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.

Název práce: Studium efektivních Lagrangianů a jejich aplikace Autor: Jaroslav Trnka Katedra: Ústav částicové a jaderné fyziky Vedoucí disertační práce: RNDr. Jiří Novotný, CSc., ÚČJF Abstrakt: V této práci studujeme různé aspekty efektivních teorií pole pro kvan- tovou chromodynamiku (QCD). V prvních dvou kapitolách se zaměříme na efek- tivní teorii pro resonance, která interpoluje mezi nízkoenergetickou efektivní teorií (Chirální poruchová teorie) a vysokoenergetickou QCD. V rámci této teorie studu- jeme jednosmyčkovou renormalizaci, jak z pohledu výpočetního pomocí SS-PP korelátoru, tak i čistě koncepčního studiem dynamicky generovaných stupňů vol- nosti. Ve čtvrté kapitole studujeme amplitudy rozptylu v rámci nelineárního sig- ma modelu, který představuje vedoucí člen nízkoenergetické efektivní teorie pro QCD. V návaznosti na nedávné objevy v rámci Yang-Mills teorie se nám podaří v rámci tohoto modelu zkonstruovat rekurzivní relace pro stromové amplitudy. Kromě čistě teoretické důležitosti tohoto faktu představuje tato metoda efektivní výpočetní nástroj nezávislý na formulaci amplitud pomocí Feynmanovských dia- gramů. Klíčová slova: efektivní teorie pole, kvantová chromodynamika, nelineární sigma model...

Submitted by ANDRES FELIPE VASQUEZ TOCORA (anfvasquezto@unal.edu.co) on 2018-10-02T21:56:33Z No. of bitstreams: 1 thesis.pdf: 3832471 bytes, checksum: 13b65d2c4a9d5e2b2c7414dd2cdfba50 (MD5) / Rejected by Hellen Sayuri Sato null (hellen@ift.unesp.br), reason: Solicitamos que realize correções na submissão seguindo as orientações abaixo - Favor inserir a ficha catalográfica no pdf , logo após a página de rosto - No PDF está faltando as palavras-chave logo após o resumo e abstract on 2018-10-03T14:34:04Z (GMT) / Submitted by ANDRES FELIPE VASQUEZ TOCORA (anfvasquezto@unal.edu.co) on 2018-10-03T16:52:45Z No. of bitstreams: 1 Thesis.pdf: 4205198 bytes, checksum: 499748f6d69605fda811e56805ac4e12 (MD5) / Approved for entry into archive by Hellen Sayuri Sato null (hellen@ift.unesp.br) on 2018-10-03T17:32:51Z (GMT) No. of bitstreams: 1 vasqueztocora_af_me_ift.pdf: 4205198 bytes, checksum: 499748f6d69605fda811e56805ac4e12 (MD5) / Made available in DSpace on 2018-10-03T17:32:51Z (GMT). No. of bitstreams: 1 vasqueztocora_af_me_ift.pdf: 4205198 bytes, checksum: 499748f6d69605fda811e56805ac4e12 (MD5) Previous issue date: 2018-03-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The main goal of this dissertation is to show the enhancement of the cross-section for the double Higgs production through pair annihilation by including effective interactions and through the non-perturbative Sommerfeld effect. Bounds to some Wilson coefficients were obtained from such enhancement, this in the scenarios of the future e+ e− -colliders (FCC-ee, ILC, CLIC). In order to achieve this, some computational tools were implemented: FeynRules, FeynArts, FormCalc, and LoopTools. It is also shown the enhancement of the double Higgs production in 2HDM and MSSM, discussing the general framework of these two models. In addition, it is studied the threshold behavior of the cross-section for the double Higgs production when a hidden sector couples to the Higgs boson, yielding resonances below the threshold energy due to non-perturbative effects. We study the Sommerfeld effect in the double Higgs production in the scenario of e+ e− -colliders. The enhancement is discussed as generated from a hidden sector coupled to the Higgs boson. Below and above threshold enhancements are presented. Such analysis is of importance in the ILC project, which will operate up to the threshold energy √s = 250 GeV. The results has been achieved by the use of computational tools like FeynArts, FormCalc, and LoopTools. / O objetivo principal dessa dissertação é, mostrar o aprimoramento da seção de choque para a produção em dobro dos bósons de Higgs, por meio de aniquilação de pares, incluindo interações efetivas e através do efeito não perturbativo de Sommerfeld. De tais aprimoramentos, os limites para alguns coeficientes de Wilson foram obtidos, isso nos cenários de futuros aceleradores de e+e- (FCC-ee, ILC, CLIC). Para atingir estes resultados, algumas ferramentas computacionais foram implementadas: FeynRules, FeynArts, FormCalc e LoopTools. Também, é mostrado o aprimoramento da produção em dobro de bósons de Higgs no “2HDM” e “MSSM”, discutindo o marco geral desses dois modelos. Além disso, foi estudado o comportamento, perto do limite de produção, da seção de choque da produção em dobro dos bósons de Higgs, quando um setor escondido é acoplado ao Higgs, produzindo ressonâncias abaixo da energia limite de produção, devido à efeitos não perturbativos.

Submitted by NATÁLIA TENÓRIO MAIA null (nmaia@ift.unesp.br) on 2017-09-15T20:22:15Z No. of bitstreams: 1 Thesis.pdf: 1131110 bytes, checksum: 34daa9c413449ad52c084f6625357b9d (MD5) / Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-09-19T17:47:51Z (GMT) No. of bitstreams: 1 maia_nt_dr_ift.pdf: 1131110 bytes, checksum: 34daa9c413449ad52c084f6625357b9d (MD5) / Made available in DSpace on 2017-09-19T17:47:51Z (GMT). No. of bitstreams: 1 maia_nt_dr_ift.pdf: 1131110 bytes, checksum: 34daa9c413449ad52c084f6625357b9d (MD5) Previous issue date: 2017-08-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nesta tese, nós investigamos os efeitos de reação de radiação devido ao spin na dinâmica de um sistema binário de corpos compactos usando uma abordagem de teoria efetiva de campos. Focamos no estágio de espiral da evolução do sistema binário que, por sua vez, provê uma hierarquia de escalas propícia à implementação de uma abordagem perturbativa, tal como a expansão pós-newtoniana. Fazemos uso de um formalismo próprio para investigar efeitos dissipativos. Provemos uma extensão desse formalismo para incluir graus de liberdade de spin. Com isso, em uma abordagem de teoria efetiva de campos, calculamos as acelerações de reação de radiação devido a efeitos de spin-órbita e spin-spin, em primeira ordem. Apresentamos, pela primeira vez, a contribuição de spin na reação de radiação devido ao tamanho finito dos corpos compactos. Também investigamos como os spins de tais corpos são afetados pela reação de radiação, na ordem pós-newtoniana de interesse. Por fim, realizamos um teste de consistência - relacionando a potência total radiada com a perda de energia induzida pelas forças dissipativas - assegurando, assim, a validade dos nossos resultados. / In this thesis, we investigate the radiation reaction effects due to spin on the dynamics of binary compact bodies, using an effective field theory framework. We focus on the inspiral phase of the binary’s evolution, which provides a hierarchy of scales that invites us to implement a perturbative approach such as the Post-Newtonian expansion. We use a formalism suitable to incorporate dissipative effects, providing an extension to include spin degrees of freedom. We use this extension of the effective field theory framework to compute the radiation reaction accelerations due to spin-orbit and spin-spin effects at leading order. We present, for the first time, the spin contribution to radiation reaction due to finite size effects. We also investigate how the spin evolution of the compact bodies is affected by the radiation reaction, at the order of interest. Finally, we perform a consistency test - relating the total radiated power to energy loss induced by the non-conservative forces - ensuring the validity of our results.

Com os próximos grandes projetos the observação do Universo, a cosmologia entrará em uma era de alta precisão de medidas. Novos dados trarão um novo entendimento da evolução do Universo, seus principais componentes e do comportamento da gravi- dade. Sendo assim, é fundamental também ter uma boa predição teórica para a formação de estrutura de larga escala em regime não-linear. A melhor maneira de resolver as equações hidrodinâmicas que descrevem o nosso universo é por meio de simulações cosmológicas na rede. Entretando, estas contém desafios, como a correta inclusão de física bariônica e a diminuição do alto tempo computacional. Uma outra abordagem muito usada é o cálculo das funções de cor- relação por meio de métodos perturbativos (em inglês, Standard Perturbation Theory, ou SPT). Entretanto, esta contém problemas variados: pode não convergir para algu- mas cosmologias e, caso convirja, não há certeza de convergência para o resultado correto. Além disso, há uma escala privilegiada nos limites integrais que envolvem o método perturbativo. Nós calculamos o resultado por esse método até terceira ordem e mostramos que o termo de terceira ordem é ainda maior que o de 2-loops e 3-loops. Isso evidencia alguns problemas descritos com o método perturbativo. O método de Teorias Efetivas de Campo aplicado ao estudo de LSS busca corrigir os problemas da SPT e, desta forma, complementar os resultados de simulações na rede. Em outras áreas da física, como a Cromodinâmica Quântica de baixas energias, EFTs também são usadas como um complemento a essas simulações na rede. EFTs melhoram a predição do espectro de potência da matéria por meio da inclusão dos chamados contra-termos, que precisam ser fitados em simulações. Estes contratermos, que são parâmetros livres, contém importante informação sobre como a física em pequenas escalas afeta a física nas escalas de interesse. Explicaremos os resultados para a predição em 3-loops de EFT, trabalho inédito. É possível usar as EFTs também no problema de conectar a campo de matéria com outros traçadores, como os halos e as galáxias, chamado de bias. Com as EFTs podemos construir uma base completa de operadores para parametrizar o bias. Será explicado como utilizar esses operadores para melhorar a predição do bias em escalas não-lineares. Serão calculados esses termos de EFT em simulações. Também será mostrado como renormalizar o bias em coordenadas de Lagrange. Por fim, será explicada outra importante aplicação das EFTs em cosmologia, mais especificamente em teorias de inflação. EFTs parametrizam desvios nas teorias de um campo único no chamado regime de slow-roll. / With future cosmological surveys, cosmology will enter in the precision era. New data will improve the constraints on the standard cosmological model enhancing our knowledge about the universe history, its components and the behavior of gravity. In this context, it is vital to come up with precise theoretical predictions for the formation of large-scale structure beyond the linear regime. The best way of solving the fluid equations that describe the large-scale universe is through lattice simulations, which faces difficulties in the inclusion of accurate baryonic physics and is very computationally costly. Another approach is the theoreti- cal calculation of the correlation statistics through the perturbative approach, called Standard Perturbation Theory (SPT). However, SPT has several problems: for some cosmologies, it may not converge and even when it converges, we cannot be sure it converges to the right result. Also, it contains a special scale that is the loop momenta upper-bound in the integral. In this work, we show results for the 3-loop calculation. The term of third order is larger than the terms of 2-loops and 3-loops, making explicit SPT problems. In this work, we describe the recent usage of Effective Field Theories (EFTs) on Large Scale Structure problems to correct SPT issues and complement cosmological simulations. EFTs are used in other areas of physics, such as low energy QCD, serving as a complement to lattice calculations. EFT improves the predictions for the matter power spectrum and bispectrum by adding counterterms that need to be fitted. The free parameters, instead of being a problem, bring relevant information about how the small-scale physics affects the scales for which we are trying to make statistical predictions. We show the calculation of the 3-loop EFT counterterms. EFTs are also used to explain main points connecting the matter density field with tracers like galaxies and halos. EFTs highlighted how to construct a complete basis of operators that parametrize the bias. We explain how we can use EFT to improve the bias prediction to non-linear scales. We compute the non-linear halo-bias by fitting the bias parameters in simulations. We also show the EFT renormalization in Lagrangian coordinates. Finally, we explain another critical EFT application to cosmology: in primordial physics. It can be used to parametrize deviations to the slow-roll theory within the inflationary paradigm.

In this thesis, we use the Coleman-Weinberg effective potential for computing the radiative corrections to scalar masses in six simple models of the quantum field theory. We probe, for example, the theory of two scalar fields, simple generalizations of the Abelian Higgs model or some classic extensions of the Standard Model. A common feature of all the theories considered is the existence of (at least) two mass scales different in order of magnitude. Being motivated by the hierarchy problem, we study mainly the sensitivity of light scalar masses on the radiative corrections induced by the heavy fields in relevant Feynman loops. We demonstrate that while the masses of scalars with zero VEV obtain corrections proportional to the masses of the heavy fields, in theories with the spontaneous symmetry breakdown is the Higgs mass always governed by the corresponding ordering parameter, i.e., by its vacuum expectation value. For the Standard Model, understood as an effective field theory, this implies that the Higgs boson mass is as stable with respect to the effects of possible new physics on very high energies as the masses of the leptons, quarks, W and Z bosons. Powered by TCPDF (www.tcpdf.org)

No description available.

In this thesis, we study low energy capture reactions and neutron-deuteron elastic scattering using halo effective field theory (EFT). At low energy, EFT provides a general framework to analyze physical systems regarding as an expansion of short-distance over large distance scales. We provide a model-independent calculation for neutron capture on carbon-14, radiative capture of 3He-4He, radiative capture of 3H-4He, and neutrondeuteron (n-d) doublet channel elastic scattering using halo EFT. These reactions play a significant role in the carbon-nitrogen-oxygen (CNO) cycle, solar neutrino flux measurement, lithium production, and big bang nucleosynthesis (BBN) in the early universe. The cross section is calculated for radiative neutron capture in carbon-14 using halo EFT. This reaction is slowest in the CNO cycle, and it acts as a bottleneck in the production of heavier nuclei A greater than 14. The capture contribution is different from Brett-Wigner resonance because of interference between resonant and non-resonant contribution. Also, we calculated, electromagnetic form factors for one-neutron halo nuclei such as carbon-15, beryllium-11, and carbon-19 using EFT. The electromagnetic form factors depend on the nucleon separation energy, effective range, and the two-body current. The EFT expressions are presented to leading order (LO) for 15C and next-to-leading order (NLO) for 11Be and 19C. We also calculated astronomical Sactor for 3He-4He and 3H-4He radiative capture reactions. The low energy Sactor for these reactions are important to understand the Li problem and neutrino physics. At the LO, the capture amplitude contains the initial state swave strong and Coulomb interactions summed to all orders. The NLO contribution comes from non-perturbative Coulomb interaction. Our calculated astrophysical Sactor for 3He- 4He is slightly above the average compared to the other measurement and prediction but consistent within current error bars. The Sactor for 3H-4He is also compatible with the experimental extrapolation. Finally, we studied doublet channel n-d scattering using halo EFT. A two dimer halo EFT is developed to describe the virtual state and three-body bound state in n-d scattering. We show the connection between virtual state and three-body bound state using S-matrix analysis and phase shift analysis which is supported by the Efimov plots.

No description available.

Donoghue's effective field theory of quantum gravity is extended to include the interaction of massless particles. The collinear divergences which accompany massless particles are examined first in the context of QED and then in quantum gravity. A result of Weinberg is extended to show how these divergences vanish in the case of gravity. The scattering cross section for hypothetical massless scalar particles is computed first, because it is simpler, and the results are then extended to photons. Some terms in the cross section are shown to correspond to the Aichelburg-Sexl metric surrounding a massless particle and to quantum corrections to that metric. The scattering cross section is also applied to calculate quantum corrections to the bending of starlight, and though small, the result obtained is qualitatively different than in the classical case. Since effective field theory includes the low-energy degrees of freedom which generate collinear divergences, the results presented here will remain relevant in any future quantum theory of gravity.