http://repositorium.sdum.uminho.pt/bitstream/1822/48763/1/1-s2.0-S037026931200857X-main.pdf

Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC

https://digital.csic.es/bitstream/10261/108964/1/experiment%20at%20the%20LHC.pdf

Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC

In a framework of the renormalizable theory of weak interaction, problems of CP-violation are studied. It is concluded that no realistic models of CP-violation exist in the quartet scheme without introducing any other new fields. Some possible models of CP-violation are also discussed. When we apply the renormalizable theory of weak interaction1l to the hadron system, we have some limitations on the hadron model. It is well known that there exists, in the case of the triplet model, a difficulty of the strangeness chang­ ing neutral current and that the quartet model is free from this difficulty. Fur­ thermore, Maki and one of the present authors (T.M.) have shown2l that, in the latter case, the strong interaction must be chiral SU ( 4) X SU ( 4) invariant as precisely as the conservation of the third component of the iso-spin 13 • In addi­ tion to these arguments, for the theory to be realistic, CP-violating interactions should be incorporated in a gauge invariant way. This requirement will impose further limitations on the hadron model and the CP-violating interaction itself. The purpose of the present paper is to investigate this problem. In the following, it will be shown that in the case of the above-mentioned quartet model, we cannot make a CP-violating interaction without introducing any other new fields when we require the following conditions: a) The mass of the fourth member of the quartet, which we will call (, is sufficiently large, b) the model should be con­ sistent with our well-established knowledge of the semi-leptonic processes. After that some possible ways of bringing CP-violation into the theory will be discussed. We consider the quartet model with a charge assignment of Q, Q -1, Q -1 and Q for p, n, A. and (, respectively, and we take the same underlying gauge group SUweak (2) X SU(1) and the scalar doublet field cp as those of Weinberg's original model.1l Then, hadronic parts of the Lagrangian can be devided in the following way:

/pdf/cp-violation-in-the-renormalizable-theory-of-weak-2o136mfvdk.pdf

CP Violation in the Renormalizable Theory of Weak Interaction

Regularization and Renormalization of Gauge Fields

We present in a manifestly gauge-invariant form the theory of classical linear gravitational perturbations in part I, and a quantum theory of cosmological perturbations in part II. Part I includes applications to several important examples arising in cosmology: a univese dominated by hydrodynamical matter, a universe filled with scalar-field matter, and higher-derivative theories of gravity. The growth rates of perturbations are calculated analytically in most interesting cases. The analysis is applied to study the evolution of fluctuations in inflationary universe models. Part II includes a unified description of the quantum generation and evolution of inhomogeneities about a classial Friedmann background. The method is based on standard canonical quantization of the action for cosmological perturbations which has been reduced to an expression in terms of a single gauge-invariant variable. The spectrum of density perturbations originating in quantum fluctuations is calculated in universe with hydrodynamical matter, in inflationary universe models with scalar-field matter, and in higher-derivative theories of gravity.

The gauge-invariant theory of classical and quantized cosmological perturbations developed in parts I and II is applied in part III to several interesting physical problems. It allows a simple derivation of the relation between temperature anistropes in the cosmic microwave background. radiation and the gauge-invariant potential for metric perturbations. The generation and evolution of gravitational waves is studied. As another example, a simple analysis of entropy perturbations and non-scale-invariant spectra in inflationary universe models is presented. The gauge-invariant theory of cosmological perturbations also allows a consistent and gauge-invariant definition of statistical fluctuations.

/pdf/theory-of-cosmological-perturbations-4w5xgujayp.pdf

Theory of Cosmological Perturbations

In a recent note' it was shown that the Goldstone theorem, ' that Lorentz-covaria. nt field theories in which spontaneous breakdown of symmetry under an internal Lie group occurs contain zero-mass particles, fails if and only if the conserved currents associated with the internal group are coupled to gauge fields. The purpose of the present note is to report that, as a consequence of this coupling, the spin-one quanta of some of the gauge fields acquire mass; the longitudinal degrees of freedom of these particles (which would be absent if their mass were zero) go over into the Goldstone bosons when the coupling tends to zero. This phenomenon is just the relativistic analog of the plasmon phenomenon to which Anderson' has drawn attention: that the scalar zero-mass excitations of a superconducting neutral Fermi gas become longitudinal plasmon modes of finite mass when the gas is charged. The simplest theory which exhibits this behavior is a gauge-invariant version of a model used by Goldstone' himself: Two real' scalar fields y„y, and a real vector field A interact through the Lagrangian density

https://link.aps.org/pdf/10.1103/PhysRevLett.13.508

Broken Symmetries and the Masses of Gauge Bosons

Broken symmetries, massless particles and gauge fields

We examine a simple relativistic theory of two scalar fields, first discussed by Goldstone, in which as a result of spontaneous breakdown of $U(1)$ symmetry one of the scalar bosons is massless, in conformity with the Goldstone theorem. When the symmetry group of the Lagrangian is extended from global to local $U(1)$ transformations by the introduction of coupling with a vector gauge field, the Goldstone boson becomes the longitudinal state of a massive vector boson whose transverse states are the quanta of the transverse gauge field. A perturbative treatment of the model is developed in which the major features of these phenomena are present in zero order. Transition amplitudes for decay and scattering processes are evaluated in lowest order, and it is shown that they may be obtained more directly from an equivalent Lagrangian in which the original symmetry is no longer manifest. When the system is coupled to other systems in a $U(1)$ invariant Lagrangian, the other systems display an induced symmetry breakdown, associated with a partially conserved current which interacts with itself via the massive vector boson.

https://link.aps.org/pdf/10.1103/PhysRev.145.1156

Spontaneous Symmetry Breakdown without Massless Bosons

The two potentials for which a particle moving non-relativistically in a spherical space under the action of conservative central force executes closed orbits are found. When the curvature is zero they reduce to the familiar Coulomb and isotropic oscillator potentials of Euclidean geometry. The corresponding vector (for the former) and symmetric tensor (for the latter) constants of motion are constructed. For each system in N dimensions the Poisson bracket algebra in classical mechanics, and the commutator algebra in quantum mechanics, of these constants of motion and the angular momentum components are constructed. It is proved that by an appropriate choice of independent constants of motion these Poisson bracket algebras may be transformed into Lie algebraic structures, those of the symmetry groups SO(N+1) and SU(N) respectively: the Hamiltonian of each system is expressed as a function of the Casimir operators of its symmetry group. The corresponding transformations of the quantum mechanical commutator algebras are performed only for N=2: the corresponding expressions for the Hamiltonian as functions of the Casimir operators yield the energy levels of the two systems.

http://iopscience.iop.org/article/10.1088/0305-4470/12/3/006/pdf

Dynamical symmetries in a spherical geometry. I

The infra-red and Raman selection rules for an infinite long-chain molecule having helical symmetry are discussed, and the normal modes of vibration are classified by the use of group theory. A weak-coupling approximation is used to derive relations between the intensities of the variously polarized spectral components arising from a single vibration frequency of the unit out of which the helix is built. A form of matrix perturbation theory is used to obtain some approximate relations between the frequencies of these components; these relations involve the angle ψ relative to the screw axis which separates successive units of the helix and provide, in principle, a method by which this angle may be measured. It is suggested that the methods discussed here may serve as a basis for the interpretation of the spectra of fibrous proteins.

https://www.jstor.org/stable/pdfplus/99210.pdf

Peter W. Higgs

Papers

Broken Symmetries and the Masses of Gauge Bosons

Broken symmetries, massless particles and gauge fields

Spontaneous Symmetry Breakdown without Massless Bosons

Dynamical symmetries in a spherical geometry. I

The vibration spectra of helical molecules: infra-red and Raman selection rules, intensities and approximate frequencies