What other work has been done by scientists to describe the energy that different particles have in a reaction and how have they displayed this?

Most of the recent understandings of particle reactions (and their energy levels) come as a result of experiments using particle accelerators. There are about 30,000 of these devices in use worldwide, but the ones that produce valuable new data in the field of high-energy physics are not as numerous. They include the Large Hadron Collider (LHC) at CERN in Europe and the Relativistic Heavy Ion Collider (RHIC) at Brookhaven Laboratory in New York (Long Island).
These devices produce incredibly high energy collisions—in the future there is even concern that these collisions could produce a black hole. Superstring theory, the current dominant model in theoretical physics, suggests this is a possibility. Most of the energy produced in these collisions is displayed, like most other scientific information, as graphs.
Many of these collisions are also displayed as particle traces. These traces chart the energy levels and nature of various particles in a given collision. They can be quite beautiful.
https://en.wikipedia.org/wiki/Particle_accelerator

https://newscenter.lbl.gov/2015/02/20/what-to-expect-next-from-the-lhc-worlds-largest-particle-accelerator/