GRACE at ONE-LOOP: Automatic calculation of 1-loop diagrams in the electroweak theory with gauge parameter independence checks

We describe the main building blocks of a generic automated package for the calculation of Feynman diagrams. These blocks include the generation and creation of a model file, the graph generation, the symbolic calculation at an intermediate level of the Dirac and tensor algebra, implementation of the loop integrals, the generation of the matrix elements or helicity amplitudes, methods for the phase space integrations and eventually the event generation. The report focuses on the fully automated systems for the calculation of physical processes based on the experience in developing GRACE-loop. As such, a detailed description of the renormalisation procedure in the Standard Model is given emphasizing the central role played by the non-linear gauge fixing conditions for the construction of such automated codes. The need for such gauges is better appreciated when it comes to devising efficient and powerful algorithms for the reduction of the tensorial structures of the loop integrals. A new technique for these reduction algorithms is described. Explicit formulae for all two-point functions in a generalised non-linear gauge are given, together with the complete set of counterterms. We also show how infrared divergences are dealt with in the system. We give a comprehensive presentation of some systematic test-runs which have been performed at the one-loop level for a wide variety of two-to-two processes to show the validity of the gauge check. These cover fermion-fermion scattering, gauge boson scattering into fermions, gauge bosons and Higgs bosons scattering processes. Comparisons with existing results on some one-loop computation in the Standard Model show excellent agreement. We also briefly recount some recent development concerning the calculation of mutli-leg one-loop corrections.Comment: 131 pages. Manuscript expanded quite substantially with the inclusion of an overview of automatic systems for the calculation of Feynman diagrams both at tree-level and one-loop. Other additions include issues of regularisation, width effects and renormalisation with unstable particles and reduction of 5- and 6-point functions. This is a preprint version, final version to appear as a Phys. Re

Realtime properties of QCD

We present a novel technique for the calculation of fundamental realtime correlation functions in functional approaches to quantum field theory, the spectral functional approach, and demonstrate its potential for the calculation of observables in quantum chromodynamics (QCD). The approach builds on spectral representations for correlation functions, such as the K\"all\'en-Lehmann representation of the propagator, and facilitates dimensional regularisation as well as on-shell renormalisation. We apply the spectral functional approach to the two most prominent functional frameworks for the calculation of non-perturbative fundamental correlation functions in QCD, which are Dyson-Schwinger equations and the functional renormalisation group. Building on this conceptual development, we calculate the spectral functions of all fundamental QCD fields, i.e., quark, gluon and ghost. We complement these results with data from spectral reconstruction with Gaussian process regression, inferring gluon and ghost spectral functions from Euclidean lattice QCD data in a Bayesian, non-parametric manner. Finally, as use cases for the spectral functional approach, we present direct computations of several QCD observables, facilitated by realtime correlator data. These include the shear viscosity of the quark-gluon plasma, the non-perturbative, timelike strong coupling constant, a crucial ingredient for scattering amplitudes, and the hadronic vacuum polarisation in the complex momentum plane, the leading QCD contribution to g-2

Analytical Quantum Field methods in Particle Physics

In this thesis we deal with different aspects of quantum field theory, particularly in non-perturbative but also perturbative regimes, applied to the intellectual construction that is the Standard Model for Particle Physics (SM), but also its extension via effective theories. We have developed the following practical contributions in different subfields of Particle Physics: qualitatively assessing why the SM has those specific symmetries, explaining the $^3P_0$ mechanism of meson decay from fundamental Quantum Chromodynamics (QCD) calculations, experimentally distinguishing Effective Theories of the Electroweak sector beyond the SM in accelerators, extrapolating LHC data (low energies) to possible resonant regions of new physics (high energies) with controlled uncertainties and studying precision calculations of QCD (high energies) in coordinate space.Comment: PhD Thesi

Techniques for high-multiplicity scattering amplitudes and applications to precision collider physics

In this thesis, we present state-of-the-art techniques for the computation of scattering amplitudes in Quantum Field Theories. Following an introduction to the topic, we describe a robust framework that enables the calculation of multi-scale two-loop amplitudes directly relevant to modern particle physics phenomenology at the Large Hadron Collider and beyond. We discuss in detail the use of finite fields to bypass the algebraic complexity of such computations, as well as the method of integration-by-parts relations and differential equations. We apply our framework to calculate the two-loop amplitudes contributing to three process: Higgs boson production in association with a bottom-quark pair, W boson production with a photon and a jet, as well as lepton-pair scattering with an off-shell and an on-shell photon. Finally, we draw our conclusions and discuss directions for future progress of amplitude computations

Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism

We describe a globalization construction for the Rozansky-Witten model in the BV-BFV formalism for a source manifold with and without boundary in the classical and quantum case. After having introduced the necessary background, we define an AKSZ sigma model, which, upon globalization through notions of formal geometry extended appropriately to our case, is shown to reduce to the Rozansky-Witten model. The relations with other relevant constructions in the literature are discussed. Moreover, we split the model as a $BF$-like theory and we construct a perturbative quantization of the model in the quantum BV-BFV framework. In this context, we are able to prove the modified differential Quantum Master Equation and the flatness of the quantum Grothendieck BFV operator. Additionally, we provide a construction of the BFV boundary operator in some cases.Comment: 85 pages, 20 figures, comments are welcom

New Structures in Gauge Theory and Gravity

Colour-kinematics duality provides new insights into the perturbative structure of quantum field theory. In particular, it recasts gravity as a double copy of gauge theory, an idea which has given rise to a variety of novel connections between these two seemingly disparate theories. In this thesis, we will explore a number of new examples of the double copy, which both extend the catalogue of cases in which it is known to apply and provide insights into theoretical structure of the correspondence. We will begin by investigating the role of non-local information in the double copy for classical solutions, leading to a topological condition that can be furnished with a double copy interpretation. As this condition is naturally expressed in terms of certain Wilson lines, we will go on to develop a double copy for the general form of these operators as well as the closely related geometrical concept of holonomy. We then further investigate the non- perturbative structure of the double copy by restricting to the self-dual sectors of gauge theory and gravity. Here we generalise the single copy structure of gravitational instantons, and provide new insights into the nature of the kinematic algebra underlying the double copy. Finally, we investigate the old idea that one-loop amplitudes in self-dual Yang-Mills and gravity are generated by an anomaly of the classical integrability of these theories. By writing explicit quantum-corrected actions for the self-dual theories, we will demonstrate a manifestation of this anomaly and uncover a novel double copy that holds at the level of the loop-integrated amplitudes

Tree-level amplitudes from the pure spinor superstring

We give a comprehensive review of recent developments on using the pure spinor formalism to compute massless superstring scattering amplitudes at tree level. The main results of the pure spinor computations are placed into the context of related topics including the color-kinematics duality in field theory and the mathematical structure of $\alpha'$-corrections.Comment: 196 pp. Invited review for Physics Reports. We welcome the readers' help in spotting typos or technical mistakes. Every correction that is firstly brought to our attention will be rewarded with 20 Euro Cent per numbered equation, to be paid in cash during the next in-person encounter with one of the authors. v2: version accepted for publication in Physics Report

Supersymmetry - When Theory Inspires Experimental Searches

We review, in the first part of this work, many pioneering works on supersymmetry and organize these results to show how supersymmetric quantum field theories arise from spin-statistics, N{\oe}ther and a series of no-go theorems. We then introduce the so-called superspace formalism dedicated to the natural construction of supersymmetric Lagrangians and detail the most popular mechanisms leading to soft supersymmetry breaking. As an application, we describe the building of the Minimal Supersymmetric Standard Model and investigate current experimental limits on the parameter space of its most constrained versions. To this aim, we use various flavor, electroweak precision, cosmology and collider data. We then perform several phenomenological excursions beyond this minimal setup and probe effects due to non-minimal flavor violation in the squark sector, revisiting various constraints arising from indirect searches for superpartners. Next, we use several interfaced high-energy physics tools, including the FeynRules package and its UFO interface that we describe in detail, to study the phenomenology of two non- minimal supersymmetric models at the Large Hadron Collider. We estimate the sensitivity of this machine to monotop production in R-parity violating supersymmetry and sgluon-induced multitop production in R-symmetric supersymmetry. We then generalize the results to new physics scenarios designed from a bottom-up strategy and finally depict, from a theorist point of view, a search for monotops at the Tevatron motivated by these findings.Comment: Habilitation thesis; 266 pages; 49 figures; 19 tables; a few references adde