Narrow Results

The usual derivation of the Lagrangian of a model for massive vector bosons, by spontaneous symmetry breaking of a gauge theory, implies that the prefactors of the various interaction terms are uniquely determined functions of the coupling constant(s) and the masses. Since, under the renormalization group (RG) flow, different interaction terms get different loop-corrections, it is uncertain whether these functions remain fixed under this flow. We investigate this question for the $U(1)$-Higgs-model to 1-loop order in the framework of Epstein–Glaser renormalization. Our main result reads: choosing the renormalization mass scale(s) in a way corresponding to the minimal subtraction scheme, the geometrical interpretation as a spontaneously broken gauge theory gets lost under the RG-flow. This holds also for the clearly stronger property of BRST-invariance of the Lagrangian. On the other hand, we prove that physical consistency, which is a weak form of BRST-invariance of the time-ordered products, is maintained under the RG-flow.

We give a simple derivation of the Higgs phenomenon in an Abelian light front gauge theory. It is based on a finite-volume quantization with antiperiodic scalar fields and periodic gauge field. An infinite set of degenerate vacua in the form of coherent states of the scalar field, that minimize the light front energy, is constructed. The corresponding effective Hamiltonian describes a massive vector field whose third component is generated by the would-be Goldstone boson. This mechanism, understood here quantum mechanically in the form analogous to the spacelike quantization, is derived without gauge fixing as well as in the unitary and the light-cone gauge.

Just like the vector gauge bosons in the gauge theories, it is now known that gravitons acquire mass in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. The point is that we should find the gravitational Higgs mechanism such that it results in massive gravity in a flat Minkowski spacetime without non-unitary propagating modes. This is usually achieved by including higher-derivative terms in scalars and tuning the cosmological constant to be a negative value in a proper way. Recently, a similar but different gravitational Higgs mechanism has been advocated by Chamseddine and Mukhanov where one can relax the negative cosmological constant to zero or positive one. In this work, we investigate why the non-unitary ghost mode decouples from physical Hilbert space in a general spacetime dimension. Moreover, we generalize the model to possess an arbitrary potential and clarify under what conditions the general model exhibits the gravitational Higgs mechanism. By searching for solutions to the conditions, we arrive at two classes of potentials exhibiting gravitational Higgs mechanism. One class includes the model by Chamseddine and Mukhanov in a specific case while the other is a completely new model.

We discuss an alternative implementation of the Higgs boson within the Standard Model which is possible if the renormalizability condition is relaxed. Namely, at energy scale Λ the Higgs boson interacts at tree-level only with matter fermions, while the full gauge invariance is still maintained. The interactions with the electroweak gauge bosons are induced at low energies through the radiative corrections. In this scenario the Higgs boson can be arbitrarily heavy, interacting with the Standard Model fields arbitrarily weakly. No violation of unitarity in the scattering of longitudinal electroweak bosons occurs, since they become unphysical degrees of freedom at energies Λ ~ TeV.

We present expressions of the Pagels–Stokar (PS) type for the masses of the $W^{\pm }$ and Z bosons in terms of the quark and lepton self-energies. By introducing a genuine new term in the gauge boson-fermion–anti-fermion vertex we manage to accomplish three main achievements: First, we show that the similar results existing in literature lead, in general, to a nonsymmetric gauge boson mass matrix and we fix this flaw. Second, we consider the case of any number of fermion generations with general mixing. Third, we include in our analysis also an arbitrary number of right-handed neutrinos, together with the left-handed and right-handed neutrino Majorana masses (self-energies). On top of that, we give also a correction to the original PS formula for the pion decay constant in QCD.

In collaboration with Jogesh Pati, Abdus Salam challenged the chiral gauge nature of the Standard Model by paving the road towards the left-right symmetric electro-weak theory. I describe here the logical and historical construction of this theory, by emphasising the pioneering and key role it played for neutrino mass. I show that it is a self-contained and predictive model with the Higgs origin of Majorana neutrino mass, in complete analogy with the SM situation regarding charged fermions.

I reflect on some of the basic aspects of present day Beyond the Standard Model particle physics, focusing mostly on the issues of naturalness, in particular on the so-called hierarchy problem. To all of us, physics as natural science emerged with Galileo and Newton, and led to centuries of unparalleled success in explaining and often predicting new phenomena of nature. I argue here that the long-standing obsession with the hierarchy problem as a guiding principle for the future of our field has had the tragic consequence of deviating high energy physics from its origins as natural philosophy, and turning it into a philosophy of naturalness.

We consider Weyl’s conformal gravity coupled to a complex matter field in Weyl geometry. It is shown that a Higgs potential naturally arises from a ${\tilde{R}}^2$ term in moving from the Jordan frame to the Einstein frame. A massless Nambu–Goldstone boson, which stems from spontaneous symmetry breakdown of the Weyl gauge invariance, is absorbed into the Weyl gauge field, thereby the gauge field becoming massive. We present a model where the gravitational interaction generates a Higgs potential whose form is a perfect square. Finally, we show that a theory in the Jordan frame is gauge-equivalent to the corresponding theory in the Einstein frame via the BRST formalism.

A gauged SO(3) symmetry is broken into its little groups of the representations ℓ = 2 and ℓ = 3. Explicit Higgs potentials leading to the spontaneous symmetry breaking are constructed. The masses of the gauge bosons and Higgs particles are calculated in terms of the renormalizable potentials. Emergence of Goldstone bosons arising from the absence of certain potential terms is also discussed. Analogous structures between the cosmic strings and disclinations of liquid crystals are noted.

We discuss an alternative to the Higgs mechanism which leads to gauge invariant masses for the electroweak bosons. The key idea is to reformulate the gauge invariance principle which, instead of being applied as usual at the level of the action, is applied at the level of the quantum fields. In other words, we define gauge invariant quantum fields which are used to build the action. In that framework, the Higgs field is not necessarily a physical degree of freedom but can merely be a dressing field that does not propagate. If the Higgs boson is not propagating, the weak interactions must become strongly coupled below 1 TeV and have a nontrivial fixed point and would thus be renormalizable at the nonperturbative level. On the other hand, if a gauge invariant Higgs boson is introduced in the model, its couplings to the fermions and the electroweak bosons can be quite different from those expected in the Standard Model.

Results from the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) in nucleus–nucleus and proton–proton collisions at c.m. energy are presented in the context of the methods of single and two-particle inclusive reactions which were used in the discovery of hard-scattering in p–p collisions at the CERN ISR in the 1970's. These techniques are used at RHIC in A + A collisions because of the huge combinatoric background from the large particle multiplicity. Topics include J/Ψ suppression, jet quenching in the dense medium (sQGP) as observed with π0 at large transverse momentum, thermal photons, collective flow, two-particle correlations, suppression of heavy quarks at large p_T and its possible relation to Higgs searches at the LHC. The differences and similarities of the measurements in p–p and A + A collisions are presented. The two discussion sessions which followed the lectures on which this article is based are included at the end.

We construct a lattice gauge theory using reduced staggered fermions and gauge fields which provides a nonperturbative realization of a complete technicolor model; one which treats both strong and weakly coupled gauge sectors on an equal footing. We show that the model is capable of developing a Higgs phase at nonzero lattice spacing via the formation of fermion condensates. We show further that while the broken symmetry associated with this phase has a vector character in the lattice theory it is realized as an axial symmetry in the continuum limit in agreement with the Vafa–Witten theorem. We discuss our result in the context of universality.

In recent papers, a microscopic model for the SM Higgs mechanism has been proposed, and an idea how to determine the 24 quark and lepton masses of all three generations has emerged in that framework. This idea is worked out in detail here by accommodating the fermion masses and mixings to microscopic parameters. The top quark mass can be given in terms of the Fermi scale and of certain exchange couplings of isospin vectors obeying a tetrahedral symmetry. The observed hierarchy in the family spectrum is attributed to a natural hierarchy in the microscopic couplings. The neutrinos will be shown to vibrate within the potential valleys of the system, thus retaining very tiny masses. This is related to a Goldstone effect inside the internal dynamics. A discussion of the quark and lepton mixing matrices is also included. The mixing angles of the PMNS matrix are calculated for an example set of parameters, and a value for the CP-violating phase is given.

A model is presented where the Higgs mechanism of the Standard Model is deduced from the alignment of a strongly correlated fermion system in an internal space with A₄ symmetry. The ground state is constructed and its energy calculated. Finally, it is claimed that the model may be derived from a field theory in 6 + 1 dimensions.

The direct discovery of gravitational waves opens of new avenues for exploring fundamental microscopic physics. In this presentation,^a I will illustrate this by obtaining the stringent bounds on the scale of quantum fuzziness of hypothetical noncommutative space–time. I also discuss how future observations of stochastic gravitational wave background can shed light on the nature of the Higgs mechanism of the electroweak symmetry breaking and the related cosmological phase transition.

Based on a talk presented at the Conference on Cosmology, Gravitational Waves and Particles, NTU, Singapore, 6–10 February 2017.

In order to have a new perspective on the long-standing problem of the mass gap in Yang–Mills theory, we study in this paper the quantum Yang–Mills theory in the presence of topologically nontrivial backgrounds. The topologically stable gauge fields are constrained by the form invariance condition and the topological properties. Obeying these constraints, the known classical solutions to the Yang–Mills equation in the three- and four-dimensional Euclidean spaces are recovered, and the other allowed configurations form the nontrivial topological fluctuations at quantum level. Together, they constitute the background configurations, upon which the quantum Yang–Mills theory can be constructed. We demonstrate that the theory mimics the Higgs mechanism in a certain limit and develops a mass gap at semiclassical level on a flat space with finite size or on a sphere.

I present a personal vision of what is essential in the field of neutrino mass, both from the point of view of what has been achieved and what could lie ahead. In the process, I offer a logical, theoretical and phenomenological rationale behind my opinions. It is however neither a summary of what was discussed in the conference nor a party-line viewpoint, rather an attempt to dig through the enormous body of material in our field in order to uncover a common unifying thread. The main focus is on the search for a predictive and self-contained theory of the origin and nature of neutrino mass, with the conclusion that the left–right symmetric model plays a special role in this aspect.

In this paper, we study consequences of the assumption that the gauge group $\mathrm{\text{SU}}(2)$ of the standard model is a nonassociative image of $\mathrm{\text{Spin}}(3)$. Such an approach allows us to take a different look at the Higgs mechanism and obtain the value of the Weinberg angle in very good agreement with the experiment.

Spontaneous breaking of Lorentz symmetry has been suggested as a possible mechanism that might occur in the context of a fundamental Planck-scale theory, such as string theory or a quantum theory of gravity. However, if Lorentz symmetry is spontaneously broken, two sets of questions immediately arise: What is the fate of the Nambu–Goldstone (NG) modes, and can a Higgs mechanism occur? A brief summary of some recent work looking at these questions is presented here.

In this paper, we raise and discuss the fundamental issue whether the interaction-induced inertia in the Higgs mechanism is the same as the charge of gravity or the gravitational mass. True physical mass has to fulfill the dual role of inertia and the gravitational charge, and should respect the weak equivalence principle. This is not yet addressed in the standard model that does not incorporate gravity. Hence, the Higgs scenario still requires a gravitational completion. Some relevant analogies where interaction-induced inertia is not the same as the gravitational charge are mentioned. Probing this line of thought will provide valuable clues and perhaps a remarkable answer to the place and role of gravity in the standard model of particle physics.