understated, yet it is important to give a fair assessment of all the possibilities and explain why SUSY could (or could not) be a valid description of nature.

Now, let’s get to the point, and bear with me here. Supersymmetry is a space-time symmetry in which Standard Model particles are suggested to have SUSY counterparts that differ by a half-integer spin. This just means that each SM fermion (half-integer spin) and each SM boson (integer spin) have a corresponding partner particle that may differ in mass by orders of magnitude. Now let’s go over some of the reasons why physicists were so tempted by SUSY in the first place.

A graphic showing a possible extension to the Standard Model with the tildes representing each corresponding super-partner. Source: from the movie “Particle Fever” by Mark Levinson.

The Players of the Game

It all started around 1966 when Japanese particle physicist, Hironari Miyazawa proposed a relationship between mesons (one quark/anti-quark pair particles) and baryons (protons, neutrons, etc..) as an extension to the Standard Model and an attempt to move a bit closer to what physicists call a Grand Unified Theory or GUT.

In the early 70s, physicists such as Bunji Sakita and Jean-Loup Gervais independently “rediscovered” Miyazawa’s conjecture of supersymmetry. Other physicists quickly began tinkering with the highly successful framework of Quantum Field Theory (QFT) and stumbled upon an even more revolutionary space-time symmetry suggested through new extensions of the Standard Model.

Eventually, in 1974, physicists Julius Wess and Bruno Zumino, both of whom have since passed away, identified a four-dimensional supersymmetric field theory, rivaling the success of QFT in its implications. In this new theory, striking consequences emerged that were suspiciously too good to be true such as a possible candidate particle for dark matter and gauge unification. Today, SUSY has been refined down to a respectable, genuine theory of nature that seemed to explain the origin of dark matter along with a whole cascade of profound implications, the Minimal Supersymmetric Standard Model (MSSM), finalized by Pierre Fayet in 1977.

There are many amazing physicists who’ve worked on supersymmetry since, making incredible new developments in the search for physics beyond the Standard Model and string theory such as Professor Michael Dine of UC Santa Cruz, one of my favorite professors that I had the pleasure of knowing and learning from during my time there. Dine, along with Ann Nelson of the University of Washington recently received the Sakurai Prize for Theoretical Physics, one of the most prestigious awards in their field:

“for groundbreaking explorations of physics beyond the standard model of particle physics, including their seminal joint work on dynamical super-symmetry breaking, and for their innovative contributions to a broad range of topics, including new models of electroweak symmetry breaking, baryogenesis, and solutions to the strong charge parity problem".

To my dismay, Ann Nelson recently passed away in 2019 in a hiking accident as outlined somberly by this New York Times article. This is heartbreaking news for the particle physics community and I lend my condolences to her family and colleagues from around the world who appreciated her brilliance and soul as a physicist and human being.

Professor Michael Dine (left) and Dr. Ann Nelson (right). Photos by: C. Lagattuta and the University of Washington, respectively.

The framework these physicists have laid out is theoretically sound, beautiful, and groundbreaking, predicting some incredible things, if true.

..If true. This is the meat of the discussion. Physics has gotten more complicated over the past century. We don’t really have lone geniuses locked away in their studies anymore unlocking the secrets of the universe (maybe more so now during the current COVID-19 pandemic..). Isaac Newton, for example independently developed an entire theory of nature and the first glimpse of gravitation with his infamous Philosophiæ Naturalis Principia Mathematica during The Great Plague of 1665 caused by the ravenous bubonic plague, inventing calculus in the process (you know.. just casually).

This was even more so with the theories of General Relativity, Quantum Mechanics, and Quantum Electrodynamics (Einstein, Bohr, Planck, Dirac, Feynman, Tomonaga, and Schwinger, respectively).

Today, we have massive groups of physicists with thousands of passionate humans working on sometimes gargantuan experiments for the progression of science and technology.

The ATLAS collaboration, one of the main experiments at CERN with around 5000 members from nearly 180 institutions across the globe. Source: CERN

It’s a momentous and exciting time for physics. Consider ATLAS, the largest scientific collaboration of particle physicists in the world. There was not one physicist who built the LHC and discovered the Higgs Boson in 2012, it was thousands of dedicated and curious people who unlocked that secret of nature. This is the new era of physics where Sapiens do what they do best; work together, organize, and communicate to achieve what would otherwise be impossible to do alone. It is a gift of our conscious experience to be instilled with human curiosity, but our social nature tends to get in the way sometimes

The Facts

Alright, so let us clear some things up and be straightforward. There has been no compelling evidence of SUSY so far in our colliders or other experiments trying to search for WIMPs such as the LUX experiment in 2016 at the Sanford Underground Research Facility (SURF) in South Dakota, or the XENON experiment at the Gran Sasso National Lab in Italy. This is not great news for WIMP hunters all over the world. However, in physics, when we do not see what we expect to see, we keep searching. This is the beauty of science; there is no failure in an experiment when looking for the cure to cancer, developing new vaccines, or sending rockets into orbit. There is only knowledge being gained about what did not work and what can be done better in the future:

Failure contains crucial information that allows us to exclude what the “true” description of nature is not.

The Debate

There is this idea that it is useless to keep searching for WIMPs or particulate dark matter simply because we haven’t seen them yet. This is a misled assumption. The work that the LUX-ZEPLIN and XENONnT collaborations do for dark matter research helps place important limits on what Dark Matter can and cannot be. This is the value of continuing the search, even when it seems like all hope is lost.

Now we have to be nice to SUSY; she’s got some decent ideas and compelling predictions that we can test experimentally. The introduction of SUSY models into our current theoretical understanding of the Standard Model has some amazing and very satisfying “coincidences” that make it attractive for the hype on Grand Unified Theories of nature; the Shangri-La of physics.

First, SUSY particles largely cancel out contributions from heavy Standard Model particles like the top quark and W/Z bosons that suggest a diverging Higgs mass up to the Planck Scale of around 10¹⁹ GeV. In English, this means that the top quark is so beefy in mass that it interacts strongly with the Higgs field, contributing quadratic diverging mass terms when you try and calculate the Higgs mass-squared parameter, essentially the quantized excitation of the field that is the Higgs boson.

A Higgs particle feels the heat of naturalness. Source: Quantum Diaries

This is fishy. Right now, our current understanding of physics is through the Standard Model, and it predicts the Higgs mass to be way larger than the observed value of 125 GeV.

There’s something in physics called ‘naturalness’ and it took me like three years to understand it but essentially, physicists really like it when new particle masses are roughly in the ballpark of particles we already know. It’s ‘natural’ in the sense that nature should be consistent and doesn’t like to have weirdly massive particles that exist at sometimes vastly different mass-energy scales. It is more of an aesthetic and philosophical thing to physicists as opposed to something tangible and mathematical.

Second, SUSY spits out a nice dark matter candidate particle. This particle must align with what we think dark matter might be, a seemingly weakly interacting form of non-luminous matter that is somehow responsible for 85% of the universe’s mass. SUSY, specifically the Minimal Supersymmetric Standard Model, predicts the existence of such a particle, a Weakly Interacting Massive Particle or WIMP for short. This particle exists through what is called “R-parity”. I do not have the necessary training yet in my studies to fully explain R-parity, but I do know that it is a conserved quantity with SM particles having a value of P=+1, SUSY having P=-1. This symmetry predicts the existence of a neutral, weakly interacting massive particle that cannot further decay into anything else and is therefore stable. This is mighty fine looking to physicists looking for dark matter.

Graphic showing Standard Model inverse coupling strengths for three of the fundamental forces as a function of interaction energy (excluding gravity..) diverging (left) and SUSY couplings (right) converging at around 10^16 GeV.

The third is Grand Unification. Basically, all the fundamental force couplings (relative strengths of interactions) change as you go to higher and higher interaction energies. Currently, the SM couplings do not converge as we would like to see in a GUT. However, when physicists introduce SUSY into the mix, they “magically” converge into one description of matter and energy at around 10¹⁶ GeV (this is a very high energy for particle physics, around 2 million Joules or roughly the energy of a vehicle moving at ~100 mph). This is also mighty fine looking to physicists interested in unifying the fundamental forces into a single description of nature, defining a new era of understanding about our universe’s origins.

The Hard Truth

You won’t find the hard truth here (sorry!) as I haven’t even taken my first Quantum Field Theory course yet as an incoming graduate student in physics. That doesn’t mean I can’t offer an opinionated yet coherent narrative for possible new particles that could explain dark matter and may be lurking in what physicists call the “hidden sector” of physics.

Now, right off the bat, I’m just going to say it: Massive Compact Halo Objects, MACHOs, and Weakly Interacting Massive Particles, WIMPs, are likely dead explanations for the intricate gravitational dance between dark energy and dark matter we observe in our universe. This does not mean we should stop studying them. In fact, we need physicists to study what nature is telling us about dark matter and dark energy to exclude all of what they are not. This, again, is the beauty of science.

SIMPs Enter the Arena

So if MACHOs and WIMPs are likely not correct descriptions of nature then what the heck is?

Graphic showing a pion composed of an up quark bound to a down anti-quark via a gluon (left) and the theoretical SIMP composed of a quark and an anti-quark bound together by an unknown type of gluon. Source: Robert Sanders, UC Berkeley

Enter SIMPs, or Strongly Interacting Massive Particles, first proposed in ~2014 by UC Berkeley Japanese theoretical physicist, Hitoshi Murayama. The distinguished professor suggests that gravitational lensing and galactic collisions from the Abell 3827 galaxy cluster may hint at previously unknown interactions between dark matter particles. Murayama is quoted speaking of excluding MACHOs:

“That study pretty much eliminated the possibility of MACHOs; I would say it is pretty much gone”

The same goes for WIMPs, possibly.

Murayama theorizes SIMPs interact strongly with themselves, potentially through gravity, yet interact very weakly with baryonic matter (protons, neutrons, etc..) and other Standard Model particles. These SIMPs would manifest as composite particles, made up of a quark/anti-quark pair, bound by a theorized novel type of gluon that has yet to be detected. Murayama conjectures that SIMPs may be the dark matter we are looking for, self-interacting through the collisions of galaxies with possibly detectable signatures.

Murayama suggests dark matter SIMPs strongly self-interact and collide through yet to be discovered interactions. Source: Robert Sanders, UC Berkeley, Kavli IMPU graphic.

To be frank, this is a somewhat controversial proposal that is gaining steam in the underground physics community, somewhat separate from mainstream physics and a bit beyond my own pay grade to explain fully.

I’ll end this article by including a quote from Murayama and let him speak for himself with his potentially groundbreaking theory of SIMPs and their relationship to dark matter, dark energy, and the true nature of reality.

“The community consensus is kind of, we don’t know how far we need to go, but at least we need to get down to this level… But because there are definitely no signs of WIMPs appearing, people are starting to think more broadly these days. Let’s stop and think about it again.” — Hitoshi Murayama

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Matthew Forman
The Startup

Astroparticle physics PhD candidate at UC Irvine, Citizen Scientist, curious Homo Sapien. instagram: @human_wavefunction, twitter: @human_wavfnctn