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Spectral properties for the two-dimensional quantum S=1 XY model were investigated with the exact diagonalization method. In the symmetry-broken phase, there appear the massive Higgs and massless Goldstone excitations, which correspond to…
The quantum $XY$ spin chain with the interactions decaying as a power law $1/r^{1+ \sigma}$ of the distance between spins $r$ was investigated with the exact diagonalization method. Here, the constituent spin is set to $S=1$, which enables…
We study the Higgs excitation in the Goldstone phase of the relativistic O(N) model in two spatial dimensions at zero temperature. The response functions of the order parameter, and its magnitude-squared, become universal functions of…
The gauge-Higgs unification theory identifies the zero mode of the extra dimensional component of the gauge field as the usual Higgs doublet. Since this degree of freedom is the Wilson line phase, the Higgs does not have the mass term nor…
In the dynamical gauge-Higgs unification, it is shown that the mass of the Higgs boson (4D scalar field) in U(1) gauge theory in $M^4 \times T^n$ ($n=1,2,3,...$) is finite to all order in perturbation theory as a consequence of the large…
The Higgs boson, a fundamental scalar, was discovered at CERN in 2012 with mass 125 GeV, a mass that turned out to be a remarkable choice of Nature. In the Standard Model of particle physics, the Higgs boson is closely linked to the…
We consider scenarios of Higgs compositeness where the Higgs doublet arises as a pseudo-Nambu Goldstone boson. Our focus is the physical scalar ("radial") excitation associated with the global symmetry breaking vacuum, which we call the…
We propose a classically scale-invariant extension of the Georgi--Machacek model by augmenting its custodial \(SU(2)_L \times SU(2)_R\)-symmetric Higgs sector -- originally composed of a doublet and two triplets -- with a gauge-singlet…
The quadratic divergences in the scalar sector of the standard model are considered. Since the divergences are present also in the unbroken theory, a natural scale for the divergence formula is proposed to be at the scale of new physics.…
Spontaneous symmetry-breaking quantum phase transitions play an essential role in condensed matter physics. The collective excitations in the broken-symmetry phase near the quantum critical point can be characterized by fluctuations of…
Second order phase transitions are universally driven by an order parameter which becomes trivial at the critical point. At the same time, collective excitations which involve the amplitude of the order parameter develop a gap which…
We investigate the amplitude (Higgs) mode of the relativistic O(N) model in the vicinity of the Wilson-Fisher quantum critical point in D=4-epsilon spacetime dimensions. We compute the universal part of the scalar spectral function near the…
As a small step toward understanding the nature of the Higgs field, a curious observation is reported that calculates the mass of the Higgs boson with a 99.7 % agreement to its experimentally measured value. Particularly, motivated by the…
The one-Higgs-doublet standard model is necessarily incomplete because of the triviality of the scalar symmetry-breaking sector. If the Higgs mass is approximately 600 GeV or higher, there must be additional dynamics at a scale $\Lambda$…
It has been suggested that electroweak symmetry breaking in the Standard Model may be natural if the Standard Model merges into a conformal field theory (CFT) at short distances. In such a scenario the Higgs mass would be protected from…
We consider a Higgs mechanism in scale-invariant theories of gravitation. It is shown that in spontaneous symmetry breakdown of scale invariance, gauge symmetries are also broken spontaneously even without the Higgs potential if the…
In view of the measured Higgs mass of 125 GeV, the perturbative renormalization group evolution of the Standard Model suggests that our Higgs vacuum might not be stable. We connect the usual perturbative approach and the functional…
Theory with $SU(2)\times U(1)$ gauge invariant electroweak Lagrangian describing standard interaction of massless quark doublet without elementary scalar Higgs sector is considered. We show in the main order of $1/N_c$ expansion, that there…
We construct a little Higgs model with the most minimal extension of the standard model gauge group by an extra U(1) gauge symmetry. For specific charge assignments of scalars, an approximate U(3) global symmetry appears in the…
We consider a minimal extension of the standard model where a real, gauge singlet scalar field is added to the standard spectrum. Introducing the Ansatz of universality of scalar couplings, we are led to a scenario which has a set of very…