Goldstone equivalence and high energy electroweak physics

The transition between the broken and unbroken phases of massive gauge theories, namely the rearrangement of longitudinal and Goldstone degrees of freedom that occurs at high energy, is not manifestly smooth in the standard formalism. The lack of smoothness concretely shows up as an anomalous growth with energy of the longitudinal polarization vectors, as they emerge in Feynman rules both for real on-shell external particles and for virtual particles from the decomposition of the gauge field propagator. This makes the characterization of Feynman amplitudes in the high-energy limit quite cumbersome, which in turn poses peculiar challenges in the study of Electroweak processes at energies much above the Electroweak scale. We develop a Lorentz-covariant formalism where polarization vectors are well-behaved and, consequently, energy power-counting is manifest at the level of individual Feynman diagrams. This allows us to prove the validity of the Effective W Approximation and, more generally, the factorization of collinear emissions and to compute the corresponding splitting functions at the tree-level order. Our formalism applies at all orders in perturbation theory, for arbitrary gauge groups and generic linear gauge-fixing functionals. It can be used to simplify Standard Model loop calculations by performing the high-energy expansion directly on the Feynman diagrams. This is illustrated by computing the radiative corrections to the decay of the top quark.

Automation of One-Loop Computations for Scattering Amplitudes and Applications to Collider Phenomenology

Valentin Hirschi

This thesis presents the automation of loop computations for the calculation of Next-to-Leading Order contributions to theoretical predictions for particle colliders. We start with the general techniques for performing such predictions and how they can be expressed as perturbative expansions in the coupling constants controlling the strength of particle interactions. This leads to the discussion of the subtleties arising when considering higher order corrections, in particular the methods employed for isolating and canceling the infrared divergences occurring at intermediate steps of the computation. We then introduce the Passarino-Veltman and Ossola-Papadopolous-Pittau loop reduction algorithms. The latter is used by the computer code MadLoop that we wrote specifically for the automation of loop computations. The main part of the thesis focuses on the description of this program, starting with its original loop diagram generation algorithm and how it is embedded within the MadGraph5 environment. An initiation to the usage of the code is given, followed by a discussion of its optimizations where particular attention is paid to the implementation of the open-loop technique. Great details about the validation of MadLoop results against those of other codes are given in appendix B for specific kinematic configurations. We also list in the main text the total rates obtained for various processes. Quantitative information on the runtime speed and numerical stability performances are presented for many processes, each representative of a certain class of complexity. This serves as a comparison benchmark, and shows that realistic studies can be performed for any 2 → 3 and most 2 → 4 processes in the Standard Model. We finish by providing two examples of phenomenology study at the Large Hadron Collider using the tools we developed. The first treats the production of a scalar or pseudo-scalar in association with a top quark pair while the second addresses the tri-boson production channel Z W+ W− with MadSpin simulating the subsequent decay to leptons. We conclude with some insights on MadLoop prospects.

EPFL2013

Effective Field Theories for New and Old Physics

Alfredo Glioti

Effective Field Theories have changed our understanding of Quantum Field Theories. This thesis shows several applications of this powerful tool in the context of the Standard Model and for searches of New Physics.The thesis starts with a review of the Standard Model and its open questions and is followed by an updated and systematic study of models of flavor in the context of Partial Compositeness in Composite Higgs theories. Following that, the question on how to measure the Wilson coefficients of the Standard Model effective operators at present and future experiments is addressed: first by using modern Machine Learning techniques by studying angular distributions for diboson production, followed then by a study on ElectroWeak radiation at a future Muon Collider and how to use it to better probe the new physics parameter space.The fourth chapter deals instead with applying Non-Relativistic Effective Theories to the study of exotic mesons in the Standard Model. The two competing interpretations, a molecule formed of two mesons or a compact tetraquark state, and their consequences are studied. In particular this study is done on the X(3872) exotic charmonium and the consequences of the two accidental tunings of this system are discussed.The last chapter addresses the problem of baryogenesis from the ElectroWeak phase transition. A new scalar sector is introduced that decouples the physics responsible for the generation of the baryon asymmetry from the weak scale. This helps solving the main problems that ElectroWeak baryogenesis models face, namely the large modifications to the Higgs physics and the need of large CP violating new effects.

EPFL2022

Non-perturbative processes with Fermion number non-conservation in different models of particle physics

Yannis Burnier

When a classical conservation law is broken by quantum corrections, the associated symmetry is said to be anomalous. This type of symmetry breaking can lead to interesting physics. For instance in strong interactions, the anomaly in the chiral current is important in the pion decay to two photons. In weak interactions, there is an anomaly in the baryon number current. Although anomalous baryon number violating transitions are strongly suppressed at small energies, they could be at the origin of the baryon asymmetry of the universe. In this thesis, we consider several issues related to the theoretical and phenomenological aspects of anomalies. Although our main aim is the study of the electroweak theory, most of the theoretical questions do not rely on its precise setup. In order to solve these problems, we design a 1+1 dimensional chiral Abelian Higgs model displaying similar nonperturbative physics as the electroweak theory and leading to many simplifications. This model contains sphaleron and instanton transitions and, as the electroweak theory, leads to anomalous fermion number nonconservation. The one-loop fermionic contribution to the probability of an instanton transition with fermion number violation is calculated in the chiral Abelian Higgs model where the fermions have a Yukawa coupling to the scalar field. These contributions are given by the determinant of the fermionic fluctuations. The dependence of the determinant on fermionic, scalar and vector mass is determined. We also show in detail how to renormalize the fermionic determinant in partial wave analysis. The 1+1 dimensional model has the remarkable property to enable the creation of an odd number of fractionally charged fermions. We point out that for 1+1 dimensions this process does not violate any symmetries of the theory, nor does it lead to any mathematical inconsistencies. We construct the proper definition of the fermionic determinant in this model and underline its non-trivial features that are of importance for realistic 3+1 dimensional models with fermion number violation. In theories with anomalous fermion number nonconservation, the level crossing picture is considered a faithful representation of the fermionic quantum number variation. It represents each created fermion by an energy level that crosses the zero-energy line from below. If several fermions of various masses are created, the level crossing picture contains several levels that cross the zero-energy line and cross each other. However, we know from quantum mechanics that the corresponding levels cannot cross if the different fermions are mixed via some interaction potential. The simultaneous application of these two requirements on the level behavior leads to paradoxes. For instance, a naive interpretation of the resulting level crossing picture gives rise to charge nonconservation. We resolve this paradox by a precise calculation of the transition probability, and discuss what are the implications for the electroweak theory. In particular, the nonperturbative transition probability is higher if top quarks are present in the initial state. Coming back to the electroweak theory, we point out that the results of many baryogenesis scenarios operating at or below the TeV scale are rather sensitive to the rate of anomalous fermion number violation across the electroweak crossover. Assuming the validity of the Standard Model of electroweak interactions, we estimate this rate for experimentally allowed values of the Higgs mass (mH = 100…300 GeV). We also discuss where the rate enters in the particle density evolution and how to compute the leading baryonic asymmetry.