Modelling electroweak interactions at lepton colliders - from the Z pole to the highest energies
This thesis investigates the influence of radiative corrections on modeling electroweak processes at future lepton colliders, aiming to enhance the precision of Standard Model tests from the Z pole to multi-TeV energies to address unresolved cosmological questions.
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For decades, the most successful theory in physics has been the Standard Model, a framework that explains how the fundamental building blocks of the universe interact. It describes a world made of tiny particles like quarks and electrons, held together by forces carried by other particles, such as photons for light and heavy bosons for the weak nuclear force. While this theory has passed every test thrown at it by massive machines that smash particles together, it leaves some of the biggest questions about our existence unanswered. It cannot explain why there is more matter than antimatter, what dark matter is, or why gravity is so much weaker than the other forces. To find answers, physicists are planning a new generation of particle colliders. These future machines will be far more powerful than anything currently in operation, capable of reaching energies that are currently unimaginable, from the precise energy where a specific particle called the Z boson is created, all the way up to multi-teraelectronvolt scales where new physics might hide.
The challenge for these future experiments is not just building the machines, but understanding the data they will produce. When particles collide at these extreme energies, they do not just bounce off each other; they emit a shower of other particles, much like sparks flying from a grinding wheel. To predict exactly what happens in these collisions, scientists rely on computer simulations. However, as the energy increases, the calculations become incredibly complex, involving billions of possible ways particles can interact. If the simulations are not precise enough, they will miss subtle signals of new physics. If they are too slow, scientists will wait years for results. A recent doctoral thesis from the University of Warsaw tackles these problems by refining how we model these high-energy collisions, specifically focusing on how particles radiate energy and how we can simplify the math without losing accuracy.
The research begins by looking at a specific energy level known as the Z pole, where the collider runs at the exact energy needed to create Z bosons. At this level, the goal is to measure how the Z boson interacts with different types of quarks, the particles that make up protons and neutrons. Currently, we know very little about how the Z boson interacts with the lighter quarks, because they are difficult to distinguish from one another in a detector. The author developed a method to separate these interactions by analyzing how often these quarks emit photons, or particles of light, during the collision. Because different quarks carry different electric charges, they emit light at different rates. By counting the events where light is emitted and comparing them to events where it is not, the method allows scientists to disentangle the properties of the up-type and down-type quarks. The study suggests that future colliders could improve the precision of these measurements by a factor of ten compared to current records, offering a much sharper test of the Standard Model.
Moving to much higher energies, where the colliders would operate at multi-teraelectronvolt scales, the nature of the collisions changes. At these speeds, the particles behave as if they are made of smaller constituents, and the collisions are often dominated by the fusion of heavy force-carrying particles. To handle the immense computational power required to simulate these events, physicists have long used an approximation called the Equivalent Vector Boson Approximation. This method treats the incoming particles as if they are emitting heavy bosons, which then collide with each other, simplifying the complex interaction into a more manageable two-step process. The thesis rigorously tested this approximation against full, exact calculations for various scenarios, such as the production of pairs of Higgs bosons or top quarks. The findings show that this shortcut works very well when the particles involved are heavy and the collision energy is high, but it can fail significantly for lighter particles or when the collision geometry is complex. The research identifies exactly where the approximation breaks down and provides specific rules for when it is safe to use, ensuring that future simulations remain reliable.
To address the limitations of the approximation, the author introduced a more advanced framework based on Electroweak Parton Distribution Functions. This approach is similar to how physicists describe protons, which are not solid balls but clouds of smaller particles called partons. In this new model, the incoming lepton beams are treated as clouds containing not just the original particle, but also a sea of other particles like photons, weak bosons, and even quarks, all generated by the intense energy of the collision. The author implemented this complex theory into a leading computer program used by physicists worldwide. By doing so, the research provides a way to resum, or add up, the most important mathematical terms that usually make calculations difficult. This allows for faster and more precise predictions for future experiments. The study demonstrates that this method can successfully describe processes that were previously too difficult to model accurately, suggesting it will be a vital tool for the next generation of particle physics.
The work also explored how these new methods apply to the search for physics beyond the Standard Model. By simulating scenarios where new, heavy particles might be created, the author showed that the improved modeling techniques could help distinguish between different theoretical possibilities. For instance, the research examined how future colliders could detect heavy, invisible particles that might make up dark matter, or how they could identify new types of force-carrying particles. The simulations indicate that with the right analysis tools, these machines could probe energy scales far beyond what is currently possible, potentially revealing the hidden structure of the universe. The thesis concludes that while the Standard Model remains robust, the path to discovering what lies beyond it requires not just bigger machines, but smarter ways of interpreting the data they produce. By refining the tools used to model these interactions, the research paves the way for a new era of discovery, where the subtle differences between theory and reality can finally be seen.
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