Probing the Higgs field using massive particles as sources and detectors

In the standard model, all massive elementary particles acquire their masses by coupling to a background Higgs field with a non-zero vacuum expectation value. What is often overlooked is that each massive particle is also a source of the Higgs field. A given particle can in principle shift the mass of a neighboring particle. The mass shift effect goes beyond the usual perturbative Feynman diagram calculations which implicitly assume that the mass of each particle is rigidly fixed. Local mass shifts offer a unique handle on Higgs physics since they do not require the production of on-shell Higgs bosons. We provide theoretical estimates showing that the mass shift effect can be large and measurable, especially near pair threshold, at both the Tevatron and the LHC. PACS 14.80.Bn; 13.40.Dk     

Higgs mechanism without Higgs particle

Until now there has been no empirical evidence for the existence of the Higgs particle, although the Higgs mechanism of symmetry breaking is very successful. We propose a scalar-tensor theory of gravity with the Higgs field of theSU(3)×SU(2)×U(1) standard model of the elementary particles as scalar field, which results finally in Einstein's gravity and in theSU(3)×SU(2)×U(1) standard model without any influence of the excited Higgs field.     

Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim

In classical Kaluza-Klein theory, with compactified extra dimensions and without scalar field, the rest mass as well as the electric charge of test particles are constants of motion. We show that in the case of a large extra dimension this is no longer so. We propose the Hamilton-Jacobi formalism, instead of the geodesic equation, for the study of test particles moving in a five-dimensional background metric. This formalism has a number of advantages: (i) it provides a clear and invariant definition of rest mass, without the ambiguities associated with the choice of the parameters used along the motion in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the discussion, and (iii) we avoid the difficulties associated with the splitting of the geodesic equation. For particles moving in a general 5D metric, we show how the effective rest mass, as measured by an observer in 4D, varies as a consequence of the large extra dimension. Also, the fifth component of the momentum changes along the motion. This component can be identified with the electric charge of test particles. With this interpretation, both the rest mass and the charge vary along the trajectory. The constant of motion is now a combination of these quantities. We study the cosmological variations of charge and rest mass in a five-dimensional bulk metric which is used to embed the standard k = 0 FRW universes. The time variations in the fine structure constant and the Thomson cross section are also discussed.     

More flipped SU(5)×U(1) baryosynthesis

We supplement a previous discussion of baryosynthesis in flipped SU(5)×U(1) GUTs by including (1) the large incoherent field energy density which is likely SU(5) is broken, and (2) the possibility of additional Higgs triplet fields suggested by four dimensional string model-building. We consider strong (weak) reheating scenarios in which the Universe is (is not) SU(5) symmetric after inflation. We find an adequate baryon asymmetry subsequent to strong reheating, whatever the number of Higgs triplets (although beware of possible difficulties with quasi-stable relic particles), whereas weak reheating requires at least two Higgs triplets.     

Monte Carlo study of a lattice gauge theory with a radially varied Higgs field

The phase structure of a gauge-scalar (Higgs) field system is studied by Monte Carlo simulations without freezing the radial mode of the scalar field. We consider Z₂ lattice gauge theory coupled to a Higgs field which is approximated by a discrete real one. Most of our analysis is done on a 4⁴ lattice. We find that the phase diagram of our model consists of three distinct phases, Higgs and confined regions being divided by a phase boundary. This phase structure forms a contrast with that presented in the model with a fixed-length Higgs field.     

Non-anomalous discrete R-symmetry, extra matters, and enhancement of the lightest SUSY Higgs mass

We consider low-energy supersymmetric model with non-anomalous discrete R-symmetry. To make the R-symmetry non-anomalous, we add new particles to the particle content of the minimal supersymmetric standard model (MSSM). Those new particles may couple to the Higgs boson, resulting in a significant enhancement of the lightest Higgs mass. We show that, in such a model, the lightest Higgs mass can be much larger than the MSSM upper bound; the lightest Higgs mass as large as 140 GeV (or larger) becomes possible.     

Higgs-field gravity

It is shown that any excited Higgs field mediates an attractive scalar gravitational interaction of Yukawa type between the elementary particles, which become massive by the ground state of the Higgs field.     

On the characterization of the higgs phase in lattice gauge theories

We consider Higgs models on a lattice in 3 or 4 dimensions. Higgs scalars are assumed to transform trivially under a finite subgroup Γ of the compact gauge groupG. We adopt 't Hooft's definition of the Higgs phase, it is characterized by a nonvanishing free energy per unit length (area) of a vortex in 3 (4) dimensions. By using a Peierls argument we show that the models are in the Higgs phase in this sense for suitable coupling constants.     

Stationary Dyonic regular and black hole solutions

We consider globally regular and black hole solutions in SU(2) Einstein–Yang–Mills–Higgs theory, coupled to a dilaton field. The basic solutions represent magnetic monopoles, monopole–antimonopole systems or black holes with monopole or dipole hair. When the globally regular solutions carry additionally electric charge, an angular momentum density results, except in the simplest spherically symmetric case. We evaluate the global charges of the solutions and their effective action, and analyze their dependence on the gravitational coupling strength. We show, that in the presence of a dilaton field, the black hole solutions satisfy a generalized Smarr type mass formula. B. Kleihaus gratefully acknowledges support by the German Aerospace Center. F. Navarro-Lérida gratefully acknowledges support by the Ministerio de Educación y Ciencia under grant EX2005-0078.     

Unity of elementary particles and forces in higher dimensions

The idea of unifying all the gauge and Yukawa forces as well as the gauge, Higgs, and fermionic matter particles naturally leads us to a simple gauge symmetry in higher dimensions with supersymmetry. We present a model in which, for the first time, such a unification is achieved in the framework of quantum field theory.     

Solution of the Higgs scalar-tensor theory without Higgs particles for static stars

Within the scalar-tensor theory of gravity with Higgs mechanism without Higgs particles, we prove that the excited Higgs potential (the scalar field) vanishes inside and outside of stellar matter for static, spherically symmetric configurations. The field equation for the metric (the tensorial gravitational field) turns out to be essentially the Einsteinian one.     

Inverse seesaw in NMSSM and 126 GeV Higgs boson

We consider extensions of the next-to-minimal supersymmetric model (NMSSM) in which the observed neutrino masses are generated through a TeV scale inverse seesaw mechanism. The new particles associated with this mechanism can have sizable couplings to the Higgs field which can yield a large contribution to the mass of the lightest CP-even Higgs boson. With this new contribution, a 126 GeV Higgs is possible along with order of 200 GeV masses for the stop quarks for a broad range of tan β. The Higgs production and decay in the diphoton channel can be enhanced due to this new contribution. It is also possible to solve the little hierarchy problem in this model without invoking a maximal value for the NMSSM trilinear coupling and without severe restrictions on the value of tan β.     

Higgs-field gravity within the standard model

Within the framework of the Glashow-Salam-Weinberg model it is shown that the Higgs field mediates an attractive scalar gravitational interaction of Yukawa type between the elementary particles which become massive by the ground state of the Higgs field after symmetry breaking.     

Searching for a light Higgs boson

The Lindé-Weinberg bound [1] on the mass of the Higgs boson does not apply if one of the fermions of the standard model is very massive [2] or in non-standard models with multiple Higgs particles [1]. We consider both the standard model and a common extension thereof to two or more Higgs doublets. If the Higgs responsible for lepton masses is very light, one reliable method for indirectly detecting it would be a more careful measurement of g − 2 for the muon. More direct is the search for Higgs particles detected in association with τ pairs in existing or defunct e⁺e⁻ colliders operating well below the Z mass. We analyze both methods in detail, and find that data from several existing colliders could eliminate large portions of parameter space - or, perhaps, find the Higgs boson.     

Probing High-Scale and Split Supersymmetry with Higgs mass measurements

We study the range of Higgs masses predicted by High-Scale Supersymmetry and by Split Supersymmetry, using the matching condition for the Higgs quartic coupling determined by the minimal field content. In the case of Split Supersymmetry, we compute for the first time the complete next-to-leading order corrections, including two-loop renormalization group equations and one loop threshold effects. These corrections reduce the predicted Higgs mass by a few GeV. We investigate the impact of the recent LHC Higgs searches on the scale of supersymmetry breaking. In particular, we show that an upper bound of 127 GeV on the Higgs mass implies an upper bound on the scale of Split Supersymmetry of about ¹⁰⁸ GeV, while no firm conclusion can yet be drawn for High-Scale Supersymmetry.     

Triviality pursuit: Can elementary scalar particles exist?

Great effort is presently being expended in the search for elementary scalar “Higgs” particles. These particles have yet to be observed. The primary justification for this search is the theoretically elegant Higgs-Kibble mechanism, in which the interactions of elemetary scalars are used to generate gauge boson masses in a quantum field theory. However, strong evidence suggests that at least a pure φ⁴ scalar field theory is trivial or noninteracting. Should this triviality persist in more complicated systems such as the standard model of the weak interaction, the motivation for looking for Higgs particles would be seriously undermined. Alternatively, the presence of gauge and fermion fields can rescue a pure scalar theory from triviality. Phenomenological constraints (such as a bounded or even predictable Higgs mass) may then be implied. In this report the evidence for triviality in various field theories is reviewed, and the implications for high energy physics are discussed.     

Nonconservation of lepton current and asymmetry of relic neutrinos

The neutrino asymmetry, \({n_v} - {n_{\bar v}}\), in the plasma of the early Universe generated both before and after the electroweak phase transition (EWPT) is calculated. It is well known that in the Standard Model the leptogenesis before the EWPT, in particular, for neutrinos, owes to the Abelian anomaly in a massless hypercharge field. At the same time, the generation of neutrino asymmetry in the Higgs phase after the EWPT has not been considered previously due to the absence of any quantum anomaly in an external electromagnetic field for such electroneutral particles as neutrinos, in contrast to the Adler anomaly for charged left- and right-handed massless electrons in the same electromagnetic field. Using the Boltzmann equation for neutrinos modified to include the Berry curvature term in momentum space, we establish a violation of the macroscopic neutrino current in the plasma after the EWPT and exactly reproduce the non-conservation of the lepton current in the symmetric phase before the EWPT that owes to the contribution of the triangle anomaly in an external hypercharge field but already without computing the corresponding Feynman diagrams. We apply the new kinetic equation to calculate the neutrino asymmetry by taking into account the Berry curvature and the electroweak interaction with plasma particles in the Higgs phase, including that after the neutrino decoupling in the absence of their collisions in the plasma. We find that this asymmetry is too small for observations. Thus, a difference between the relic neutrino and antineutrino densities, if it exists, must appear already in the symmetric phase of the early Universe before the EWPT.     

Fock space construction of the massless dipole field

We construct the Fock space representation of the free massless scalar dipole field in terms of creation and annihilation operators for the eigenvectors of the momentum operator. The Poincaré group is implemented unitarily only on a subspace of the full (positive metric) Hilbert space. The subspace possesses a hermitean, local, irreducible scalar field constructed out of the (non-hermitean) dipole field. Thus this subspace is a perfect candidate for a physical subspace of observable particles. We show that this possibility is however excluded by the fact that these particles interact with an external c-number source in a manner that violates unitarity. We illustrate our construction by applying it to the linearized Higgs model with external c-number source and examine the (non-trivial) dynamics of the dipole degrees of freedom in this case. An explicit separation of the physical degrees of freedom from the unphysical ones is presented for this interacting model.     

Null Geodesics in Five-Dimensional Manifolds

We analyze a class of 5D non-compact warped-product spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the so-called canonical coordinate gauge of Mashhoon et al. We confirm that if the 5D manifold in our model is Ricci-flat, then there is an induced cosmological constant in the 4D sub-manifold. We derive the general form of the 5D Killing vectors and relate them to the 4D Killing vectors of the embedded spacetime. We then study the 5D null geodesic paths and show that the 4D part of the motion can be timelike—that is, massless particles in 5D can be massive in 4D. We find that if the null trajectories are affinely parameterized in 5D, then the particle is subject to an anomalous acceleration or fifth force. However, this force may be removed by reparameterization, which brings the correct definition of the proper time into question. Physical properties of the geodesics—such as rest mass variations induced by a variable cosmological "constant," constants of the motion and 5D time-dilation effects—are discussed and are shown to be open to experimental or observational investigation.     

Singularities in Einstein–conformally coupled Higgs cosmological models

The dynamics of Einstein–conformally coupled Higgs field (EccH) system is investigated near the initial singularities in the presence of Friedman–Robertson–Walker symmetries. We solve the field equations asymptotically up to fourth order near the singularities analytically, and determine the solutions numerically as well. We found all the asymptotic, power series singular solutions, which are (1) solutions with a scalar polynomial curvature singularity but the Higgs field is bounded (‘Small Bang’), or (2) solutions with a Milne type singularity with bounded spacetime curvature and Higgs field, or (3) solutions with a scalar polynomial curvature singularity and diverging Higgs field (‘Big Bang’). Thus, in the present EccH model there is a new kind of physical spacetime singularity (‘Small Bang’). We also show that, in a neighbourhood of the singularity in these solutions, the Higgs sector does not have any symmetry breaking instantaneous vacuum state, and hence then the Brout–Englert–Higgs mechanism does not work. The large scale behaviour of the solutions is investigated numerically as well. In particular, the numerical calculations indicate that there are singular solutions that cannot be approximated by power series.