Aspects of UA (1) breaking in the Nambu and Jona-Lasinio model

The six-quark instanton induced ’t Hooft interaction, which breaks the unwanted U_A (1) symmetry of QCD, is a source of perturbative corrections to the leading order result formed by the four-quark forces with the U_L (3) × U_R (3) chiral symmetry. A detailed quantitative calculation is carried out to bosonize the model by the functional integral method. We concentrate our efforts on finding ways to integrate out the auxiliary bosonic variables. The functional integral over these variables cannot be evaluated exactly. We show that the modified stationary phase approach leads to a resummation within the perturbative series and calculate the integral in the “two-loop” approximation. The result is a correction to the effective mesonic Lagrangian which may be important for the low-energy spectrum and dynamics of the scalar and pseudoscalar nonets.     

Eight-quark interactions as a chiral thermometer

A NJL Lagrangian extended to six [1–3] and eight quark interactions [4] is applied to study temperature effects [5] (SU(3) flavor limit, massless case), and [6] (realistic massive case). The transition temperature can be considerably reduced as compared to the standard approach, in accordance with recent lattice calculations [7]. The mesonic spectra built on the spontaneously broken vacuum induced by the’ t Hooft interaction strength, as opposed to the commonly considered case driven by the four-quark coupling, undergoes a rapid crossover to the unbroken phase, with a slope and at a temperature which is regulated by the strength of the OZI violating eight-quark interactions. This strength can be adjusted in consonance with the four-quark coupling and leaves the spectra unchanged, except for the sigma meson mass, which decreases. A first order transition behavior is also a possible solution within the present approach.     

Complete Gluonic Phase in Two-Flavour Colour Superconductivity

We study a typical complete gluonic phase （LGP） in two-flavour colour superconductivity （2SC） by calculating the essential cubic and quartic interfering term between the gluonic condensates （Az^（8）） and/Az^（6）） with a gauged NJL model. It is proven that the coefficients of the cubic interfering term and the vacuum contributions of the cubic and quartic interfering term are all equal to zeroes. The coefficients of the quartic interfering term and the /Az^（6）） ＇s quartic self-interaction term at stationary points of Larkin-Ovchinnikov-Fulde-Ferrell （LOFF） phase are calculated. Comparisons among the effective potentials of LOP, g2SC and LOFF phase indicate that LOP could be the genuine ground state of 2SC for some reasonable paxameters.     

The ’t Hooft vertex revisited

In 1976 ’t Hooft introduced an elegant approach towards understanding the physical consequences of the topological structures that appear in non-Abelian gauge theories. These effects are concisely summarized in terms of an effective multi-fermion interaction. These old arguments provide a link between a variety of recent and sometimes controversial ideas including discrete chiral symmetries appearing in some models for unification, ambiguities in the definition of quark masses, and flaws with some simulation algorithms in lattice gauge theory.     

A study of 't Hooft and Wilson loops

An investigation is undertaken for 't Hooft loop operators in four-dimensional gauge theories. For the first time, a perimeter law is shown to be their behavior in weak coupling Wilson lattice (and continuum) non-abelian SU(N) gauge theories for all N. However, it is also argued that this perimeter law is poor criterion for quark confinement. Rather, it is suggested that non-leading long-distance behavior is what is crucial and relevant in distinguishing non-abelian from abelian (and hence confining from non-confining) theories. A new object, “the 't Hooft line”, is introduced to measure this non-leading behavior and is computed in strong coupling on the lattice. There, one finds magnetic screening characterized by a magnetic screening mass, m_s. It is shown to all orders in strong coupling that m_s is the glueball mass, a result which is expected to persist in weak coupling and in the continuum. Two further consequences of this work are that pure non-abelian gauge theories cannot be in a Higgs phase and that in such models that absence of massless physical particles implies confinement.Finally, non-leading behavior in Wilson loops is examined. The present picture of confinement suggests the absence of van der Waals forces in Yang-Mills theories.     

Clebsch-Gordan coefficients for the extended quantum-mechanical Poincaré group and angular correlations of decay products

This paper describes Clebsch-Gordan coefficients (CGCs) for unitary irreducible representations (UIRs) of the extended quantum-mechanical Poincaré group . ‘Extended’ refers to the extension of the 10 parameter Lie group that is the Poincaré group by the discrete symmetries C, P, and T; ‘quantum mechanical’ refers to the fact that we consider projective representations of the group. The particular set of CGCs presented here is applicable to the problem of the reduction of the direct product of two massive, unitary irreducible representations (UIRs) of with positive energy to irreducible components. Of the 16 inequivalent representations of the discrete symmetries, the two standard representations with U_CU_P = ±1 are considered. Also included in the analysis are additive internal quantum numbers specifying the superselection sector. As an example, these CGCs are applied to the decay process of the ? (4S) meson.     

Point-form quantum field theory

We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form x_μx^μ = τ². This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free—a feature characteristic of Dirac’s “point-form” of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincaré generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.     

Which Green functions does the path integral for quasi-Hermitian Hamiltonians represent?

We explain how Feynman diagrams and the functional integral for quasi-Hermitian theories “know” about the metric η. The answer turns out be that their derivation is based fundamentally on the Heisenberg equations of motion and the canonical equal-time commutation relations, which only take their standard form when matrix elements are evaluated using η.     

Noise-driven synchronization of a FitzHugh-Nagumo ring with phase-repulsive coupling: A perspective from the system’s nonequilibrium potential

We study a one-dimensional array of N autonomous units with excitable FitzHugh-Nagumo dynamics coupled in phase-repulsive way to form a ring, and submitted to a common subthreshold harmonic signal and independent Gaussian white noises with a common intensity η. By varying η, two macroscopic regimes are observed. For some value of noise intensity, a transition from the rest state to an activated one-with almost half of the neurons excited forming an “...-activated-inhibited-activated-... ” structure along the ring-takes place. For larger values of η, the inverse transition is also observed, and both states alternate in a synchronized way with the signal. Moreover, measures of activation and coherent behavior become maximal for intermediate values of η. The origin of these collective effects is explained in terms of the system’s nonequilibrium potential. In particular, the levels of noise for activation and synchronization are theoretically estimated.     

Hidden symmetry of the CKM and neutrino-mapping matrices

We propose that the smallness of the light quark masses is related to the smallness of the T (i.e. CP) violation in hadronic weak interactions. Accordingly, for each of the two quark sectors (“upper” and “lower”) we construct a 3 × 3 mass matrix in a bases of unobserved quark states, such that the “upper” and “lower” basis states correspond exactly via the W^± transitions in the weak interaction. In the zeroth approximation of our formulation, we assume T conservation by making all matrix elements real. In addition, we impose a “hidden symmetry” (invariance under simultaneous translations of all three basis quark states in each sector), which ensures a zero mass eigenstate in each sector.Next, we simultaneously break the hidden symmetry and T invariance by introducing a phase factor e^iχ in the interaction for each sector. The Jarlskog invariant J_CKM, as well as the light quark masses are evaluated in terms of the parameters of the model. Comparing formulas, we find that most unknown factors drop out, resulting in a simple relation with , to leading order in χ and m_s/m_b, with A, λ the Wolfenstein parameters. (Because of the large top quark mass, the contribution from upper quark sector can be neglected.) Setting J_CKM = 3.08 × 10⁻⁵, m_b = 4.7 GeV (1s mass), m_s = 95 MeV, A = 0.818, and λ = 0.227, we find , consistent with the accepted value m_d = 3 − 7 MeV.We make a parallel proposal for the lepton sectors. With the hidden symmetry and in the approximation of T invariance, both the masses of e and ν₁ are zero. The neutrino-mapping matrix V_ν is shown to be of the same Harrison-Perkins-Scott form which is in agreement with experiments. We also examine the correction due to T violation, and evaluate the corresponding Jarlskog invariant J_ν.     

Yang-Mills instantons and the S-matrix

We present a scheme for calculating gauge-invariant S-matrix elements in the presence of instantons. We exploit the conformal invariance of the zero-mass field equations. The asymptotic in and out states are defined by their values on null infinity $\text{J}$. We use this method to calculate to lowest-order S-matrix elements for scalar particles and fermions in a dilute gas of SU(2) instantons and anti-instantons. The scalar particles acquire an effective mass and an effective interaction of the form $\text{exp}\text{(?(?}{}^2\text{/16π) ?}\text{?}\text{)}$, where ? is the scale of the instanton, plus other interactions which cannot be presented by a local effective lagrangian. The fermions acquire the effective lagrangian obtained by 't Hooft. In the case of a single flavour of fermions, this corresponds to a mass term.     

The NN → NNη reaction close to threshold

The pp → ppη and np → npη reactions at energies near the η production threshold are studied in a non-relativistic one boson exchange model, where the (1535 MeV) S11 resonance is excited through the exchange of π, η, ? and ω mesons and subsequently decays into an ηN pair. Energy integrated cross sections and energy spectra of the out going η's are reported. Providing NN and ηN final state interactions are taken into account coherently, the model reproduces both the scale and energy dependence of the cross section for the pp → ppη reactions up to 100 MeV. Final state interaction corrections due to the nucleon-nucleon and meson-nucleon forces influence strongly the scale and shape of the cross sections. The shape of the energy spectra of the outgoing η's provides a clear signature of the ηN force.     

Hidden supersymmetry in quantum bosonic systems

We show that some simple well-studied quantum mechanical systems without fermion (spin) degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the bound state Aharonov-Bohm, the Dirac delta and the Pöschl-Teller potential problems, in which the unbroken and broken N = 2 supersymmetry of linear and nonlinear (polynomial) forms is revealed.     

Light hadron spectra in the constituent quark model with the Kobayashi-Kondo-Maskawa-’t Hooft effective UA (1) symmetry breaking interaction

We make a critical comparison of several versions of instanton-induced interactions present in the literature, all based on ITEP group’s extension to three colours and flavours of ’t Hooft’s effective lagrangian, with the predictions of the phenomenological Kobayashi-Kondo-Maskawa (KKM) chiral quark lagrangian. We analyze the effects of all versions of the effective U_A (1) symmetry breaking interactions on light hadron spectra in the non-relativistic constituent quark model. We show that the KKMT force, when used as a residual hyperfine interaction reproduces the correct ordering of pseudoscalar and vector mesons even without explicitly taking chiral symmetry into account. Moreover, the nucleon spectra are also correctly reproduced, only the Roper resonance remains too high, albeit lower than usual, at 1660 MeV. The latter’s lower than expected mass is not due to a small excitation energy, as in the Glozman-Riska (GR) model, but to a combination of colour, flavour, and spatial wave function properties that enhance the relevant matrix elements. The KKMT interaction explicitly depends on flavour and spin of the quarks, but unlike the GR flavour-spin one it has a firm footing in QCD. In the process we provide several technical advances, in particular we show the first explicit derivation of the three-body Fierz transformation and apply it to the KKM interaction. We also discuss the ambiguities associated with the colour degree of freedom.     

The radial problem in gauge field theory models

The study of spontaneous symmetry breaking patterns in theories in which the ground state is determined by the minima of a potential invariant under the symmetry group of the system may be traced back to the solution of two classes of problems, that we shall quote in Tolédano and Dmitriev’s suggestive words [P. Tolédano, V. Dmitriev, Reconstructive Phase Transitions in Crystals and Quasicrystals, World Scientific, Singapore, 1996] as angular and radial problem, respectively. Whilst the former problem, i.e., the determination of the isotropy-type stratification, has been extensively treated both in condensed matter physics and in particle physics, the radial problem, in particular the construction of the phenomenological potential allowing the realization of all the symmetry allowed symmetry phases, has up to now substantially been disregarded in gauge field theory, because renormalizability limits to four the degree of the Higgs potential and it is widely thought that spontaneous radiative mass generation can anyway fix the issue. Through a rigorous analysis in the framework of geometric invariant theory (-matrix approach) we review these facts, focussing our attention on the role of radiative corrections. Then, we propose a way of reconciling renormalizability requirement and tree-level observability of all the phases allowed by the symmetry. The idea will be illustrated in simple extensions of two-Higgs-doublet SM, with additional scalar singlets and discrete symmetries. This will allow us to explain the rationale behind all the extensions of the Higgs sectors so far proposed to generate the observed Baryon asymmetry of our Universe at the EW Phase Transition.     

Instanton-induced flavour mixing in mesons

The U_L(N_f)×U_R(N_f) chiral symmetric version of the Nambu-Jona-Lasinio model is extended by the 't Hooft determinant and bosonized for an arbitrary number of flavours N_f. The resulting effective meson lagrangian is explicitly calculated to leading order in the derivatives for three flavours. The 't Hooft determinant induces flavour mixing of the mesons with diagonal flavour content (π⁰, η, η′, and their scalar chiral partners δ⁰, S, ϵ) and pushes up the physical η′-mass. The η-η′ mixing angle is found to be −31°.     

Anyonic order parameters for discrete gauge theories on the lattice

We present a new family of gauge invariant non-local order parameters for (non-abelian) discrete gauge theories on a Euclidean lattice, which are in one-to-one correspondence with the excitation spectrum that follows from the representation theory of the quantum double D(H) of the finite group H. These combine magnetic flux-sector labeled by a conjugacy class with an electric representation of the centralizer subgroup that commutes with the flux. In particular, cases like the trivial class for magnetic flux, or the trivial irrep for electric charge, these order parameters reduce to the familiar Wilson and the ’t Hooft operators, respectively. It is pointed out that these novel operators are crucial for probing the phase structure of a class of discrete lattice models we define, using Monte Carlo simulations.     

Microstructure related photoluminescence in a-CNx films deposited by reactive rf magnetron sputtering

We investigated the photoluminescence (PL) properties of carbon nitride films (CN_x) deposited by rf magnetron sputtering and compared them to their microstructure depending on the target self-bias. While many of the data are compatible with ‘a-C:H like’ PL properties the observed variation of the PL efficiency η with respect to the target bias cannot be easily explained by the standard models. It is suggested that the observed variation of η is rather dominated by a change in microstructure which depends on the bombardment intensity during growth than by the concentration of non-radiative centres.     

Canonical quantization of Galilean covariant field theories

The Galilean-invariant field theories are quantized by using the canonical method and the five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. This method is motivated by the fact that the extended Galilei group in 3 + 1 dimensions is a subgroup of the inhomogeneous Lorentz group in 4 + 1 dimensions. First, we consider complex scalar fields, where the Schrödinger field follows from a reduction of the Klein-Gordon equation in the extended space. The underlying discrete symmetries are discussed, and we calculate the scattering cross-sections for the Coulomb interaction and for the self-interacting term λΦ⁴. Then, we turn to the Dirac equation, which, upon dimensional reduction, leads to the Lévy-Leblond equations. Like its relativistic analogue, the model allows for the existence of antiparticles. Scattering amplitudes and cross-sections are calculated for the Coulomb interaction, the electron-electron and the electron-positron scattering. These examples show that the so-called ‘non-relativistic’ approximations, obtained in low-velocity limits, must be treated with great care to be Galilei-invariant. The non-relativistic Proca field is discussed briefly.