Intrinsic quantum mechanics behind the Standard Model?

Baryons are described by a Hamiltonian on an intrinsic U(3) Lie group configuration space with electroweak degrees of freedom originating in specific Bloch wave factors. By opening the Bloch degrees of freedom pairwise via a U(2) Higgs mechanism, the strong and electroweak energy scales become related to yield the Higgs mass 125.085+/-0.017 GeV and the usual gauge boson masses. From the same Hamiltonian we derive both the relative neutron to proton mass ratio and the N and Delta mass spectra. All compare rather well with the experimental values. We predict neutral flavour baryon singlets to be sought for in negative pions scattering on protons or in photoproduction on neutrons and in invariant mass like S + (2455)D from various decays above the open charm threshold, e.g. at 4499, 4652 and 4723 MeV. The fundamental predictions are based on just one length scale and the fine structure coupling. The interpretation is to consider baryons as entire entities kinematically excited from laboratory space by three impact momentum generators, three rotation generators and three Runge-Lenz generators to internalize as nine degrees of freedom covering colour, spin and flavour. Quark and gluon fields come about when the intrinsic structure is projected back into laboratory space depending on which exterior derivative one is taking. With such derivatives on the measurescaled wavefunction, we derived approximate parton distribution functions for the u and d valence quarks of the proton that compare well with established experimental analysis.

Studying similarity of objects by looking at their shapes arises naturally in many applications. However, under different viewpoints one and the same object appears to have different shapes. In addition, the correspondences between their feature points are unknown to the viewer. In this paper, we introduce the concept of intrinsic shape of an object that is invariant to affine-permutation shape distortions. We study geometry of the intrinsic shape space in the framework of differentiable manifolds with the emphasis on the computational aspects. We represent the intrinsic shape space as a folded Grassmann manifold. This allows us to easily analyze and compare different intrinsic shapes under the affine-permutation distortion without explicitly computing and recovering these intrinsic shapes. We present the mathematical equations for connecting two intrinsic shapes by a geodesic, measuring their similarity, and morphing one intrinsic shape onto another.

We calculate the pion mass from Goldstone modes in the Higgs mechanism related to the neutron decay. The Goldstone pion modes acquire mass by a vacuum misalignment of the Higgs field. The size of the misalignment is controlled by the ratio between the electronic and the nucleonic energy scales. The nucleonic energy scale is involved in the neutron to proton transformation and the electronic scale is involved in the related creation of the electronic state in the course of the electroweak neutron decay. The respective scales influence the mapping of the intrinsic configuration spaces used in our description. The configuration spaces are the Lie groups U(3) for the nucleonic sector and U(2) for the electronic sector. These spaces are both compact and lead to periodic potentials in the Hamiltonians in coordinate space. The periodicity and strengths of these potentials control the vacuum misalignment and lead to a pion mass of 135.2(1.5) MeV with an uncertainty mainly from the fine structure coupling at pionic energies. The pion decay constant 92 MeV results from comparing the fourth-order self-coupling in an effective pion field theory with the corresponding fourth-order term in the Higgs potential. We suggest analogies with the Goldberger-Treiman relation.

We prove thermodynamic and ultraviolet stable stability bounds for lattice scalar QCD quantum models, with multiflavor real or complex scalar Bose matter fields and a compact, connected gauge Lie group [Formula: see text], [Formula: see text] with Lie algebra dimension [Formula: see text]. Our models are defined on a finite hypercubic lattice [Formula: see text], [Formula: see text], [Formula: see text], with [Formula: see text], even, sites on a side, [Formula: see text] sites, and with free boundary conditions. The models action is a sum of a minimally coupled Bose-gauge part and a Wilson pure-gauge plaquette action. We use local, scaled scalar multiflavor Bose fields. The scaling is global, [Formula: see text]-dependent and noncanonical, and corresponds to an a priori renormalization. The Wilson action is a sum over positive plaquette actions times a factor [Formula: see text], with the gauge coupling [Formula: see text] in [Formula: see text], [Formula: see text]. By local gauge invariance, to eliminate the excess of gauge variables, sometimes we use an enhanced temporal gauge, leaving only [Formula: see text] for [Formula: see text], retained bonds. Fixing this gauge does not alter the value of the partition function. Considering the original physical, unscaled partition function [Formula: see text], where [Formula: see text] is the unscaled (bare) hopping parameter and [Formula: see text] are the boson fields bare masses, and letting [Formula: see text] and [Formula: see text], we show that the scaled partition function [Formula: see text] satisfies the thermodynamic and ultraviolet stable stability bounds [Formula: see text], with finite constants [Formula: see text], independent of the lattice size [Formula: see text] of [Formula: see text] and the spacing [Formula: see text]. For the normalized finite-lattice free energy [Formula: see text], a finite thermodynamic limit ([Formula: see text]) for [Formula: see text], and then the continuum limit [Formula: see text], both exist in the sense of subsequences. They give the model normalized free energies [Formula: see text]. The finiteness of [Formula: see text] is the only question addressed here! The use of the Weyl integration formula is essential in showing these bounds. It allows us to replace the gauge integral over [Formula: see text] gauge bond matrix elements by the integration over its [Formula: see text] eigenvalues. A new global upper bound on the Wilson plaquette action is obtained, which is quadratic in the gluon fields. Our method bypasses the use of diamagnetic inequality and can be extended to treat more general lattices and Lie gauge groups.

Functional methods provide access to the non-perturbative regime of quantum chromo- dynamics. Hence, they allow investigating confinement and chiral symmetry breaking. In this dissertation, correlation functions of Yang-Mills theory and unquenched two-flavor QCD are computed from the functional renormalization group. Employing a self-consistent vertex expansion of the effective action, Yang-Mills correlation functions are obtained in four as well as in three spacetime dimensions. To this end, confinement and Slavnov-Taylor identities are discussed. Our numerical results show very good agreement with corresponding lattice results. Next, unquenched two-flavor QCD is considered where it is shown that the unquenched two-flavor gluon propagator is insensitive to the pion mass. Furthermore, the necessity for consistent truncations is emphasized. Finally, correlation functions of finite-temperature Yang-Mills theory are computed in a truncation that includes the splitting of the gluon field into directions that are transverse and longitudinal to the heat bath. In particular, it includes the splitting of the three- and four-gluon vertices. The obtained gluon propagator allows to extract a Debye screening mass that coincides with the hard thermal loop screening mass at high temperatures, but is meaningful also at temperatures below the phase transition temperature.

Solving the sigma-term puzzle without strangeness mixing

We study the binding energy differences of the valence proton and neutron of the mirror nuclei, 15O–15N, 17F–17O, 39Ca–39K and 41Sc–41Ca, using the quark-meson coupling model. The calculation involves nuclear structure and shell effects explicitly. It is shown that binding energy differences of a few hundred keV arise from the strong interaction, even after subtracting all electromagnetic corrections. The origin of these differences may be ascribed to the charge symmetry breaking effects set in the strong interaction through the u and d current quark mass difference. In this report, we first review the quark-meson coupling model. In particular, we discuss about the nucleon mass in nuclear medium. Then, we present details of the charge symmetry breaking in finite nuclei, especially the Okamoto-Nolen-Schiffer anomaly.

The objective of this thesis is the analysis of a fully developed, turbulent Poiseuille flow with wall transpiration, i.e. uniform blowing and suction on the lower and upper walls correspondingly. In the present study Lie group analysis of two-point correlation (TPC) equations and a set of Direct Numerical Simulations (DNS) of the three-dimensional, incompressible Navier-Stokes equations are used. The former is applied to find symmetry transformations and in turn to derive invariant solutions of the set of two- and multi-point correlation equations, while the latter is used to simulate turbulent channel flow with wall-transpiration at different Reynolds numbers and transpiration velocities. Both tools are used to find new mean velocity scaling laws. Consequently, it is shown that the transpiration velocity is a symmetry breaking, which implies a logarithmic scaling law in the core region of the channel. DNS validates the result of Lie symmetry analysis and, hence, aids establishing a new logarithmic law of deficit-type. The region of validity of the new logarithmic law is very different from the usual near-wall log-law and the slope constant in the core region differs from the von Karman constant and is equal to 0.3. Apart from the new log-law, extended forms of the linear viscous sublayer law and the near-wall log-law are derived. It is shown that these extended laws, as a particular case, include classical scaling laws obtained for the non-transpirating case. For the near-wall log-law it is found that transpiration only changes the additive constant (C) leaving the von Karman constant unaltered. The results present in the presented thesis indicate that high-Reynolds number and high-transpiration effects counterbalance in the near-wall region and amplify each other in the core region of the flow. It is found that at very high transpiration rates the flow tends to become laminar. Finally, structural analysis of the near-wall regions reveal that wall-blowing boosts generation of hairpin-type vortical structures and amplifies large scale motions (LSMs). Third and forth chapters of the present thesis are heavily based on the paper Avsarkisov, Oberlack & Hoyas (2014).

It is shown that an alternative to the standard scalar quantum electrodynamics (QED) is possible. In this new version, there is only global gauge invariance as far as the charged scalar fields are concerned, although local gauge invariance is kept for the electromagnetic field. The electromagnetic coupling has the form jμ(Aμ +∂μB) where B is an auxiliary field and the current jμ is Aμ independent, so that no "sea gull terms" are introduced. As a consequence of the absence of sea gulls, it is seen that no Klein paradox appears in the presence of a strong square well potential. In a model of this kind, spontaneous breaking of symmetry does not lead to photon mass generation, instead the Goldstone boson becomes a massless source for the electromagnetic field. When spontaneous symmetry breaking takes place infrared questions concerning the theory and generalizations to global vector QED are discussed. In this framework, Q-Balls and other nontopological solitons that owe their existence to a global U(1) symmetry can be coupled to electromagnetism and could represent multiply charged particles now in search in the large hadron collider (LHC). Furthermore, we give an example where an "Emergent" Global Scalar QED can appear from an axion–photon system in an external magnetic field. Finally, formulations of Global Scalar QED that allow perturbative expansions without sea gulls are developed.

\nQuantum Chromodynamics (QCD), the theory of strong interactions, in principle describes the interaction of quark and gluon fields. However, due to the self-coupling of the gluons, quarks and gluons are confined into hadrons and cannot exist as free particles. The quantitative understanding of this confinement phenomenon, which is responsible for about 98% of the mass of the visible universe, is one of the major open questions in particle physics. The measurement of the excitation spectrum of hadrons and of their properties gives valuable input to theory and phenomenology.\nIn the Constituent Quark Model (CQM) two types of hadrons exist: mesons, made out of a quark and an antiquark, and baryons, which consist of three quarks. But more advanced QCD-inspired models and Lattice QCD calculations predict the existence of hadrons with exotic properties interpreted as excited glue (hybrids) or even pure gluonic bound states (glueballs).\nThe C<sc>ompass</sc> experiment at the CERN Super Proton Synchrotron has acquired large data sets, which allow to study light-quark meson and baryon spectra in unprecedented detail. The presented overview of the first results from this data set focuses in particular on the light meson sector and presents a detailed analysis of three-pion final states. A new JPC = 1++ state, the a1(1420), is observed with a mass and width in the ranges m = 1412 − 1422MeV/c2 and Γ = 130 − 150MeV/c2.\n

Quantum Chromodynamics (QCD), the theory of strong interactions, in principle describes the interaction of quark and gluon fields. However, due to the self-coupling of the gluons, quarks and gluons are confined into hadrons and cannot exist as free particles. The quantitative understanding of this confinement phenomenon, which is responsible for about 98% of the mass of the visible universe, is one of the major open questions in particle physics. The measurement of the excitation spectrum of hadrons and of their properties gives valuable input to theory and phenomenology. In the Constituent Quark Model (CQM) two types of hadrons exist: mesons, made out of a quark and an antiquark, and baryons, which consist of three quarks. But more advanced QCD-inspired models and Lattice QCD calculations predict the existence of hadrons with exotic properties interpreted as excited glue (hybrids) or even pure gluonic bound states (glueballs). The Compass experiment at the CERN Super Proton Synchrotron has acquired large data sets, which allow to study light-quark meson and baryon spectra in unprecedented detail. The presented overview of the first results from this data set focuses in particular on the light meson sector and presents a detailed analysis of three-pion final states. A new JPC = 1++ state, the a1(1420), is observed with a mass and width in the ranges m = 1412 − 1422MeV/c2 and Γ = 130 − 150MeV/c2.

Using methods of effective field theory, we show that after resummation of Sudakov logarithms the spectral densities of interacting quark and gluon fields in ordinary quantum field theories such as QCD are virtually indistinguishable from those of “unparticles” of a hypothetical conformal sector coupled to the Standard Model, recently studied by Georgi. Unparticles are therefore less exotic that originally thought. Models in which a hidden sector weakly coupled to the Standard Model contains a QCD-like theory, which confines at some scale much below the characteristic energy of a given process, can give rise to signatures closely resembling those from unparticles.

Confinement and hadronization

In earlier work [1], we studied an extension of the canonical symplectic structure in the cotangent bundle of an affine space Q = R N, by additional terms implying the Poisson non-commutativity of both configuration and momentum variables. In this article, we claim that such an extension can be done consistently when Q is a Lie group G.

It is well known that chiral symmetry breaking (χSB) in QCD with Nf = 2 light quark flavors can be described by orthogonal groups as O (4) → O (3), due to local isomorphisms. Here we discuss the question how specific this property is. We consider generalized forms of χSB involving an arbitrary number of light flavors of continuum or lattice fermions, in various representations. We search systematically for isomorphic descriptions by nonunitary, compact Lie groups. It turns out that there are a few alternative options in terms of orthogonal groups, while we did not find any description entirely based on symplectic or exceptional Lie groups. If we adapt such an alternative as the symmetry breaking pattern for a generalized Higgs mechanism, we may consider a Higgs particle composed of bound fermions and trace back the mass generation to χSB. In fact, some of the patterns that we encounter appear in technicolor models. In particular if one observes a Higgs mechanism that can be expressed in terms of orthogonal groups, we specify in which cases it could also represent some kind of χSB of techniquarks.