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Publication# The S-matrix Bootstrap Reloaded

Résumé

Quantum field theories (QFTs) are the backbone upon which the edifice of modern physics is built. In this thesis we explore the S-matrix bootstrap which is a non-perturbative method that constrains the vast space of QFTs by using consistency conditions that they must satisfy. The thesis is divided into two parts.In part I of the thesis we study the S-matrix bootstrap for particles with spin in 4 spacetime dimensions and apply the formalism to scattering of identical Majorana fermions to estimate bounds on their quartic couplings and their cubic (Yukawa) coupling to scalar particles. In part II of the thesis, we consider the scattering of massless (Goldstone) excitations on a long flux tube. We use the S-matrix bootstrap to constrain Wilson coefficients of higher dimension operators in the low energy flux tube effective field theory. These constraints naturally translate to bounds on the ground state and excited state energy levels of long flux tubes. The techniques used in this thesis should be extendable to many other systems, both massive and massless. We conclude by discussing some of these possibilities.

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État fondamental

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Tube de flux magnétique

Un tube de flux magnétique caractérise une région de l'espace où règne un fort champ magnétique occupant un territoire approximativement tubulaire. Ce champ, à la surface de sa zone de répartition, e

Andrea Guerrieri, Aditya Hebbar

We bootstrap the S matrix of massless particles in unitary, relativistic two dimensional quantum field theories. We find that the low energy expansion of such S matrices is strongly constrained by the existence of a UV completion. In the context of flux tube (FT) physics, this allows us to constrain several terms in the S matrix low energy expansion or-equivalently-on Wilson coefficients of several irrelevant operators showing up in the FT effective action. These bounds have direct implications for other physical quantities; for instance, they allow us to further bound the ground state energy as well as the level splitting of degenerate energy levels of large FTs. We find that the S matrices living at the boundary of the allowed space exhibit an intricate pattern of resonances with one sharper resonance whose quantum numbers, mass, and width are precisely those of the world-sheet axion proposed by Athenodorou, Bringoltz, and Teper and Dubovsky, Flauger, and Gorbenko. The general method proposed here should be extendable to massless S matrices in higher dimensions and should lead to new quantitative bounds on irrelevant operators in theories of Goldstones and, also, in gauge and gravity theories.

José Luis Abelleira Fernández, Werner Friedrich Herr, Tatiana Pieloni, Ngoc Thanh Trinh, Frank Zimmermann

The physics programme and the design are described of a new collider for particle and nuclear physics, the Large Hadron Electron Collider (LHeC), in which a newly built electron beam of 60 GeV, to possibly 140 GeV, energy collides with the intense hadron beams of the LHC. Compared to the first ep collider, HERA, the kinematic range covered is extended by a factor of twenty in the negative four-momentum squared, Q^2, and in the inverse Bjorken x, while with the design luminosity of 1e33 cm-2 s-1 the LHeC is projected to exceed the integrated HERA luminosity by two orders of magnitude. The physics programme is devoted to an exploration of the energy frontier, complementing the LHC and its discovery potential for physics beyond the Standard Model with high precision deep inelastic scattering measurements. These are designed to investigate a variety of fundamental questions in strong and electroweak interactions. The LHeC thus continues the path of deep inelastic scattering (DIS) into unknown areas of physics and kinematics. The physics programme also includes electron-deuteron and electron-ion scattering in a (Q^2 1/x) range extended by four orders of magnitude as compared to previous lepton-nucleus DIS experiments for novel investigations of neutron's and nuclear structure, the initial conditions of Quark-Gluon Plasma formation and further quantum chromodynamic phenomena. The LHeC may be realised either as a ring-ring or as a linac-ring collider. Optics and beam dynamics studies are presented for both versions, along with technical design considerations on the interaction region, magnets including new dipole prototypes, cryogenics, RF, and further components. A design study is also presented of a detector suitable to perform high precision DIS measurements in a wide range of acceptance using state-of-the art detector technology, which is modular and of limited size enabling its fast installation. The detector includes tagging devices for electron, photon, proton and neutron detection near to the beam pipe. Civil engineering and installation studies are presented for the accelerator and the detector. The LHeC can be built within a decade and thus be operated while the LHC runs in its high-luminosity phase. It so represents a major opportunity for progress in particle physics exploiting the investment made in the LHC.

By using the first-principles approach, we derive a system of three quantum kinetic equations governing the production and evolution of charged scalar particles by an electric field in an expanding universe. Analyzing the ultraviolet asymptotic behavior of the kinetic functions, we found the divergent parts of the electric current and the energy-momentum tensor of the produced particles and determined the corresponding counterterms. The renormalized system of equations is used to study the generation of electromagnetic fields during and after inflation in the kinetic coupling model L-EM = -(1/4)f(2)(phi)F-mu nu F-mu nu with the Ratra coupling function f = exp(beta phi/M-p). It is found that the electric current of created particles is retarded with respect to the electric field. This leads to an oscillatory behavior of both quantities in agreement with the results obtained previously in phenomenological kinetic and hydrodynamical approaches.

2020