Asymptotic scale invariance and its consequences

Scale invariance supplemented by the requirement of the absence of new heavy particles may play an important role in addressing the hierarchy problem. We discuss how the Standard Model may become scale invariant at the quantum level above a certain value of the Higgs field value without addition of new degrees of freedom and analyze phenomenological and cosmological consequences of this setup, in particular, possible metastability of the electroweak vacuum and Higgs inflation.

Scale-Invariant Models of Gravity and Particle Physics and their Cosmological Implications

Daniel Zenhäusern

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.

EPFL2011

Euclidean classical solutions in quantum field theory and gravity: Higgs vacuum metastability and the hierarchy problem

Andrey Shkerin

The thesis is dedicated to two groups of questions arising in modern particle physics and cosmology. The first group concerns with the problem of stability of the electroweak (EW) vacuum in different environments. Due to its phenomenological significance, the problem attracts high attention in recent research. We contribute to this research in two directions. First, we study decay rate of the EW vacuum at the inflationary stage of the universe. While in a low density, low temperature environment characteristic of the present-day universe the Standard Model EW vacuum is safely long-lived, the situation may be different during inflation. We estimate tunneling transition via Coleman-De Luccia instanton in this case and confirm that it is exponentially suppressed, contrary to the claims made in the literature. Second, we compute the lifetime of the EW vacuum in a scale-invariant extension of the Standard Model and gravity, known as the Higgs-Dilaton theory. The theory passes phenomenological tests and provides us with a plausible cosmological scenario. To confirm its viability, it is necessary to check if the EW vacuum in this theory is sufficiently safe. We perform this check and find that features of the Higgs-Dilaton theory yield additional stabilization of the low-energy vacuum, compared to the Standard Model case. Another group of questions addressed in the thesis is related to the hierarchy problem. Combining quantum scale invariance with the absence of new degrees of freedom above the EW scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the Planck scales remains unexplained. We suggest that this hierarchy can be a manifestation of a non-perturbative effect relating low-energy and strong-gravity domains of the theory. To support this suggestion, we construct instanton configurations and investigate their contribution to the vacuum expectation value of the Higgs field. The effect we find relies on properties of the theory in the ultraviolet regime. Non-minimal coupling of the Higgs field to the Ricci scalar and an approximate Weyl invariance of the theory in this regime are important ingredients of the mechanism. Dynamical gravity plays a crucial role in the effect as it leads to existence of instanton solutions suitable for generating the EW scale.

EPFL2018

Non-perturbative processes with Fermion number non-conservation in different models of particle physics

Yannis Burnier

When a classical conservation law is broken by quantum corrections, the associated symmetry is said to be anomalous. This type of symmetry breaking can lead to interesting physics. For instance in strong interactions, the anomaly in the chiral current is important in the pion decay to two photons. In weak interactions, there is an anomaly in the baryon number current. Although anomalous baryon number violating transitions are strongly suppressed at small energies, they could be at the origin of the baryon asymmetry of the universe. In this thesis, we consider several issues related to the theoretical and phenomenological aspects of anomalies. Although our main aim is the study of the electroweak theory, most of the theoretical questions do not rely on its precise setup. In order to solve these problems, we design a 1+1 dimensional chiral Abelian Higgs model displaying similar nonperturbative physics as the electroweak theory and leading to many simplifications. This model contains sphaleron and instanton transitions and, as the electroweak theory, leads to anomalous fermion number nonconservation. The one-loop fermionic contribution to the probability of an instanton transition with fermion number violation is calculated in the chiral Abelian Higgs model where the fermions have a Yukawa coupling to the scalar field. These contributions are given by the determinant of the fermionic fluctuations. The dependence of the determinant on fermionic, scalar and vector mass is determined. We also show in detail how to renormalize the fermionic determinant in partial wave analysis. The 1+1 dimensional model has the remarkable property to enable the creation of an odd number of fractionally charged fermions. We point out that for 1+1 dimensions this process does not violate any symmetries of the theory, nor does it lead to any mathematical inconsistencies. We construct the proper definition of the fermionic determinant in this model and underline its non-trivial features that are of importance for realistic 3+1 dimensional models with fermion number violation. In theories with anomalous fermion number nonconservation, the level crossing picture is considered a faithful representation of the fermionic quantum number variation. It represents each created fermion by an energy level that crosses the zero-energy line from below. If several fermions of various masses are created, the level crossing picture contains several levels that cross the zero-energy line and cross each other. However, we know from quantum mechanics that the corresponding levels cannot cross if the different fermions are mixed via some interaction potential. The simultaneous application of these two requirements on the level behavior leads to paradoxes. For instance, a naive interpretation of the resulting level crossing picture gives rise to charge nonconservation. We resolve this paradox by a precise calculation of the transition probability, and discuss what are the implications for the electroweak theory. In particular, the nonperturbative transition probability is higher if top quarks are present in the initial state. Coming back to the electroweak theory, we point out that the results of many baryogenesis scenarios operating at or below the TeV scale are rather sensitive to the rate of anomalous fermion number violation across the electroweak crossover. Assuming the validity of the Standard Model of electroweak interactions, we estimate this rate for experimentally allowed values of the Higgs mass (mH = 100…300 GeV). We also discuss where the rate enters in the particle density evolution and how to compute the leading baryonic asymmetry.

EPFL2006