Effective field theories can be used to describe measurements at e⁺e⁻ colliders over a wide kinematic range while allowing reliable error predictions and systematic extensions. We show this in two physical situations. First, we give a factorization formula for the e⁺e⁻ thrust distribution dσ/dτ with thrust T and τ = 1 − T based on soft collinear effective theory. The result is applicable for all τ, i.e. in the peak, tail, and far-tail regions. We present a global analysis of all available thrust distribution data measured at center-of-mass energies Q = 35 to 207 GeV in the tail region, where a two parameter fit to the strong coupling constant α(s)(m(Z)) and the leading power correction parameter Ω₁ suffices. We find α(s)(m(Z)) = 0.1135 ± (0.0002)expt ± (0.0005)hadr ± (0.0009)pert, with x²/dof = 0.91, where the displayed 1-sigma errors are the total experimental error, the hadronization uncertainty, and the perturbative theory uncertainty, respectively. In addition, we consider cumulants of the thrust distribution using predictions of the full spectrum for thrust. From a global fit to the first thrust moment we extract α(s)(m(Z)) and Ω₁. We obtain α(s)(m(Z)) = 0.1140 ± (0.0004)exp ± (0.0013)hadr ± (0.0007)pert which is compatible with the value from our tail region fit. The n-th thrust cumulants for n ≥ 2 are completely insensitive to Ω₁, and therefore a good instrument for extracting information on higher order power corrections, Ω'(n)/Qⁿ, from moment data. We find (˜Ω₂)^1/2 = 0.74 ± (0.11)exp ± (0.09)pert GeV. Second, we study the differential cross section dσ/dx of e⁺e⁻-collisions producing a heavy hadron with energy fraction x of the beam energy in the center-of-mass frame. Using a sequence of effective field theories we give a definition of the heavy quark fragmentation function in the endpoint region x → 1. From the perspective of our effective field theory approach we revisit the heavy quark fragmentation function away from the endpoint and outline how to develop a description of the heavy quark fragmentation function valid for all x. Our analysis is focused on Z-boson decays producing one B-meson. Finally, we will give a short outlook of how we want to apply our approach to determine the leading nonperturbative power corrections of the b-quark fragmentation function from LEP experiments.

In this thesis jet production and cosmological constraints on decaying dark matter are studied. The powerful framework of effective field theory is applied in both cases to further our knowledge of particle physics. We first discuss how to apply the Soft Collinear Effective Theory (SCET) for calculating hadronic jet production rate. By applying SCET power counting, we develop a consistent approach to perform phase space integrations. This approach is then successfully applied to one-loop calculations with regard to a variety of jet algorithms. This allows us to study if the soft contribution can be factorized from the collinear ones. In particular we point out the connection between such factorization and the choice of ultraviolet regulator. We then further our study of the (exclusive) kt and C/A jet algorithms in SCET with the introduction of an additional regulator. Regularizing the virtualities and rapidities of graphs in SCET, we are able to write the next-to-leading-order dijet cross section as the product of separate hard, jet, and soft contributions. We show how to reproduce the Sudakov form factor to next-to-leading logarithmic accuracy previously calculated by the coherent branching formalism. Our resummed expression only depends on the renormalization group evolution of the hard function, rather than on that of the hard and jet functions as is usual in SCET. Finally we present a complete analysis of the cosmological constraints on decaying dark matter. For this, we have updated and extended previous analyses to include Lyman-alpha forest, large scale structure, and weak lensing observations. Astrophysical constraints are not considered in this thesis. The bounds on the lifetime of decaying dark matter are dominated by either the late-time integrated Sachs-Wolfe effect for the scenario with weak reionization, or CMB polarisation observations when there is significant reionization. For the respective scenarios, the lifetimes for decaying dark matter are constrained by Gamma^{-1} > 100 Gyr and (f*Gamma)^{-1} > 5.3 x 10^8 Gyr (at 95.4% confidence level), where the phenomenological parameter f is the fraction of decay energy deposited into the baryonic gas. This allows us to constrain particle physics models with dark matter candidates, by analyzing effective operators responsible for the dark matter decays into Standard Model particles.

In this thesis jet production and cosmological constraints on decaying dark matter are studied. The powerful framework of effective field theory is applied in both cases to further our knowledge of particle physics. We first discuss how to apply the Soft Collinear Effective Theory (SCET) for calculating hadronic jet production rate. By applying SCET power counting, we develop a consistent approach to perform phase space integrations. This approach is then successfully applied to one-loop calculations with regard to a variety of jet algorithms. This allows us to study if the soft contribution can be factorized from the collinear ones. In particular we point out the connection between such factorization and the choice of ultraviolet regulator. We then further our study of the (exclusive) kt and C/A jet algorithms in SCET with the introduction of an additional regulator. Regularizing the virtualities and rapidities of graphs in SCET, we are able to write the next-to-leading-order dijet cross section as the product of separate hard, jet, and soft contributions. We show how to reproduce the Sudakov form factor to next-to-leading logarithmic accuracy previously calculated by the coherent branching formalism. Our resummed expression only depends on the renormalization group evolution of the hard function, rather than on that of the hard and jet functions as is usual in SCET. Finally we present a complete analysis of the cosmological constraints on decaying dark matter. For this, we have updated and extended previous analyses to include Lyman-alpha forest, large scale structure, and weak lensing observations. Astrophysical constraints are not considered in this thesis. The bounds on the lifetime of decaying dark matter are dominated by either the late-time integrated Sachs-Wolfe effect for the scenario with weak reionization, or CMB polarisation observations when there is significant reionization. For the respective scenarios, the lifetimes for decaying dark matter are constrained by Gamma^{-1} > 100 Gyr and (f*Gamma)^{-1} > 5.3 x 10^8 Gyr (at 95.4% confidence level), where the phenomenological parameter f is the fraction of decay energy deposited into the baryonic gas. This allows us to constrain particle physics models with dark matter candidates, by analyzing effective operators responsible for the dark matter decays into Standard Model particles.

Theoretical predictions for generic multi-scale observables in Quantum Chromodynamics (QCD) typically suffer from large Sudakov logarithms associated with the emission of soft or collinear radiation, whose presence spoils the perturbative expansion in the coupling strength which underlies most calculations in QCD. A canonical way to improve predictions wherever these logarithms appear is to resum them to all perturbative orders, which can conveniently be achieved using Effective Field Theory (EFT) methods. In an age of increasing automation using computers, this task is still mostly performed manually, observable-by-observable. In this thesis we identify the 2-loop soft function as a crucial ingredient for the resummation of QCD Sudakov logarithms to Next-to-next-to-leading logarithmic (NNLL) accuracy in Soft-Collinear Effective Theory (SCET), for wide classes of observables involving two massless colour-charged energetic particles, such as dijet event shapes at lepton colliders, or colour singlet production at hadron colliders. We develop a method to evaluate these soft functions using numerical methods based on sector decomposition and the choice of a convenient parametrisation for the phase space. This allows the factorisation of all implicit (real emission) and explicit (virtual correction) divergences made manifest by dimensional and analytic regularisation. The regulator pole coefficients can then be evaluated numerically following a subtraction and expansion, and two computational tools are presented to perform these numerical integrations, one based on publicly available tools, the other based on our own code. Some technical improvements over naive straightforward numerical evaluation are demonstrated and implemented. This allows us to compute and verify two of three colour structures of the 2-loop bare soft functions for wide ranges of observables with a factorisation theorem. A number of example results - both new and already known - are shown to demonstrate the reach of this approach, and a few possible extensions are sketched. This thesis therefore represents a crucial step towards automation of resummation for generic observables to NNLL accuracy in SCET.

The future of new physics searches at the LHC will be to look for hadronic signals with jets. In order to distinguish a hadronic signal from its background, it is important to develop advanced collider physics techniques that make accurate theoretical predictions. This work centers on phenomenological and formal studies of Quantum Chromodynamics (QCD), including resummation of hadronic observables using Soft Collinear Effective Theory (SCET), calculating anomalous dimensions of multi-Wilson line operators in AdS, and improving jet physics analysis using multiple event interpretations. / Physics

Effective field theories (EFTs) provide frameworks to systematically improve perturbation expansions in quantum field theory. This improvement is essential in quantum chromodynamics (QCD) predictions, both at low energy in the description of low momentum hadron-hadron scattering and at high energy in the description of electron-positron, proton-proton, proton-electron collisions. It is also important in quantum electrodynamics (QED), when electrons interact with a high-intensity, long-wavelength classical field. I introduce the principles and methods of effective field theory and describe my work in three EFTs: First, in the perturbative QCD region, I use soft collinear effective theory (SCET) to prove that strong interaction soft radiation is universal and to increase the QCD accuracy to next-to-next-to-next-to leading logarithm order for new particle searches in hadron colliders. I also compute a new class of non-perturbative, large logarithmic enhancement arising near the elastic limits of deep inelastic scattering and Drell-Yan processes. Second, in the QCD confinement region, I use heavy hadron chiral perturbation theory to study near-threshold enhancements in the scattering of 𝐷 and 𝜋 mesons near the threshold for the excited 𝐷-meson state, 𝐷*, as well as in the scattering of 𝐷 and 𝐷* mesons near the threshold for the exotic hadron X(3872). This work provides a clear picture of the hadronic molecule X(3872) and more profound understanding of the nuclear force between hadrons. Finally, inspired by SCET, I construct a new electron-laser effective field theory to describe highly-relativistic electrons traveling in strong laser fields, extract the universal distribution of electrons in strong electromagnetic backgrounds and its evolution in energy from the separated momentum scales of emitted photons and classical radiation, and predict the rate of wide angle photon emission. I conclude with limitations of EFT methods and some perspectives on what new work may be achieved with these EFTs.