Particle physicists at CERN are trying to unlock the secrets of the universe by testing our current theory about how it works and looking for holes. These holes are suspected to come in the form of yet undiscovered particles that our current theory can’t describe. The Large Hadron Collider (LHC) in Geneva, Switzerland speeds up protons and smashes them together in the hopes of creating and detecting one of these new particles, or, frankly, any anomaly in our current description of the way the laws of physics work.
When trying to poke holes in a theory, knowing what not to look for is as, if not more, important than knowing what to look for. This sounds kind of strange, but the idea is that we can’t know if we have found something new, unless we are certain that we know what isn’t new. Particle physicists call this boring, old stuff “background”, and the exciting, new stuff “signal”. So, in short, a key part of looking for new physics is being able to accurately model the background.
Unfortunately, it is very difficult to model backgrounds from the foundational concepts in physics, so particle physicists typically rely on choosing some ad hoc function, with little to no grounding in the physics of the scenario, then tweaking the dials of the function until it matches the background in an area where we expect no new physics, the control region. From this, they then hope that this function faithfully represents the expected background in the region where we do expect signal, aptly called the signal region.
However, handling searches in this way leads to unseemly statistical effects that make any findings of an analysis less statistically significant. In order to say we have found new physics, we require that there is a 1 in 3,500,000 chance that the deviations we saw were a random fluctuations in the data. To put this in perspective, the chance of you getting hit by lightning in your lifetime is 1 in 3000. This terribly high bar means any kind of loss of statistical significance really hurts the chances of discovering new physics.
Fortunately, Dr. Meghan Frate and Professor Daniel Whiteson from UC Irvine, along with collaborators from MIT and industry, have found a unified statistical treatment of background modeling that is far more flexible than the traditional methods. The method utilizes Gaussian Processes (GPs). This technique, while fairly new to particle physics, is quite commonly used for modeling in the fields of geostatistics, climate, exoplanets, and machine learning. The paper explains the concept and addresses some of the issues that prevented this technique from being widely utilized in particle physics sooner.
Fundamentally, a GP is a collection of random variables that are related to their immediate neighbors by a Gaussian function (a bell curve). These various Gaussian distributions are stitched together with something called a kernel function. The Gaussian distributions are very general and we can directly encode our knowledge of the laws of physics into the kernel function. This means that the GP is more robust at describing many possible functions. Because of its ubiquity, GPs allow a unified statistical treatment of different types of backgrounds and the suspected signal. This means using GPs will result in less of a loss of statistical significance in the results.
While this paper doesn’t come with a new discovery, it is exciting in that it presents a method that will help particle physicists make new discoveries. And these discoveries will bring us one step closer to figuring out the nature of the universe.
If you would like to read more, the paper can be found here: https://arxiv.org/pdf/1709.05681.pdf
Post by Jessica Howard, graduate student working on her PhD in Particle Physics at UCI.