Higgs field theory12/29/2022 ![]() Let’s think about the budget of a large country like the U.S. In fact, the naive size of the corrections is enormously larger than the 126 GeV mass of that we observe!Ĭonfused? Now is a good time to bring in the analogy. The funny thing about the mass of the Higgs is that the corrections are not small. ![]() #Higgs field theory plus#The physical mass that we observe is this initial estimate plus the corrections. There will also be corrections, let’s call them ΔM (where Δ is pronounced “delta” and it indicates “change to”). #Higgs field theory free#In the Standard Model, there is a free parameter that can be thought of as an initial estimate for the Higgs mass, let’s call it M₀. It turns out that all quantities that we can predict receive similar quantum corrections, even the mass of the Higgs boson. It is because of tests like these that we take the predictions of this conceptual framework very seriously. To put it into perspective, it’s slightly better than hitting a hole in one from New York to China (that distance is about 10,000 km =1 billion cm). This is a real tour de force for relativistic quantum field theory and represents one of the most stringent tests of any theory in the history of science. Moreover, we can measure it to a comparable accuracy. But we can calculate it to an exquisite accuracy (about ten digits). It turns out that this correction is small - about one part in a thousand. Those corrections are shown pictorially in the Feynman diagrams below. In standard quantum mechanics, the prediction is that g=2 however, with relativistic quantum field theory we expect corrections. To illustrate this difference, let’s consider a property of the electron and muon called its “g-factor” that relates its magnetic moment and spin. The key point here is that relativistic quantum field theory goes beyond the initial formulation of quantum mechanics. As you might guess from the name, it’s based on the pillars of relativity, quantum mechanics, and field theory. The first thing to know is that the Standard Model (and most other theories we are testing) is based on a conceptual framework called Relativistic Q uantum Field Theory (QFT). Why we take our theory seriouslyīefore discussing the fine tuning, we need need a few prerequisites. I took on this topic recently for a public lecture and came up with an analogy that I would like to share. ![]() Unfortunately, it is notoriously difficult to explain. The fine-tuning problem is related to the slippery concept of naturalness, and has driven the bulk of theoretical work for the last several decades. However, the Higgs itself is the source of one of the deepest mysteries of particle physics: the fine tuning problem. Of course, we know there are other phenomena - like dark matter, the dominance of matter over anti-matter, the mass of neutrinos, etc. - that aren’t explained by the Standard Model. Its discovery completes the tremendously successful Standard Model of particle physics. The discovery of the Higgs boson was a triumph for particle physics. ![]()
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