0000000000015078
AUTHOR
Victor Ilisie
Lagrangians, Hamiltonians and Noether’s Theorem
This chapter is intended to remind the basic notions of the Lagrangian and Hamiltonian formalisms as well as Noether’s theorem. We shall first start with a discrete system with N degrees of freedom, state and prove Noether’s theorem. Afterwards we shall generalize all the previously introduced notions to continuous systems and prove the generic formulation of Noether’s Theorem. Finally we will reproduce a few well known results in Quantum Field Theory.
QCD exotics versus a standard model Higgs boson
The present collider data put severe constraints on any type of new strongly interacting particle coupling to the Higgs boson. We analyze the phenomenological limits on exotic quarks belonging to nontriplet $SU(3{)}_{C}$ representations and their implications on Higgs searches. The discovery of the standard model Higgs, in the experimentally allowed mass range, would exclude the presence of exotic quarks coupling to it. Thus, such QCD particles could only exist provided that their masses do not originate in the SM Higgs mechanism.
Bounds on neutral and charged Higgs from the LHC
After the discovery of a Standard Model-like boson with mass of about 125 GeV the possibility of an enlarged scalar sector arises naturally. Here we present the current status of the phenomenology of the two-Higgs-doublet models with a special focus on the charged Higgs sector. If one considers a fermiophobic charged Higgs (it does not couple to fermions at tree level), all present experimental bounds are evaded trivially, therefore one needs to consider other decay and production channels. In this work we also present some of the interesting features of this specific scenario.
Relativistic Kinematics and Phase Space
Here we present a list of the most important formulae needed for calculating relativistic collisions and decays. It includes one-to-two and one-to-three body decays, and the two-to-two scattering process both in the center of mass and laboratory frames. It also includes simplified general formulae of one, two and three-body Lorentz invariant phase space. No explicit calculation is performed, however the reader is highly encouraged to reproduce the results presented here.
Massive Spin One and Renormalizable Gauges
For many decades of the last century, physicists were struggling to define consistent (renormalizable and unitarity preserving) models for spin-one massive particles (Proca fields). As we know, this was beautifully achieved by Weinberg, Salam and Glashow in 1967 when they proposed an electroweak unified theory which we now call the Standard Model. The electroweak symmetry breaking mechanism, among other things, generates mass terms for the W and Z bosons, while preserving renormalizability and unitarity. The longitudinal degrees of freedom of the massive spin-one particles are given by the Goldostone bosons. Choosing one gauge or another might seem just a matter of convenience and in most c…
Effective Field Theory
Effective field theories (EFTs) are a highly important topic in Quantum Field Theory. Here we are going to shortly present some important highlights as well as the renormalization group equations for the Wilson coefficients. Afterwards we shall focus on one illustrative example and present the \(\textit{matching}\) procedure at the one-loop level. The infrared behaviour of EFTs is also covered with this example.
LHC constraints on two-Higgs doublet models
The recent discovery of a Standard Model-like boson with mass of about 126 GeV seems to be the first direct information on the electroweak symmetry breaking mechanism. Using the available experimental data from the LHC and Tevatron we study the implications on the parameter space of the Two-Higgs Doublet Model extension of the Standard Model. The generic structure of the Aligned Two-Higgs Doublet Model (ATHDM) is imposed in the Yukawa sector; also the models with discrete Z2 symmetries are analyzed.
Dimensional Regularization. Ultraviolet and Infrared Divergences
The cornerstone of Quantum Field Theory is renormalization. We shall speak more about in the next chapters. Before, it is necessary to discuss the method. The best and most simple is, of course, dimensional regularization (doesn’t break the symmetries, doesn’t violate the Ward Identities, preserves Lorentz invariance, etc.). When explained consistently, it becomes very simple and clear. Here, we shortly discuss ultraviolet (UV) and infrared (IR) divergences with a few examples. However, in Chap. 8, we shall extensively treat one-loop two and three-point functions and analyse many more examples of IR and UV divergences.
Low-mass fermiophobic charged Higgs phenomenology in two-Higgs-doublet models
After the recent discovery of a Higgs-like boson, the possibility of an enlarged scalar sector arises as a natural question. Experimental searches for charged scalars have been already performed with negative results. We analyze the phenomenology associated with a fermiophobic charged Higgs (it does not couple to fermions at tree level), in two-Higgs-doublet models. All present experimental bounds are evaded trivially in this case, and one needs to consider other decay and production channels. We study the associated production of a charged Higgs with either a $W$ or a neutral scalar boson, and the relevant decays for a light fermiophobic charged Higgs. The interesting features of this scen…
Symmetries and Effective Vertices
When facing the computation of more realistic processes, the calculations can become lengthy very fast as the number of Feynman diagrams grows. Before starting the calculation process the problem should be reduced to its minimal form. Here we will present an example of how to reduce the number of calculated diagrams for a given process (which in this case will be a Higgs-like scalar decay to two photons through a charged scalar loop) using gauge symmetry.
Towards a general analysis of LHC data within two-Higgs-doublet models
The data accumulated so far confirm the Higgs-like nature of the new boson discovered at the LHC. The Standard Model Higgs hypothesis is compatible with the collider results and no significant deviations from the Standard Model have been observed neither in the flavour sector nor in electroweak precision observables. We update the LHC and Tevatron constraints on CP-conserving two-Higgs-doublet models without tree-level flavour-changing neutral currents. While the relative sign between the top Yukawa and the gauge coupling of the 126 GeV Higgs is found be the same as in the SM, at 90% CL, there is a sign degeneracy in the determination of its bottom and tau Yukawa couplings. This results in …
Vectors, Tensors, Manifolds and Special Relativity
Assuming that the reader is familiar with the notion of vectors, within a few pages, with a few examples, the reader will get to be familiar with the generic picture of tensors. With the specific notions given in this chapter, the reader will be able to understand more advanced tensor courses with no further effort. The transition between tensor algebra and tensor calculus is done naturally with a very familiar example. The notion of manifold and a few basic key aspects on Special Relativity are also presented.
The Higgs Era
Después del descubrimiento de un bosón escalar con masa alrededor de 125, el Modelo Estándar parece funcionar perfectamente, pero todavía hay mucho espacio (y necesidad) para nueva física. A pesar de su enorme éxito, el Modelo Estándar deja muchas preguntas sin responder y muchas cuestiones abiertas. A falta del conocimiento de una simetría fundamental de la Naturaleza que nos indique el camino, hemos de analizar fenomenologicamente cualquier extensión del Modelo que pueda responder al menos a alguna de estas preguntas. En este trabajo estudiamos dos tipos de extensiones del Modelo Estándar, las dos relacionadas con el sector escalar. En la primera parte de la tesis estudiamos la posible ex…
LHC constraints on two-Higgs doublet models
A new Higgs-like boson with mass around 126 GeV has recently been discovered at the LHC. The available data on this new particle is analyzed within the context of two-Higgs doublet models without tree-level flavour-changing neutral currents. Keeping the generic Yukawa structure of the Aligned Two-Higgs Doublet Model framework, we study the implications of the LHC data on the allowed scalar spectrum. We analyze both the CP-violating and CP-conserving cases, and a few particular limits with a reduced number of free parameters, such as the usual models based on discrete Z(2) symmetries.
One-Loop Two and Three-Point Functions
In this chapter we present a few relevant calculations of one-loop, one and two-point (scalar, vector and tensor) functions. IR and UV divergences are extensively treated. One example of IR-pole cancellation is presented. The two and three-body phase space integrals in D dimensions, needed for the calculation of IR divergent cross sections are also given. Last, the usage of the generic parametrization ( 6.27) for non-integer powers of propagators (which appear when one needs to integrate over the four-momentum, logarithmic functions that depend on the four-momentum) is shown with a simple two-loop example. With the tools given here, the reader should find straightforward to construct any hi…