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Register a new userLectures: From quantum mechanics to the Standard Model
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Ben Gripaios
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The goal of these lectures is to introduce readers with a basic knowledge of undergraduate physics (specifically non-relativistic quantum mechanics, special relativity, and electromagnetism) to the `current theory of everything: the Standard Model of particle of physics. By the end of the course, readers should be able to make predictions for simple processes at the Large Hadron Collider, such as decay rates of the Higgs boson. Some discussion of the ongoing search for physics beyond the Standard Model is also included. Based on lectures given at the Universities of Cambridge (UK) and Canterbury (New Zealand).
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We cover some current topics in Beyond the Standard Model phenomenology, with an emphasis on collider (particularly Large Hadron Collider) phenomenology. We begin with a review of the Standard Model and some unresolved mysteries that it leaves. Then, we shall heuristically introduce supersymmetry, grand unified theories and extra dimensions as paradigms for expanding the Standard Model. The collider phenomenology of such models is too rich and complex to review, but we give some key examples of how the new states associated with the models might be inferred in Large Hadron Collider events. Before concluding, we finish with a brief description of a quantum field theory approximation that can be used in some cases to reduce model dependence: effective field theory. We show how this can be employed to explain recent measurements of decays of $B$ mesons, which disagree with Standard Model predictions.
This write-up of lectures given at TASI 2020 provides an introduction into precision tests of the electroweak Standard Model. The lecture notes begin with a hands-on review of the (on-shell) renormalization procedure, and subsequently highlight a few subtleties that occur in the renormalization of a theory with electroweak symmetry breaking and massive gauge bosons. After that a set of typical electroweak precision observables is introduced, as well as a range of input parameter measurements that are needed for making predictions within the Standard Model. Finally, it is discussed how comparisons of the electroweak precision observables between experiment and theory can be used to stress-test the Standard Model and probe new physics.
These are the notes of a set of four lectures which I gave at the 2012 CERN Summer School of Particle Physics. They cover the basic ideas of gauge symmetries and the phenomenon of spontaneous symmetry breaking which are used in the construction of the Standard Model of the Electro-Weak Interactions.
Recently, we have found an exact solution to the full set of Dyson-Schwinger equations of the non-interacting part of the Higgs sector of the Standard Model obtained by solving the 1-point correlation function equation. In this work we extend this analysis considering also the other possible solution that is the one experimentally observed in the Standard Model. Indeed, the same set of Dyson-Schwinger equations can be exactly solved for the Standard Model with a constant as a solution for the 1-point correlation function. Differently from the Standard Model solution, the one we have found has a mass spectrum of a Kaluza-Klein particle. This could be a clue toward the identification of a further space dimension. Gap equations are obtained in both cases as also the running self-coupling equations.
We explore the possibility that scale symmetry is a quantum symmetry that is broken only spontaneously and apply this idea to the Standard Model (SM). We compute the quantum corrections to the potential of the higgs field ($phi$) in the classically scale invariant version of the SM ($m_phi=0$ at tree level) extended by the dilaton ($sigma$). The tree-level potential of $phi$ and $sigma$, dictated by scale invariance, may contain non-polynomial effective operators, e.g. $phi^6/sigma^2$, $phi^8/sigma^4$, $phi^{10}/sigma^6$, etc. The one-loop scalar potential is scale invariant, since the loop calculations manifestly preserve the scale symmetry, with the DR subtraction scale $mu$ generated spontaneously by the dilaton vev $musimlanglesigmarangle$. The Callan-Symanzik equation of the potential is verified in the presence of the gauge, Yukawa and the non-polynomial operators. The couplings of the non-polynomial operators have non-zero beta functions that we can actually compute from the quantum potential. At the quantum level the higgs mass is protected by spontaneously broken scale symmetry, even though the theory is non-renormalizable. We compare the one-loop potential to its counterpart computed in the traditional DR scheme that breaks scale symmetry explicitly ($mu=$constant) in the presence at the tree level of the non-polynomial operators.
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