Asymptoticity of QCD and massive, oriented eventshapes: A study in the large-B0 limit and applications to jet physics

Abstract

[En] With the appearance and development of the broad and powerful theories of General Relativity and the Standard Model, theoretical physics came to the realization that a single theory explaining the behavior of all kinds of matter and energy may be possible. The phenomenology of three of the four fundamental interactions of nature the strong, weak and electromagnetic interactions has been accurately described to a great extent with the language of Quantum Field Theory (QFT) in the Standard Model, although the incorporation of an adequate description of gravity still remains a wall we have not yet climbed. General Relativity is considered to be incompatible with QFT, and thus ultimately incompatible with the Standard Model itself. Such incompatibilities are not by any means the purpose of this work, but its inevitable conclusion serves as a starting point: if there is to be a coherent explanation for the four interactions of nature, improvements in any (or both) theories have yet to come. Improvements on a scientific model can occur in one of two main ways. On the one hand, there is the intuitive way of extending the model to describe new phenomenology. In particle physics, extensions of the Standard Model are an effort collectively known as Beyond the Standard Model Physics (BSM). BSM deals with neutrino oscillations, matter-antimatter asymmetry, the strong CP problem, dark matter and dark energy, all of them problems that the Standard Model cannot explain in its current state. However, it is important to realize there is a second way in which progress in a model can be made: by pushing forward not the boundaries of the model itself, but the boundaries of our understanding of it. During the last century, theoretical physics has seen how, in searching for the most fundamental theory, a price of technical complexification has been paid. We went from a classical view of the world requiring only algebraic and differential calculus to theories built on the language of more and more advanced mathematical objects. Special Relativity abandoned the Euclidean space, and later General Relativity was built by employing Differential Geometry, which added tensor calculus and the properties of space into the physicists' toolkit. Other ingredients such as Probability theory and strategies such as perturbation theory have been progressively standardized in physics thanks to the developments in Thermodynamics and Quantum Mechanics, and they have become so common nowadays that it is hard to think there was a time not that long ago when physicists were unfamiliar with concepts such as matrices and tensors. In any case, it is clear that improvements in the understanding of these methods were key in advancing the physical knowledge of the time and developing it to the extent we find today. The way this intertwines with the current situation of the Standard Model is simply that it is no exception to the rule: the use of perturbation theory and the machinery of Feynman diagrams implies that results for matrix elements and observables are given in the form of infinite power series. The difficulty in the computation of the coefficients of these series increases exponentially with the order of the expansion, and the state-of-the-art knowledge indicates they have in general zero convergence radius1. In QCD, the language of renormalon calculus and Operator Product Expansion (OPE) has been developed to deal with divergent series. Renormalon calculus is based on the study of asymptotic divergent series and deals with the problems of assigning a finite estimate and an uncertainty, usually called ambiguity, to the sum of the series. OPE adds non-perturbative corrections that cancel the ambiguities of the perturbative series. In sum, computations within the perturbative approach to the StandardModel are carried out in the language of divergent power series that need to be supplemented with non-perturbative corrections, in which theoretical physics does not have the full mastery yet. Parts I and II of this thesis are dedicated to build on this topic through a detailed review and a number of applications and studies. In chapter 1 we introduce the concepts of asymptotic series, summation methods for divergent series and Borel summation, and we particularize them to series in QCD, in which the factorial growth of the coefficients translates into poles in the Borel plane known as renormalons. We present all these ideas formally but we also complement with several illustrative examples. We end the chapter by introducing the large-B0 limit, a rearrangement of the usual perturbative QCD expansion in alphas in which the leading order contribution is an infinite tower of terms that can be computed with a single computation of one-loop difficulty. It is in this limit in which the asymptotic properties of QCD can be studied.