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Ultimo aggiornamento 19 gen 2018
Giovanni Stagnitto
Sesso M
Esperimento ATLAS
Tipo Laurea Magistrale
Destinazione dopo il cons. del titolo Dottorato (estero)
Università Universita' Di Pavia
Titolo Scale dependence of physical observables and theoretical uncertainties
Abstract The Large Hadron Collider, operating at CERN since 2009, has recently started its Run II operational phase, with protons circulating at 13 TeV c. m. e., and a packed schedule of physics runs is already planned for the next 20 years. With the expected increase of luminosity, more and more accurate experimental measurements will be achieved. In order to stress the Stan- dard Model and potentially detect the presence of new physics, the precision of theoretical predictions will be a relevant factor in order to accomplish a good comparison between theory and experiment. Usually the physical observables in the context of the Quantum Field Theory of strong interactions, the Quantum Chromodynamics (QCD), are expressed as perturbation series in the strong coupling αs, but only the first terms of this expansion are actually explic- itly evaluated, mixing analytical derivations with Monte Carlo integrations. These fixed-order predictions are recently becoming available up to higher and higher power of αs, increasing a lot the precision of our calculation. However, the “truncation” of the QCD perturbative series is not completely harmless: there is a source of uncertainty coming from the missing higher orders, which seems to be unavoidable. This problem about fixed-order predictions always comes with another issue: perturbative calculations are expressed as function of parameters with the dimension of energy (referred as scales), which are introduced in the renormalization procedure or in the factorization theorems. These scales are unphysical, i.e.physical observables should not depend on them. While this is true and guaranteed for an all-order prediction, fixed-order calculations retain a dependence on the unphysical scales, and this must be taken into account. Usually, in order to estimate the missing higher order uncertainties, a naif scale variation procedure is adopted: the uncertainty interval is estimated by varying the calculation of each observable using different renormalization or factorization scales (for example by varying them between Q/2 and 2Q, where Q is a typical energy of the process). However, this method is completely arbitrary and it has no theoretical foundation nor a real statistical meaning. An alternative Bayesian approach has been recently evaluated: it is based on some hypothesis about the order of magnitude of the coefficients of the perturbative series and it allows to associate a meaningful degree of belief to each interval. This work is based on the researches carried out in the last few months during my intern- ship at the Laboratoire de Physique Théorique et Hautes Energies (LPTHE) in Paris, in the context of the Erasmus+ Traineeships program, under the supervision of Matteo Cacciari and in continuous contact with Daniela Rebuzzi. After a first study of the main articles and reviews about the thesis subject, my work has focused on the unphysical scale(s) dependence of physical observables, which comes with some characteristic logarithmic terms for the coefficient of the series. This thesis work is organized as follows. In Chapter 1 the renormalization and factorization scales are introduced, together with a discussion about the structure of QCD prediction and traditional techniques for the estimate of uncertainties. In Chapter 2 some original recurrence relations are found, which allow to derive the scale dependence of the short-distance Wilson coefficients for Deep Inelastic Scattering (DIS) and the partonic cross section in p-p collision at any desidered order in perturbation theory. The Bayesian approach for the estimate of theoretical uncertainties is discussed in Chapter 3. Finally, in Chapter 4, the total and differential cross section for the Vector Boson Fusion channel for Higgs production at LHC is considered as a case study for both the study of scale dependence of physical observables and the comparison between different methods for the estimate of missing higher order uncertainties.
Anno iscrizione 2015
Data conseguimento 20 lug 2017
Luogo conseguimento Universita di Pavia
D. Rebuzzi M. Cacciari (LPTHE, Paris)  
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