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Mathematical Moments 170: Smashing Particles up Against Mathematics

A diagram with CMS (Compact Muon Solenoid) logo in top right corner. Diagram shows a blue cylinder with yellow, green, and red rays connected at a central point.
A diagram showing subatomic particles decaying in the Compact Muon Solenoid (CMS) particle detector at CERN
image © CERN

At large particle colliders such as SLAC in California and CERN in Geneva, Switzerland, physicists send subatomic particles careening toward each other at high speeds, hoping to generate collisions that result in new collections of particles. In a new paper, mathematicians joined with physicists to show that techniques from geometry can help analyze the results of those collisions.

Particle collisions take place within detectors, chambers whose walls can measure the energy and momentum of subatomic elements. After a collision, debris explodes towards the detectors. Physicists then use the detector data to reconstruct what happened during the collision itself.

To study this mathematically, three physicists proposed a new tool in 2019. Their tool, adapted from machine learning, represents collisions as energy patterns recorded by the detector. Called the Earth Mover's Distance, it allows researchers to compare the similarity of two different collisions. Specifically, it quantifies how much one pattern of energy would have to be modified before it resembled another. The researchers found that the Earth Mover's Distance simplified many concepts from particle physics. For example, under the Earth Mover's Distance framework, a once-complex formula for how much a collision could be decomposed into sub-collisions became a short and simple equation. In the new paper, the team of physicists and mathematicians demonstrated that not only was the Earth Mover's Distance useful, it was precisely the right perspective to take. According to the paper, no other distance could capture the nuances of particle collisions quite the same way.

Dr. Abiy Tasissa discusses "Earth Mover's Distance" and the mathematics he uses to study the shape of jets created by colliding particles.

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