Pseudoscalar Field Research Articles

Dimensional Structural Constants from Chiral and Conformal Bosonization of QCD

We derive the dimensional nonperturbative part of the QCD effective action for scalar and pseudoscalar meson fields by means of chiral and conformal bosonization. The related structural coupling constants L5 and L8 of the chiral Lagrangian are estimated using general relations which are valid in a variety of chiral bosonization models without explicit reference to model parameters. The asymptotics for large scalar fields in QCD is elaborated, and model-independent constraints on dimensional coupling constants of the effective meson Lagrangian are evaluated. We determine also the interaction between scalar quarkonium and the gluon density and obtain the scalar glueball-quarkonium potential.

Electromagnetic form-factors of pions and kaons in the time-like region

The π +, K + and K 0 charge radii and form factors in the time-like region are analysed in an effective lagrangian context. This lagrangian, writen in terms of the pseudoscalar, vector and photon fields, incorporates Vector Meson Dominance ideas and the main features of flavour symmetry. A reasonable description of the data is achieved.

Batalin–Fradkin Approach to (1 + 1)-Dimensional Massive Vector Fields and the Gluonic Effective Action for Hard Thermal Loops

The Lagrangian of (1 + 1)-dimensional massive vector fields is studied. Since this system has second class constraints, the method of Batalin–Fradkin, which introduces new fields to convert second class constraints into first class ones, is applied in an extended manner. Instead of the usual treatment, which uses the Stueckelberg field as a new field, we can use a pseudoscalar field. We will show there are at least two ways to introduce a pseudoscalar. At the quantum level, one way leads to the system that is equivalent to the original system, and the other way gives an inequivalent system. The relation of these two ways is clarified. As an application of the latter way, we consider QCD at finite temperature and the gluonic effective action for hard thermal loops is constructed.

The UL(3) × UR(3) Extended Nambu–Jona-Lasinio Model in Differential Regularization

We employ the method of differential regularization to calculate explicitly the one-loop effective action of a bosonized UL(3) × UR(3) extended Nambu–Jona-Lasinio model consisting of scalar, pseudoscalar, vector and axial vector fields.

Another calculation of the Higgs mass and the top mass from the principles of H. B. Nielsen: $m_H\cong 163$ GeV for $M_t\cong 190$ GeV

We calculate the Higgs mass and the top mass starting from the principle that there are two, essentially degenerate minima in the Higgs effective potential; the second is at about the Planck energy scale M P = 1.2 × 1019 GeV. Thus the parameter of the quartic self-coupling λ h vanishes, as does β λH at M P. The new element is the addition of a quantum interaction term which couples the square of the Higgs field to the square of a pseudoscalar field, in the domain of the energy scale between about 1014 GeV and M P. We modify β λH at one loop. The pseudoscalar field which is introduced may be the field which is responsible for a spontaneous breakdown of discrete symmetry — for CP noninvariance at an energy scale of (1015–1016) GeV. The result is then a closer value for m H ≅ 163 GeV for the top pole-mass M t ≅ 190 GeV; both values are now close to the electroweak scale parameter \(\langle {\phi _H}\rangle /\sqrt 2 = 175{\text{ GeV}}\). In terms of dimensionless running coupling parameters, which determine the masses near to the electroweak scale, we get \(\sqrt {{\lambda _H}} \cong 0.06\) and \(gt/\sqrt 2 \cong 0.72\), values that are close to each other and close to unity.

Kantowski-Sachs string cosmologies

We present new exact solutions of the low-energy-effective-action string equations with both dilaton $\ensuremath{\varphi}$ and axion $H$ fields nonzero. The background universe is Kantowski-Sachs-type. We consider the possibility of a pseudoscalar axion field $h$ [${H=e}^{\ensuremath{\varphi}}{(\mathrm{dh})}^{*}$] that can be either time or space dependent. The case of a time-dependent $h$ reduces to that of a stiff perfect-fluid cosmology. For a space-dependent $h$ there is just one nonzero time-space-space component of the axion field $H$, and this corresponds to a distinguished direction in space which prevents the models from isotropizing. Also, in the latter case, both the axion field $H$ and its tensor potential $B$ $(H=dB)$ are dependent on time and space, yet the energy-momentum tensor remains time dependent as required by the homogeneity of the cosmological model.

Nonlinear approach toNNinteractions using self-interacting meson fields

Motivated by the success of models based on chiral symmetry in $\mathrm{NN}$ interactions, we investigate self-interacting scalar, pseudoscalar, and vector meson fields and their impact for $\mathrm{NN}$ forces. We parametrize the corresponding nonlinear field equations and get analytic wavelike solutions. A probability amplitude for the propagation of particle states is calculated and applied in the framework of a boson-exchange $\mathrm{NN}$ potential. Using a proper normalization of the meson fields makes all self-scattering amplitudes finite. The same normalization is able to substitute for the phenomenological form factors used in conventional boson-exchange potentials and thus yields a phenomenological understanding of this part of the $\mathrm{NN}$ interaction. We find an empirical scaling law which relates the meson self-interaction couplings to the pion mass and self-interaction coupling constant. Our model yields $\mathrm{np}$ phase shifts comparable to the Bonn B potential results and deuteron properties, in excellent agreement with experimental data.

Explicit CP Violation in the Higgs Sector of the Next-to-Minimal Supersymmetric Standard Model

We analyze explicit CP violation in the Higgs sector of the next-to-minimal supersymmetric standard model which contains an additional gauge singlet field N. It is shown that there is no mixing among scalar and pseudoscalar Higgs fields in the two Higgs doublets, and scalar-pseudoscalar mixings could exist between two Higgs doublets and the singlet N, and between N itself. CP symmetry is conserved in the extreme limits of < N > >> v, < N > << v, and tan beta >> 1. In the region of < N > = O(v) and tan beta = O(1), large scalar-pseudoscalar mixings are realized, and this effect can reduce the lightest Higgs mass. The mass difference between no mixing and mixing case is about 10 - 30 GeV. The neutron electric dipole moment in this model is consistent with the present experimental upper limit provided that squark and gaugino masses are heavy enough of O(1) TeV.

HAMILTONIAN BRST QUANTIZATION OF (1 + 1)-DIMENSIONAL MASSIVE VECTOR FIELDS

The Lagrangian of a (1 + 1)-dimensional massive vector field is quantized. Since it gives the system with second-class constraints, following Batalin and Fradkin, we introduce additional fields. Although the Stueckelberg field is usually introduced, we can use a pseudoscalar field instead. The duality between them is discussed. We show that the Stueckelberg mass term is equivalent to the Laplace transform of the Lagrangian of the gauged Wess-Zumino-Witten model.

Worldline path integrals for fermions with scalar, pseudoscalar and vector couplings

A systematic derivation is given of the worldline path integrals for the effective action of a multiplet of Dirac fermions interacting with general matrix-valued classical background scalar, pseudoscalar, and vector gauge fields. The first path integral involves worldline fermions with antiperiodic boundary conditions on the worldline loop and generates the real part of the one-loop (Euclidean) effective action. The second path integral involves worldline fermions with periodic boundary conditions and generates the imaginary part of the (Euclidean) effective action, i.e. the phase of the fermion functional determinant. Here we also introduce a new regularization for the phase of functional determinants resembling a heat-kernel regularization. Compared to the known special cases, our worldline Lagrangians have a number of new interaction terms; the validity of some of these terms is checked in perturbation theory. In particular, we obtain the leading order contribution (in the heavy mass expansion) to the Wess-Zumino-Witten term, which generates the chiral anomaly.

Worldline path integrals for fermions with general couplings

We derive a worldline path integral representation for the effective action of a multiplet of Dirac fermions coupled to the most general set of matrix-valued scalar, pseudoscalar, vector, axial vector and antisymmetric tensor background fields. By representing intemal degrees of freedom in terms of worldline fermions as well, we obtain a formulation which manifestly exhibits chiral gauge invariance.

Phase structure of the linear sigma model in R1+1.

The phase structure of the two-dimensional linear {sigma} model is investigated within the method based on canonical transformations and the renormalization group formalism. The phase diagram in the ({ital Y},{ital G}) plane is constructed, where {ital Y} and {ital G} are the Yukawa and boson self-interaction coupling constants. The Hamiltonians describing the system in each phase are obtained. It is shown that the contribution of pseudoscalar fields diminishes the vacuum energy density in the phase with broken chiral symmetry. This results in a rather complicated phase structure of the linear {sigma} model. The most representative features of the phase picture are the dynamical breaking of chiral symmetry for an arbitrary small Yukawa coupling and the presence of critical and triple points in the phase diagram.

Relativistic Transport Equations for Electromagnetic, Scalar, and Pseudoscalar Potentials

We propose a particular form of relativistic transport equations arising from the classical limit of single-time Wigner function for Dirac particles evolving in the presence of scalar, pseudoscalar, and electromagnetic fields. These relativistic Vlasov-type equations for the particle and the antiparticle sector of the Fock space can be also obtained assuming the validity of the Liouville′s equation given a suitable classical Hamiltonian and the associated force.

Bound and quasi-bound fermion-antifermion states in the Yukawa model

The Hamiltonian variational method is used to derive relativistic fermion-antifermion (NN) wave equations with interactions mediated by a neutral scalar (or pseudoscalar) ( pi 0) field. A simple mod NN>+ mod NN pi 0>+ mod pi 0 pi 0> Fock-space ansatz is used to derive the coupled integral wave equations. Approximate (numerical) solutions of the equations are presented for a range of values of the masses and coupling constant, for purely bound and decaying (NN to pi 0 pi 0) states. The domain of top-quark and higgs-particle masses for which tt bound states ('toponium') occur due to higgs exchange only is calculated. We find that tt bound states due to higgs exchange can arise for mt>or=401 GeV provided that the higgs particle mass is at least 50 GeV.

CP violation in tau -->3 pi nu tau.

We consider CP violating effects in the decays $\tau\rightarrow (3\pi)\nu_\tau$ where both the ${\rm J}^{\rm P}=1^+$ resonance, $a_1$, and ${\rm J}^{\rm P}=0^-$ resonance, $\pi^\prime$, can contribute. The interference between the $a_1$ and $\pi^\prime$ resonances can lead to enhanced CP-violating asymmetries whose magnitudes depend crucially on the $\pi^\prime$ decay constant, $f_{\pi^\prime}$. We make an estimate of $f_{\pi^\prime}$ with a simplified chiral Lagrangian coupled to a massive pseudoscalar field, and we compare the estimates from the non-relativistic quark model and from the QCD sum rule with the estimate from the `mock' meson model. We then estimate quantitatively the size of CP-violating effects in a multi-Higgs-doublet model and scalar-leptoquark models. We find that, while CP-violating effects in the scalar-leptoquark models may require more than $10^{10}$ $\tau$ leptons, CP-violating effects from the multi-Higgs-doublet model can be seen at the $2\sigma$ level with about $10^7$ $\tau$ leptons using the chiral Lagrangian estimate of $f_{\pi^\prime}=(1\sim 5)\times 10^{-3}$ GeV.

Gravity and global symmetries.

There exists a widely spread notion that gravitational effects can strongly violate global symmetries. It may lead to many important consequences. We will argue, in particular, that nonperturbative gravitational effects in the axion theory lead to a strong violation of CP invariance unless they are suppressed by an extremely small factor 10^{-82}. One could hope that this problem disappears if one represents the global symmetry of a pseudoscalar axion field as a gauge symmetry of the Ogievetsky-Polubarinov-Kalb-Ramond antisymmetric tensor field. We will show, however, that this gauge symmetry does not protect the axion mass from quantum corrections. The amplitude of gravitational effects violating global symmetries could be strongly suppressed by e^{-S}, where S is the action of a wormhole which may eat the global charge. Unfortunately, in a wide variety of theories based on the Einstein theory of gravity the action appears to be fairly small, S = O(10). However, we have found that the existence of wormholes and the value of their action are extremely sensitive to the structure of space on the nearly Planckian scale. We consider several examples (Kaluza-Klein theory, conformal anomaly, R^2 terms) which show that modifications of the Einstein theory on the length scale l ~ 10 M_P^{-1} may strongly suppress violation of global symmetries. We have found also that in string theory there exists an additional suppression of topology change by the factor e^{-{8\pi^2\over g^2}}. This effect is strong enough to save the axion theory for the natural values of the stringy gauge coupling constant.

Yukawa couplings for the spinning particle and the world-line formalism

We construct the world-line action for a Dirac particle coupled to a classical scalar or pseudo-scalar background field. This action can be used to compute loop diagrams and the effective action in the Yukawa model using the world-line path-integral formalism for spinning particles.

The chiral extension of lattice QCD

The chiral extension of Quantum Chromodynamics (XQCD) adds to the standard lattice action explicit pseudoscalar meson fields for the chiral condensates. With this action, it is feasible to do simulations at the chiral limit with zero mass Goldstone modes. We review the arguments for why this is expected to be in the same universality class as the traditional action. We present preliminary results on convergence of XQCD for naive fermions and on the methodology for introducing counter terms to restore chiral symmetry for Wilson fermions.

Extended chiral transformations including diquark fields as parameters

We introduce an extended chiral transformation, which depends both on pseudoscalar and diquark fields as parameters, and determine its group structure. Assuming soft symmetry breaking in the diquark sector, the bosonisation of a quasi-Goldstone ud-diquark is performed. In the chiral limit the ud-diquark mass is defined by the gluon condensate, m ud ≃300 MeV. The diquark charge radius is <r ud 2> 1 2 ≃0.5 fm.

Effective gauge-invariant nuclear lagrangian

Starting from a lagrangian invariant under the local gauge transformations of the group U(1) × SU(2) × SU(2) we derive an effective nuclear lagrangian containing massive vector and axial-vector fields together with a massless vector field, the electromagnetic field. The masses of the neutral and charged ϱ-mesons are split. The equivalence of the isovector electromagnetic and neutral ϱ-meson currents is obtained. Pseudo-scalar and axial-vector fields are mixed, forming the pion and axial-vector meson fields. A gauge-invariant tensor interaction is discussed.