Pseudoscalar Field Research Articles

Stabilization of the linear SU(2) Nambu-Jona-Lasinio soliton via vector mesons

The solitonic sector of the SU(2) NJL model with sigma , pi , rho , A1 and omega mesons is investigated. The scalar and pseudo-scalar meson fields are not constrained to the chiral circle condition, i.e. sigma 2(r)+ pi 2(r) not=fpi 2. We show numerically that the repulsive omega meson prevents the recently discovered collapse of the hedgehog soliton. A comparison of the linear and the nonlinear NJL model leads to similar solitonic properties, although the deviations from the chiral circle condition are found not to be small.

On the exact description of the Dirac particle in the scalar and pseudoscalar fields

The problem of the exact solutions of the Dirac equation in the presence of the scalar and pseudoscalar fields is investigated by means of an algebraic method. Such an approach allows the author to find all the configurations of the scalar and pseudoscalar fields where separation of variables is possible. Some general recommendations for the search of exact solutions of the Dirac equation in Cartesian coordinates are proposed and some exact solutions in curvilinear coordinates are discussed.

Q2-dependence of meson mixing in few-body charge symmetry breaking. π0-η mixing to one loop in chiral perturbation theory

It is pointed out that the meson mixing matrix elements usually considered responsible for the bulk of the observed few-body charge symmetry breaking are naturally q2-dependent in QCD. For π0-η mixing, using the usual representation of the pseudoscalar fields, the leading q2-dependence can be explicitly calculated using chiral perturbation theory to one loop, the result being a significant decrease in the magnitude of the matrix element in going from timelike to spacelike values of q2. Since it is the latter range of q2 which is relevant to NN scattering and the few-body bound state, this result calls into serious question the standard treatment of few-body charge symmetry breaking contributions associated with π0-η and ϱ-ω mixing.

Axial anomalies in finite QED

We study the quantized massive Dirac field coupled to external vector, axial vector and pseudoscalar fields. We discuss the symmetries of this model and calculate the axial anomalies. We do this within the framework of finite QED. We thus avoid any UV regularization and any formal manipulation of divergent quantities.

Determination of pseudo-Goldstone-boson-photon coupling by the differential time delay of pulsar signals.

Pseudo-Goldstone bosons couple with photons through a P and T violating interaction of the form ${\cal {L_I}}=g_{a\gamma \gamma}~ a F\tilde F$. Strong magnetic fields in rotating compact stars induce a non-zero ${\vec E}\cdot{\vec B}$ outside the stellar surface which acts as a source for the pseudo-scalar field. Pulsar signals propagating through this pseudo-scalar `hair' suffer a differential time lag between the left and the right circularly polarised modes because of the P and T violating pseudoscalar boson-photon interaction. Determination of this time lag upto a microsecond accuracy can lead to a measurment of (or rule out) pseudo-Goldstone boson-photon coupling upto $g_{a \gamma \gamma}\leq 4.6 \times 10^{-9}~GeV^{-1}$.

A pseudoscalar field in the [formula omitted] interaction in heavy quarkonium?

In view of the failure of all currently proposed models (and in particular those supposing a q q interaction arising from the exchange of vector and scalar fields only) to simultaneously account for all the measurements of the fine structure splitting of χ states in the charmonium and bottomonium systems we report here the results of a simple attempt to fit these measurements by introducing a pseudoscalar field. In a model with a minimal number of parameters we are able to agree with all fine structure measurements.

Effects of a Nambu-Goldstone boson on the polarization of radio galaxies and the cosmic microwave background

A coupling gϕ E·B to a pseudoscalar field ϕ affects the polarization properties of electromagnetic waves as they propagate through background fields. We analyse the bounds imposed on g from astronomical polarization measurements. If ϕ is the Nambu-Goldstone boson field of a global symmetry spontaneously broken at an energy scale v, the g= Nα πv , with N a model-dependent numerical coefficient. For an exactly massless Nambu-Goldstone boson that N⪆50 is incompatible with the observed correlation between polarization properties and shape of distant radio galaxies and quasars, unless there was inflation after the breakdown of the global symmetry. We also show that propagation through intervening magnetic fields induces a small degree of linear polarization in the cosmic microwave background.

Some generalizations of Volkov’s problem

Exact solutions of the Dirac equation in the presence of wave fields are considered in this work. In contrast to classical Volkov’s problem (electron in the field of plane electromagnetic wave) wave fields of various tensorial structure, namely scalar, vector (electromagnetic), tensor, pseudo-vector, pseudo-scalar fields and their superpositions are considered. There are marked situations in which exact solutions are possible without a procedure of separation of variables by means of the first-or second-order ordinary differential equations. Essential feature of the approach proposed here is the effective use of concrete representation of degenerate matrices, by means of which the problem of exact solutions of the Dirac equation may be reduced to investigation of a comparatively simple system of equations containing two ordinary differential equations and two functional-algebraic ones.

The SU (3) Skyrme model with vector mesons in the collective approach

We study the SU (3) extension of the Skyrme model with vector mesons in the collective quantization scheme. Pseudoscalar kaon fields as well as space-time components of the K ∗ vector meson fields get excited due to the collective rotation of the classical soliton. A variational approach is implemented to obtain the moments of inertia. The effect of the strange excitations on the corresponding moment of inertia is found to be small. The resulting baryon spectrum obtained by exact diagonalization of the collective hamiltonian, which also contains a term similar to the hypercharge operator, is discussed.

THE THEORETICAL BACKGROUND OF THE FIFTH FORCE

Theoretical ideas of the fifth force(s) are reviewed, placing emphasis on the issue of how one can derive the two most important properties: the coupling strength roughly comparable with, or somewhat weaker than, gravity and the force-range of a macroscopic distance. Dilaton models, five-dimensional theory, and models of scalar fields induced from pseudoscalar fields as Nambu-Goldstone bosons of internal symmetries via CP violation are reanalyzed critically. All of these theories aim at predicting new types of phenomena to probe physics characterized by mass scales much higher than is accessible by other conventional means. Most of the theoretical predictions are shown to be consistent with effects expected to be discovered below the present experimental upper bounds. We are still waiting for more experiments with better sensitivity.

New theoretical lower bounds on the Higgs sector of minimal SUSY

We show the existence of a new theoretical one-loop lower bound on the lightest Higgs boson h of the minimal supersymmetric standard model. This bound restricts considerably the parameter space of the model for tan β<1 and allows for the pseudoscalar Higgs field A to be actually lighter than h in some regions of parameter space. The lower bound on the heavy Higgs field H is correspondingly increased. Our numerical results are obtained for the case of degenerate squark masses but can be readily generalized. We conclude that the one-loop analysis favors the embedding of the model in the SUSY GUTs scenario with radiative electroweak symmetry breaking.

Solitonic solutions of the Nambu-Jona-Lasinio model: Selfconsistency and mean-field-quantities

We consider a partially bosonized version of the Nambu-Jona-Lasinio model in the SU(2-flavour sector (u and d quarks) with classical scalar and pseudoscalar meson fields (σ and π). The polarization of the Dirac sea (fermion-1-loop effects) is fully included. The theory is regularized by using the Schwinger proper time method. Adjusting the parameters of the model in the vacuum and mesonic sector to the pion mass m π and the pion decay constant f π we are left with the constituent quark mass M as the only free parameter. The theory is solved for a system with baryon number B = 1 for various values of M by using a selfconsistent procedure. For M < M cr ≈ 360 MeV no solitonic solution exists. For M cr < M < 725 MeV one obtains N c = 3 explicit valence quarks, whereas for M > 725 MeV their contribution is contained in the regularized Dirac sea. We calculate important mean-field quantities as the classical energy E, the isoscalar quadratic baryon radius 〈 R 2〉, the isoscalar electric and the pion-nucleon form factor, the axial vector coupling constant g A and the nuclear sigma commutator Σ. Hereby the linear and the non-linear version of the model are compared and the effect of a finite pion mass is studied. It turns out that the physically relevant range of M is slightly above the critical point M cr favouring a clear valence quark picture.

Singlet axial-vector current and the "proton-spin" question.

As a preliminary we consider the phenomenology of the European Muon Collaboration experimental result without assuming SU(3) invariance. The most reliable conclusion is that the singlet axial-vector current matrix element is rather small. We calculate this matrix element in a variety of chiral-soliton models in which the axial anomaly equation is satisfied. There are a number of subtleties which we explore. It turns out that reasonable chiral models including only pseudoscalar fields give a zero matrix element. Taking "short-distance" effects consistently into account via the inclusion of vector mesons or explicit quarks does give a small nonzero result. The situation is closely analogous to the prediction of a nonzero result for the nonelectromagnetic part of the neutron-proton mass difference in these chiral models.

The Bäcklund transform for the Liouville field in a curved background

We discuss the Bäcklund transformation which maps the Liouville field on a curved 2D manifold to a noninteracting pseudoscalar field on the same curved manifold. For the classical theory, we show that the transformations imply the respective field equations as well as the equality of energy-momentum tensors. In addition we extend the treatment to canonical hamiltonian dynamics, with a view to the quantum theory. In particular, we show how the canonical phase space action transforms under the Bäcklund transformation. This will be useful in understanding how the Bäcklund transformation works in path integral quantization. Finally, we consider how these results can be used to describe subcritical string theory.

Coulomb law and hypercomplex approach to electrodynamics

For a Coulomb-type field of a single point charge, generalized expressions are considered which are obtained on the basis of a hypercomplex generalization of electrodynamics with magnetic charges [1]. Along with the usual electrostatic field, in this approach a single charge can create a magnetic field, provided that the space points around the charge are oriented in a different way than the field source (charge) itself. Aside from vector fields, such a charge can create scalar and pseudoscalar fields, if time flows differently at the field points around the charge than at the location of the charge, or if the charge itself moves with respect to a fixed reference frame. The sources of the dual symmetry of the Maxwell equations are discussed.

Is QED trivial?

This talk summarizes a recent lattice investigation of the chiral phase transition in non-compact QED with light dynamical Kogut-Susskind fermions done in collaboration with M. Göckeler, R. Horsley, E. Laermann, P. Rakow, R. Sommer and U.-J. Wiese. The phase transition is found to be of second order, so that we can take the continuum limit. Near the critical point the theory is shown to be well described by a Gaussian model of non-interacting scalar and pseudoscalar fields.

Quantum dynamics of the D=3 abelian Higgs model and spontaneous breaking of parity

Several D=3 gauge models where the macroscopic Chern-Simons (CS) terms is induced via scalar fields are described. The first is the usual abelian Higgs model where, as shown by Khlebnikov, there is a non-trivial one-loop correction to the tree-level CS coupling. A refined treatment of this model based on the one-loop effective potential is given. Other models include fermions and the fermion-(pseudo) scalar interaction but no tree-level CS term. In all cases the central point for spontaneous parity breaking is the formation of non-zero (pseudo) scalar field condensates.

Phenomenological dispersive effects in scalar, pseudoscalar, electromagnetic propagation

By assuming a general Lagrangian for the interaction of scalar and pseudoscalar fields with the electromagnetic field, we calculate the dispersion in frequency of scalar, pseudoscalar electromagnetic waves in an external magnetic field.

QED — A lattice investigation of the chiral phase transition and the nature of the continuum limit

We simulate non-compact QED with light dynamical Kogut-Susskind fermions and in the quenched approximation. In both cases we confirm the existence of a second-order chiral phase transition at strong coupling. Near the critical point the theory is shown to be well described by a gaussian model of non-interacting scalar and pseudoscalar fields. We do not find any support for Miransky scaling. Rather, the critical exponents are consistent with their mean field values.

Regularization scheme dependence of vacuum observables in the Nambu-Jona-Lasinio model

We consider a bosonized version of the Nambu-Jona-Lasinio model consisting of classical scalar and pseudoscalar fields. Various regularization schemes (sharp covariant and non-covariant, proper-time and Pauli-Villars) are used in order to determine ultraviolet divergent vacuum observables such as the quark condensate 〈¯qq〉 and the current quark mass. Both quantities turn out to be very sensitive to the special choice of the scheme applied. Without further modification the proper-time and Pauli-Villars scheme appear to be unable to reproduce simultaneously the commonly used values of the quark condensate and the current quark mass.