More than a Lifetime: Towards Precision Predictions for -Meson Decays in the Standard Model and Beyond
This thesis advances the theoretical understanding of B-meson lifetimes by calculating higher-order QCD corrections within the Heavy Quark Expansion, extending these methods to model-independent Beyond the Standard Model scenarios, and investigating B-mesogenesis to bridge precision flavour physics with dark matter and cosmic asymmetry constraints.
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The universe is built on a delicate balance between matter and antimatter. In the moments after the Big Bang, these two forms of matter should have annihilated each other completely, leaving behind only a sea of light. Yet, we exist. The visible universe is made almost entirely of matter, a fact that remains one of the deepest mysteries in physics. To understand how this imbalance arose, scientists study the behavior of heavy particles called B-mesons. These short-lived particles are like tiny laboratories where the fundamental forces of nature play out. By watching how they decay, or break apart, researchers can look for subtle differences in how matter and antimatter behave. If these particles decay in ways that the current laws of physics cannot explain, it could reveal the hidden mechanisms that allowed our universe to survive.
For decades, the Standard Model has served as the rulebook for these interactions. It describes how particles transform and interact with incredible precision. However, the rulebook is known to be incomplete. It cannot explain why there is more matter than antimatter, nor does it account for dark matter, the invisible substance that holds galaxies together. To find the missing pieces, physicists are pushing their calculations to the absolute limit of precision. They are looking for the smallest possible deviations from the expected behavior. This is the work of Ali Mohamed, a researcher who has spent years refining the mathematical tools used to predict how B-mesons live and die. His work does not just test the existing rules; it builds a new framework to catch any new physics that might be hiding in the details.
The core of this research relies on a method called the Heavy Quark Expansion. Imagine trying to understand the motion of a heavy boulder rolling down a hill. You can describe its main path easily, but to be truly precise, you must also account for the small bumps, the wind, and the friction of the ground. In the world of subatomic particles, the "boulder" is a heavy bottom quark inside a B-meson, and the "bumps" are the complex interactions with the lighter particles surrounding it. For a long time, scientists could only calculate the main path with high accuracy. The smaller corrections were too difficult to compute, leaving a gap in our understanding. Mohamed's thesis fills these gaps. He has calculated the next level of corrections, pushing the precision of these predictions further than ever before.
In the first part of his work, Mohamed focused on the Standard Model itself. He calculated the contributions of specific interactions that occur at a very small scale, corresponding to corrections that are one ten-thousandth the size of the main effect. While this sounds tiny, in the world of high-precision physics, these corrections are essential. Without them, the theoretical predictions would not match the experimental data. He derived complete mathematical descriptions for how these heavy quarks interact with their surroundings during non-leptonic decays, a process where the quark changes flavor without emitting a lepton. These new calculations provide the necessary foundation for future experiments to test the Standard Model with unprecedented rigor.
The second part of the research looks beyond the known rules. Mohamed extended his calculations to include a wide range of hypothetical new forces that could exist. He created a general framework that allows physicists to test many different theories of new physics at once, without having to start from scratch for each one. This approach is particularly powerful because it includes a specific type of interaction known as the Darwin term, which describes how the quark feels the changing strength of the force field around it. This term has a surprisingly large effect on the lifetime of the particle. By calculating how this term behaves in the presence of new, unknown forces, Mohamed provided a tool that can be used to search for deviations in current and future experiments.
The most dramatic application of this work involves a specific theory called B-Mesogenesis. This theory suggests that the same process that creates the matter-antimatter imbalance in the universe also produces a particle of dark matter. In this scenario, a B-meson does not just decay into ordinary particles; it occasionally decays into a visible proton and an invisible dark matter particle. This invisible particle carries away energy, making the decay look like a missing piece in the puzzle. Mohamed investigated whether this theory could be true by calculating how often these decays should happen. He used two different methods to get the answer. The first method looked at the decay as a general process, summing up all possible outcomes. The second method looked at a specific outcome: the B-meson turning into a single proton and the invisible particle.
By comparing these two calculations, Mohamed was able to set strict limits on the theory. He found that for the theory to explain the existence of our universe, the decay into a proton and dark matter must happen at a certain minimum rate. He then compared this required rate with the limits set by real-world experiments conducted by the BaBar, Belle, and Belle II collaborations. These experiments have looked for exactly this kind of missing energy and have not seen it yet. The result is a powerful constraint: the theory is only viable in a very narrow range of possibilities. If the dark matter particle is too heavy, the math breaks down, and the theory fails. If it is too light, the decay rate would be too high, and experiments would have already seen it.
Perhaps the most surprising finding concerns the limits of the mathematical tools themselves. When the dark matter particle in the theory is heavy, the standard method of calculation, which relies on treating the particle as a small correction, begins to fail. Mohamed identified the exact point where this happens. He found that for certain masses, the small corrections become larger than the main effect, signaling that the standard approach is no longer reliable. This discovery is crucial because it tells future researchers where they must stop using these tools and develop new ones. It defines the boundary of our current understanding and shows where the next breakthroughs must occur.
Ultimately, this work bridges the gap between the abstract mathematics of particle physics and the concrete reality of experimental data. It refines the tools we use to measure the universe and provides a clear path for testing theories that could explain the origin of matter and the nature of dark matter. By pushing the calculations to their limits, Mohamed has shown us exactly where the Standard Model holds firm and where it might crack under the weight of new physics. The search for the missing pieces of our universe continues, but now we have a sharper lens through which to look.
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