We show that the minimal Weyl-invariant Einstein-Cartan gravity in combination with the Standard Model of particle physics contains just one extra scalar degree of freedom (in addition to the graviton and the Standard Model fields) with the properties of an axion-like particle which can solve the strong CP-problem. The smallness of this particle’s mass as well as of the cosmological constant is ensured by tiny values of the gauge coupling constants of the local Lorentz group. The tree value of the Higgs boson mass and that of Majorana leptons (if added to the Standard Model to solve the neutrino mass, baryogenesis and dark matter problems) are very small or vanishing, opening the possibility of their computability in terms of the fundamental parameters of the theory due to nonperturbative effects.

Germany

Georgios Karananas

Switzerland

Mikhail Shaposhnikov

Belgium

Sebastian Zell

Weyl-invariant Einstein-Cartan gravity: unifying the strong CP and hierarchy puzzles

In recent works [1,2], we have shown how n-point correlation functions in perturbative QFT can be computed without running into intermediate divergences. Here we want to illustrate explicitly that one can calculate the quantum effective potential by the same method. As a main example, we consider a theory with two fields having large and small vacuum expectation values (vev). We show that no fine-tuning between the physical quantities is needed to keep the hierarchy between the vevs of different fields.

Sander Mooij

Effective potential in finite formulation of QFT

We propose a new class of single-field scalar quantum field theories with non-polynomial interactions leading to a two-point Green's function that can be naturally continued beyond the naive cutoff scale. This provides a new prospect for self-completing theories in the UV-domain. In our approach, the formal power series for the scalar potential has a vanishing radius of convergence and is defined through Borel resummation. We discuss concrete examples, among others with a spectral function that vanishes at large momenta, potentially leading to an asymptotically free theory. Finally, we give an outlook on future research, with a view towards possible applications to inflation and gravity.

Non-polynomial interactions as a path towards a non-renormalizable UV-completion

I describe the sterile neutrino dark matter candidate and discuss how it may fit into the overall picture of physics beyond the Standard Model.

Sterile neutrinos as dark matter

We find the conditions under which scale-invariant Einstein-Cartan gravity with scalar matter fields leads to an approximate conformal invariance of the flat space particle theory up to energies of the order of the Planck mass. In the minimal setup, these models, in addition to the fields of the Standard Model and the graviton, contain only one extra particle — a massless dilaton. Theories of this type can pave the way for a self-completion all the way up the Planck scale and lead to rather universal inflationary predictions, close to those of the simplest Higgs-inflation scenario in the metric theory of gravity.

Scale invariant Einstein-Cartan gravity and flat space conformal symmetry

In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of the scale symmetry. Besides that, the fundamental theory must include gravity, whereas all known extensions of the conformal invariance to the curved space-time suffer from the Weyl anomaly. We show that conformal symmetry can be made free from quantum anomaly only in flat space. The presence of gravity would reduce the global symmetry group of the fundamental theory to the scale invariance only. We discuss how the effective Lagrangian respecting the scale symmetry can be used for the description of particle phenomenology and cosmology.

Finland

United Kingdom

Anna Tokareva

Anomaly-free scale symmetry and gravity

We study a finite, divergence-free approach to renormalisation originally proposed in the early '70s by Blaer and Young, and Callan. It is based on equations similar to the Callan-Symanzik equations and introduced in the context of the <math><mi>λ</mi><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup></math> theory. We generalise this method to the case of two interacting scalar fields, with obvious generalisation to an arbitrary number of fields.

Netherlands

Finite Callan-Symanzik renormalisation for multiple scalar fields

The standard way to do computations in Quantum Field Theory (QFT) often results in the requirement of dramatic cancellations between contributions induced by a “heavy” sector into the physical observables of the “light” (or low energy) sector – the phenomenon known as “technical hierarchy problem”. This procedure uses divergent multi-loop Feynman diagrams, their regularisation to handle the UV divergences, and then renormalisation to remove them. At the same time, the ultimate outcome of the renormalisation is the mapping of several finite parameters defining the renormalisable field theory into different observables (e.g. all kinds of particle cross-sections). In this paper, we first demonstrate how to relate the parameters of the theory to observables without running into intermediate UV divergences. Then we go one step further: we show how in theories with different mass scales, all physics of the “light” sector can be computed in a way that does not require dramatic cancellations induced by the physics of the “heavy” sector. The existence of such a technique suggests that the “hierarchy problem” in renormalisable theories is not really physical, but rather an artefact of the conventional procedure to compute correlation functions. If the QFT is defined by the “divergencies-free” method all fine-tunings in theories with well-separated energy scales may be avoided.

QFT without infinities and hierarchy problem

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing nature. The origin of scales, such as the Higgs vacuum expectation value (VEV), may result from the spontaneous breakdown of the conformal symmetry by the dilaton field. In this work, we study whether this classical setup can be implemented in quantum theory and be phenomenologically viable by presenting an explicit construction where the exact conformal symmetry can be preserved and is anomaly-free while being spontaneously broken. Not only the Higgs mass but also the genuine quantum scales such as the QCD confinement radius are generated by the dilaton VEV. We also discuss the extension of these ideas to the theories with dynamical gravity and show that the only finite subgroup of the local Weyl transformations which is anomaly-free corresponds to the global scale symmetry. This means that the conformal invariance of the flat space theory is explicitly broken down to the scale symmetry by gravitational effects related to the Weyl anomaly.

Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly

For inflation driven by the Higgs field coupled non-minimally to gravity, we study the cutoff energy scale above which perturbation theory breaks down. Employing the metric formulation, we first give an overview of known results and then provide a new way to calculate a lower bound on the cutoff. Our approach neither relies on a gauge choice nor does it require any calculation of amplitudes. Instead, it exploits the fact that the S-matrix is invariant under field redefinitions. In agreement with previous findings, we demonstrate that the cutoff is significantly higher during inflation than in vacuum, which ensures the robustness of semi-classical predictions. Along the way, we generalize our findings to the Palatini formulation and comment on a useful parametrization of the Higgs doublet in both scenarios.