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Publication# Gravitational causality and the self-stress of photons

Résumé

We study causality in gravitational systems beyond the classical limit. Using on-shell methods, we consider the 1-loop corrections from charged particles to the photon energy-momentum tensor - the self-stress - that controls the quantum interaction between two on-shell photons and one off-shell graviton. The self-stress determines in turn the phase shift and time delay in the scattering of photons against a spectator particle of any spin in the eikonal regime. We show that the sign of the beta-function associated to the running gauge coupling is related to the sign of time delay at small impact parameter. Our results show that, at first post-Minkowskian order, asymptotic causality, where the time delay experienced by any particle must be positive, is respected quantum mechanically. Contrasted with asymptotic causality, we explore a local notion of causality, where the time delay is longer than the one of gravitons, which is seemingly violated by quantum effects.

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Particule matérielle

Le terme « particule matérielle » (material particle en anglais) désigne une petite portion d'un corps, de matière solide ou fluide, constituée d'un nombre suffisamment grand de particules élémentaire

Photon

Le photon est le quantum d'énergie associé aux ondes électromagnétiques (allant des ondes radio aux rayons gamma en passant par la lumière visible), qui présente certaines caractéristiques de partic

Quantum

En physique, quantum (mot latin signifiant « combien » et dont le pluriel s'écrit « quanta ») représente la plus petite mesure indivisible, que ce soit celle de l'énergie, de la quantité de mouvement

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Currently, the best theoretical description of fundamental matter and its gravitational interaction is given by the Standard Model (SM) of particle physics and Einstein's theory of General Relativity (GR). These theories contain a number of seemingly unrelated scales. While Newton's gravitational constant and the mass of the Higgs boson are parameters in the classical action, the masses of other elementary particles are due to the electroweak symmetry breaking. Yet other scales, like ΛQCD associated to the strong interaction, only appear after the quantization of the theory. We reevaluate the idea that the fundamental theory of nature may contain no fixed scales and that all observed scales could have a common origin in the spontaneous break-down of exact scale invariance. To this end, we consider a few minimal scale-invariant extensions of GR and the SM, focusing especially on their cosmological phenomenology. In the simplest considered model, scale invariance is achieved through the introduction of a dilaton field. We find that for a large class of potentials, scale invariance is spontaneously broken, leading to induced scales at the classical level. The dilaton is exactly massless and practically decouples from all SM fields. The dynamical break-down of scale invariance automatically provides a mechanism for inflation. Despite exact scale invariance, the theory generally contains a cosmological constant, or, put in other words, flat spacetime need not be a solution. We next replace standard gravity by Unimodular Gravity (UG). This results in the appearance of an arbitrary integration constant in the equations of motion, inducing a run-away potential for the dilaton. As a consequence, the dilaton can play the role of a dynamical dark-energy component. The cosmological phenomenology of the model combining scale invariance and unimodular gravity is studied in detail. We find that the equation of state of the dilaton condensate has to be very close to the one of a cosmological constant. If the spacetime symmetry group of the gravitational action is reduced from the group of all diffeomorphisms (Diff) to the subgroup of transverse diffeomorphisms (TDiff), the metric in general contains a propagating scalar degree of freedom. We show that the replacement of Diff by TDiff makes it possible to construct a scale-invariant theory of gravity and particle physics in which the dilaton appears as a part of the metric. We find the conditions under which such a theory is a viable description of particle physics and in particular reproduces the SM phenomenology. The minimal theory with scale invariance and UG is found to be a particular case of a theory with scale and TDiff invariance. Moreover, cosmological solutions in models based on scale and TDiff invariance turn out to generically be similar to the solutions of the model with UG. In usual quantum field theories, scale invariance is anomalous. This might suggest that results based on classical scale invariance are necessarily spoiled by quantum corrections. We show that this conclusion is not true. Namely, we propose a new renormalization scheme which allows to construct a class of quantum field theories that are scale-invariant to all orders of perturbation theory and where the scale symmetry is spontaneously broken. In this type of theory, all scales, including those related to dimensional transmutation, like ΛQCD, appear as a consequence of the spontaneous break-down of the scale symmetry. The proposed theories are not renormalizable. Nonetheless, they are valid effective theories below a field-dependent cut-off scale. If the scale-invariant renormalization scheme is applied to the presented minimal scale-invariant extensions of GR and the SM, the goal of having a common origin of all scales, spontaneous breaking of scale invariance, is achieved.

High-energy particle physics is going through a crucial moment of its history, one in which it can finally aspire to give a precise answer to some of the fundamental questions it has been conceived for. On the one side, the theoretical picture describing the elementary strong and electroweak interactions below the TeV scale, the Standard Model, has been well consolidated over the decades by the observation and the precise characterization of its constituents. On the other hand, the enormous technological potentialities nowadays available, and the skills accumulated in decades of collider experiments with increasingly high complexity, render for the first time plausible the possibility of addressing complicated and conceptually deep questions like the ones at hand. The best incarnation of this high level of sophistication is the CERN Large Hadron Collider (LHC), the most powerful experimental apparatus ever built, which is designed to shed light on the true nature of fundamental interactions at energies never attained before, and which has already started to open a new era in physics with the recent discovery of the longed-for Higgs boson, a true milestone for the human knowledge as well as one of the most important discoveries in the modern epoch. The knowledge that has been and is going to be reached in these crucial years would of course not be conceivable without a deep interplay between the theoretical and the experimental efforts. In particular, on the theoretical side, not only there are wide groups of researchers devoted to building possible extensions to the Standard Model, which draws the guidelines of current and future experiments, but also there is a vast community whose research is rather aimed at the precise predictions of all the physical observables that could be measured at colliders, and at the systematic improvement of the approximations that currently constrain such predictions. On top of representing the state-of-the-art of the human understanding of the properties that regulate elementary-particle interactions and of the formalisms that describe them, the developments of this line of research have an immediate and significant impact on experiments. Firstly, these detailed calculations are the very theoretical predictions against which experimental data are compared, so they are crucial in establishing the validity or not of the theories according to which they are performed. Secondly, the signals one wants to extract from data at modern colliders are so tiny and difficult to single out that the experimental searches themselves need be supplemented by a detailed work of theoretical modelling and simulation. In this respect, high-precision computations play an essential role in all analysis strategies devised by experimental collaborations, and in many aspects of the detector calibration. It is clear that, for theoretical computations to be useful in experimental analyses and simulations, the predictions they yield should be reliable for all possible configurations of the particles to be detected. Thus the key feature for the present theoretical collider physics is not particularly the computation of observables with high precision only in a limited region of the phase space, but the capability of combining (‘matching’) in a consistent way different approaches, each of which is reliable in a particular kinematic regime. With this perspective, matching techniques represent one of the most promising and successful theoretical frameworks currently available, and are considered as eminently valuable tools both on the theoretical and on the experimental sides. Matched computations are based on a perturbation-theory approach for the description of configurations in which the scattering products are well separated and/or highly energetic: in particular the precision currently attained for all but a few of the relevant processes within the Standard Model is the next-to-leading order (NLO) in powers of the strong quantum-chromodynamics (QCD) coupling constant αS; for the description of configurations in which the particles outgoing the collisions are close to each other and/or have low energy, it can be shown that the perturbation-theory expansion breaks down, and then a complementary method, like the parton shower Monte Carlo (PSMC), has instead to be employed. The task of matching is precisely that of giving a prediction that interpolates between the two approaches in a smooth and theoretically-consistent way. This thesis is focused on MC@NLO, a high-energy physics formalism capable of matching computations performed at the NLO in QCD to PSMC generators, in such a way as to retain the virtues of both approaches while discarding their mutual deficiencies. In particular, the thesis reports on the work successfully achieved in extending MC@NLO from its original numerical implementation, tailored on the HERWIG PSMC, to the other main PSMC programs currently employed by experimental collaborations, PYTHIA and Herwig++, confirming the advocated universality of the method. Differences in the various realizations are explained in detail both at the formal level and through the simulation of various Standard-Model reactions. Moreover we describe how the MC@NLO framework has been developed so as to render its implementation automatic with respect to the physics process one is about to simulate: beyond yielding an enormous increase in its potential for present and future collider phenomenology, and upgrading the standard of precision for high-energy computations to the NLO+PSMC level, this development allows for the first time the application of the MC@NLO formalism to a huge number of relevant and highly complicated reactions, through an implementation which is also easily usable by people well-outside the community of experts in QCD calculations. As example of this new version, called aMC@NLO, recent results are presented for complex scattering processes, involving four or five final-state particles. Finally, possible extensions of the framework to theories beyond the Standard Model, like the supersymmetric version of QCD, are briefly introduced.

In this PhD thesis we deal with two mathematical problems arising from quantum mechanics. We consider a spinless non relativistic quantum particle whose configuration space is a two dimensional surface S. We also suppose that the particle feels the effect of an homogeneous magnetic field perpendicular to the surface S. In the first case S = R × SL1, the infinite cylinder of circumference L, corresponding to periodic boundary conditions, while in the second one S = R2. In both cases the particle feels the effect of an additional suitable potential. We are thus left with the study of two specific classes of Schrödinger operators. The operator of the first class generates the dynamics of the particle when it is submitted to an Anderson-type random potential, as well as to a non random potential confining the particle along the cylinder axis in an interval of length L. In this case we describe the spectrum and classify it by the quantum mechanical current carried by the corresponding eigenfunctions. We prove that there are spectral regions in which all the eigenvalues have an order one current with respect to L, and spectral regions where eigenvalues with order one current and eigenvalues with infinitesimal current with respect to L are intermixed. These results are relevant for the theory of the integer quantum Hall effect. The second Schrödinger operator class corresponds to the physical situation where the potential is the sum of a "local" potential and of a potential due to a weak constant electric field F. In this case we show that the resonant states, induced by the electric field, decay exponentially at a rate given by the imaginary part of the eigenvalues of some non self-adjoint operator. Moreover we prove an upper bound on this imaginary part that turns out to be of order exp(-1/F2) as F goes to zero. Therefore the lifetime of the resonant states is at least of order exp(-1/F2).