In order to explain the structure of matter and thus the existence of our world, physics attempts to discover and understand the smallest building blocks of matter with the help of experiments. One of the largest research facilities of all is the Large Hadron Collider (LHC) at the CERN research center near Geneva. Here, protons are collided with very high energy and the newly created particles are detected. Theoretical Physics is working on making predictions for such experiments. A major contribution to this is now being made by theoretical work aimed at a fundamental simplification for the calculation of scattering processes.

Scattering processes are described by probabilities, the so-called scattering amplitudes. Complex calculations are required to predict the latter. Dr. Dmitry Chicherin, Prof. Dr. Johannes Henn and Prof. Dr. Emery Sokatchev have investigated how symmetry can be used to make a comparatively simple prediction without complex calculations. Symmetry here means that the properties of the particles remain unchanged under a series of symmetry transformations, for example under certain transformations of space-time. “You can find the solution to an equation very efficiently and more easily if you know the symmetry,” explained Emery Sokatchev during a guest visit to Johannes Gutenberg University Mainz (JGU).

Particle collisions take place in accelerators at extremely high energies, which is why the mass of the particles can usually be neglected. In this case, an additional symmetry of spacetime, called conformal symmetry, passes, which is responsible for massless particles. “How exactly can we use this symmetry to predict the results?” is how Sokatchev formulates the initial question of the investigation – with which the scientists are breaking new ground, as there is hardly any work on this topic, which is considered to be very difficult.

“We chose a problem that is difficult to calculate using traditional methods and then used a non-trivial example to show how our new equation works,” says Sokatchev. This means that the result consists of two parts: First, we worked out what conformal symmetry tells us about scattering amplitudes and formulated this in the form of an equation. This equation restricts the solution. In the second step, the physicists explicitly solved the equation for a two-by-three process, i.e. for a collision of two particles that produces three particles. “It was an important point for us to see how this differential equation can be applied and how the solution can be worked out,” adds Johannes Henn, Professor of Mathematics Physics at JGU.

And whether the result is correct? The analytical solution that has now been presented describes how the scattering process depends on the energy of the particles and the scattering angle. On the one hand, there were assumptions as to what structure the solution might have. According to Henn, this has been confirmed. In addition, numerical solutions can be used for verification. This test was also passed.

The results were published in the renowned scientific journal Physical Review Letters.

However, this does not answer all the questions for the future. “The current contribution is a highlight of our research in this field,” says Henn. “But there are still some puzzles, for example what the general solution to these differential equations is.” A topic that will be discussed with Mathematics experts in the future.

The joint work on the theoretical question of what conformal symmetry can tell us about scattering processes was supported by the Cluster of Excellence “Precision Physics, Fundamental Interactions and Structure of Matter” (PRISMA) at Johannes Gutenberg University Mainz. In particular, PRISMA supported the seven-month guest stay of Emery Sokatchev, scientist at the Laboratoire d’Annecy-le-Vieux de Physique Théorique, Université Savoie Mont Blanc.

Johannes Henn came to Mainz University in June 2015 from the Institute for Advanced Study in Princeton and was awarded an ERC Consolidator Grant in 2017 for his research in theoretical and mathematical physics, one of the EU’s most highly endowed grants for individual scientists. In October 2018, Henn will accept an offer of appointment as Director at the Max Planck Institute for Physics in Munich.