Meson Theory Research Articles

Scaling behavior in soliton models

In the framework of chiral soliton models we study the behavior of static nucleon properties under rescaling of the parameters describing the effective meson theory. In particular we investigate the question of whether the Brown-Rho scaling laws are general features of such models. When going beyond the simple Skyrme model we find that restrictive constraints need to be imposed on the mesonic parameters in order to maintain these scaling laws. Furthermore, in the case when vector mesons are included in the model it turns out that the isoscalar form factor no longer scales according to these laws. Finally we note that, in addition to the exact scaling laws of the model, one may construct approximate local scaling laws, which depend of the particular choice of Lagrangian parameters.

Soft deconfinement — critical phenomena at the Mott transition in a field theory for quarks and mesons

Critical phenomena associated with Mott transitions are investigated in the finite temperature SUf(3) Nambu-Jona-Lasinio model, that describes quarks u, d, s and bound mesons π, K. Critical exponents for the behavior close to the Mott temperature TM are determined for the static properties of a pion, such as mπ(T), gπqq(T), fπ(T), 〈r2〉π, and the pion polarizabilities αC,N, as well as for the behavior of mK(T), gKqs(T) fK(T) in the strange sector. The effect of the Mott transitions on the qq and ππ scattering lengths and for hadronization cross sections σqq→ππ(T) is discussed. Divergencies that occur in these quantities at TM indicate an intransparence with respect to hadronic and photonic probes, much like the phenomenon of critical opalescence. Physically, the Mott transition models the deconfinement transition expected of QCD since it corresponds to a delocalizayion of the bound states when the temperature is raised above TM.

BARYONS AS THREE-FLAVOR SOLITONS

The description of baryons as soliton solutions of effective meson theories for three-flavor (up, down and strange) degrees of freedom is reviewed and the phenomenological implications are illuminated. In the collective approach the soliton configuration is equipped with baryon quantum numbers by canonical quantization of the coordinates describing the flavor orientation. The baryon spectrum resulting from exact diagonalization of the collective Hamiltonian is discussed. The prediction of static properties, such as the baryon magnetic moments and the Cabibbo matrix elements for semileptonic hyperon decays, are explored with regard to the influence of flavor symmetry breaking. In particular, the role of strange degrees of freedom in the nucleon is investigated for both the vector and axial vector current matrix elements. The latter are discussed extensively within the context of the proton spin puzzle. The influence of flavor symmetry breaking on the shape of the soliton is examined, and observed to cause significant deviations from flavor-covariant predictions on the baryon magnetic moments. Short range effects are incorporated by a chirally invariant inclusion of vector meson fields. These extensions are necessary for properly describing the singlet axial vector current and the neutron–proton mass difference. The effects of the vector meson excitations on baryon properties are also considered. The bound state description of hyperons and its generalization to baryons containing a heavy quark are illustrated. In the case of the Skyrme model a comparison is made between the collective quantization scheme and the bound state approach. Finally, the Nambu–Jona-Lasinio model is employed to demonstrate that hyperons can be described as solitons in a microscopic theory of the quark flavor dynamics. This is explained for both the collective and the bound state approaches to strangeness.

Quenched chiral perturbation theory for heavy-light mesons.

We formulate quenched chiral perturbation theory for heavy-light mesons coupled to pions, and calculate the one-loop chiral logarithmic corrections to ${\mathit{f}}_{\mathit{B}}$, ${\mathit{f}}_{{\mathit{B}}_{\mathit{s}}}$, ${\mathit{B}}_{\mathit{B}}$, and ${\mathit{B}}_{{\mathit{B}}_{\mathit{s}}}$. We also calculate these corrections for ``partially quenched'' theories. In both theories, the chiral logarithms diverge in the chiral limit, indicating that (partially) quenched theories should not be used to study this limit. Comparing the chiral logarithms to those in QCD, we estimate the errors caused by (partial) quenching. By forming suitable ratios, we can reduce the uncertainties in our estimates. \textcopyright{} 1996 The American Physical Society.

Effective chiral Lagrangians for spin-1 mesons

The commonly used types of effective theory for vector mesons are reviewed and their relationships clarified. They are shown to correspond to different choices of field for spin-1 particles and the rules for transforming between them are described. The importance of respecting chiral symmetry is stressed. The choice of fields that transform homogeneously under the nonlinear realisation of chiral symmetry imposes no preconceptions about the types of coupling for the mesons. This representation thus provides a convenient framework for relating different theories. It is also used to elucidate the nature of the assumptions in specific hidden-gauge and massive Yang-Mills models that have been widely used.

Axial-vector properties of the nucleon with 1/Nc corrections in the solitonic SU(3)-NJL model.

Expectation values of the axial-vector currents are calculated within the semibosonized SU(3)-NJL model in the next to leading order of a 1/${\mathit{N}}_{\mathit{c}}$ expansion. These 1/${\mathit{N}}_{\mathit{c}}$ corrections are shown to come from two distinctive sources: (1) the anomalous part of the Euclidean effective action related to the Wess-Zumino term of the SU(3) Skyrme model and (2) the real, nonanomalous part which in this order of 1/${\mathit{N}}_{\mathit{c}}$ has no counterpart within any local effective meson theory. The appearance of the type (2) terms is due to the time ordering of the collective operators entering the formulas for the axial-vector constants. They substantially improve the phenomenology of the model. The question of regularization of these quantities is discussed. The analytic symmetry-breaking terms in the strange quark mass play a minor role for ${\mathit{g}}_{\mathit{A}}^{(3)}$ and ${\mathit{g}}_{\mathit{A}}^{(0)}$. They are, however, important for ${\mathit{g}}_{\mathit{A}}^{(8)}$. Finally, the numerical values for the ${\mathit{g}}_{\mathit{A}}$'s, ${\mathit{g}}_{\mathit{A}}^{(0)}$=0.37, ${\mathit{g}}_{\mathit{A}}^{(3)}$=1.38, and ${\mathit{g}}_{\mathit{A}}^{(8)}$=0.31, reproduce reasonably well the recent data from lepton scattering (${\mathit{g}}_{\mathit{A}}^{(0)}$=0.31, ${\mathit{g}}_{\mathit{A}}^{(3)}$=1.26, and ${\mathit{g}}_{\mathit{A}}^{(8)}$=0.35). \textcopyright{} 1995 The American Physical Society.

Effective hadron theory

The low-energy flavour dynamics is approximated by the NJL model from which effective hadron theories are derived. In the light meson sector emphasis is put on a recent one-meson loop calculation of the π-π phase shifts and the electromagnetic form factor of the pion, where isospin symmetry breaking is included, giving rise to the ϱ-ω-mixing. I also discuss the relation between the two different common phenomenological forms of vector meson dominace. The description of baryons either as chiral solitons of the meson fields or as bound quark-diquark states or as hybrids of both is briefly reviewed. Recent results for the hyperon radiative decays obtained within the Skyrme model are presented. Finally the NJL model is extended to heavy quark flavours and converted into an effective meson theory, which describes the interplay between chiral and heavy quark symmetry.

Baryons as solitons in effective chiral field theories

This lecture comprises some recent developments concerning the description of baryons as topological solitons in effective chiral meson theories. In the first part one-loop corrections to the classical tree approximation are discussed. This involves renormalization of low-energy coupling constants and evaluation of the finite next-to-leading-order terms in the 1 N c expansion. In contrast to the corresponding procedure in the meson sector the magnitude of the chiral gradients involved in the soliton profile requires that counter terms and finite loop contributions be calculated to all chiral orders. Recent results for various nucleon observables are presented. They show that the 1 N c expansion essentially works as expected. In the second part electro-magnetic nucleon form factors (FFs) with relativistic corrections are evaluated in a chiral soliton model including vector mesons. The magnetic FF G M p is shown to agree well with new SLAC data for spacelike Q 2 up to 30 (GeV/c) 2 if superconvergence is enforced. The electric FF G E p is dominated by a zero in the few (GeV/c) 2 region due to a low-lying zero in the non-relativistic electric FF in tree approximation. The third part describes how to extract the strong πNN form factor from chiral soliton models, taking due care of the local metric created by the presence of the soliton. When used in a one-boson-exchange model for the nucleon-nucleon (NN) interaction, deuteron properties and phase parameters of NN scattering are reproduced as well as in conventional NN models that apply a hard monopole form factor at the πNN vertex.

U(2)L x U(2)R chiral theory of mesons.

A $U(2)_{L}\times U(2)_{R}$ chiral theory of pseudoscalar, vector, and axial-vector mesons has been proposed. VMD has been revealed from this theory. The physical processes of normal parity and abnormal parity have been studied by using the same lagrangian and the universality of coupling has been revealed. Two new mass relations between vector and axial-vector mesons have been found. Weinberg's first sum rule and new relations about the amplitude of $a_{1}$ decay are satisfied. KSFR sum rule is satisfied pretty well. The $\rho$ pole in pion form factor has been achieved. The theoretical results of $\rho\rightarrow\pi\pi$, $\omega\rightarrow \pi\pi$, $a_{1}\rightarrow\rho\pi$ and $\pi\gamma$, $\tau\rightarrow \rho\nu$, $\tau\rightarrow a_{1}\nu$, $\pi^{0}\rightarrow \gamma\gamma$, $\omega \rightarrow\pi\gamma$, $\rho\rightarrow\pi\gamma$, $f_{1} \rightarrow\rho\pi\pi$, $f_{1}\rightarrow\eta\pi\pi$, $\rho\rightarrow\eta\gamma$, $\omega \rightarrow\eta\gamma$ are in good agreement with data. Weinberg's $\pi\pi$ scattering lengths and slopes and $a^{0}_{2}$, $a^{2}_{2}$, and $b^{1}_{1}$ have been obtained. Especially, the $\rho$ resonance in the amplitude $T^{1}_{1}$ of $\pi\pi$ scattering has been revealed from this theory. Two coefficients of chiral perturbation theory have been determined and they are close to the values used by chiral perturbation theory.

U(3)L x U(3)R chiral theory of mesons.

The chiral theory of mesons of two flavors have been extended to mesons containing strange flavor. Two new mass relations between vector and axial-vector mesons have been obtained. In chiral limit, the physical processes of normal parity and abnormal parity have been studied. Due to the universality of the coupling of this theory many interesting results have been obtained. In chiral limit theoretical results are in reasonable agreement with data.

SCALAR DILATON-QUARKONIUM MESON IN NUCLEON-NUCLEON INTERACTION

The problem of missing the central attraction in the NN interaction has been reinvestigated within the effective meson theory, based on chiral and conformal anomalies of QCD. The parameters of the model are chosen to describe correctly Fπ, gπNN and N−Δ mass splitting. The resulting central scalar-isoscalar part of the potential is in qualitative agreement with phenomenological one.

Properties of Deuteron Bound State from Meson and Quark Theories for the Nucleon-Nucleon Interaction

The properties of the nucleon-nucleon bound state in the deuteron are considered. Nucleon-nucleon interactions of the Yukawa, Reid and Paris potential forms are used to describe the deuteron bound state. Also, the nucleon-nucleon interaction with different meson exchanges derived from the meson theory as well as the nucleon-nucleon interaction with quark exchange derived from the quark theory by introducing the quark-quark potential with one gluon exchange are used to investigate the deuteron properties. The deuteron binding energy, quadrupole moment, effective range, root-mean-square radius and the D/S ratio are calculated by using different nucleon-nucleon interactions. The obtained results of the present calculations are in good agreement with the experimental values.

Quenched chiral perturbation theory for heavy-light mesons.

Quenched chiral perturbation theory is extended to include heavy-light mesons. Non-analytic corrections to the decay constants, Isgur-Wise function and masses and mixing of heavy mesons are then computed. The results are used to estimate the error due to quenching in lattice computations of these quantities. For reasonable choices of parameters, it is found that quenching has a strong effect on $f_{B_s}/f_B$, reducing it by as much as $28\%$. The errors are essentially negligible for the Isgur-Wise function and the mixing parameter.

Effective meson lagrangian with chiral and heavy quark symmetries from quark flavor dynamics

By bosonization of an extended NJL model we derive an effective meson theory which describes the interplay between chiral symmetry and heavy quark dynamics. This effective theory is worked out in the low-energy regime using the gradient expansion. The resulting effective lagrangian describes strong and weak interactions of heavy B and D mesons with pseudoscalar Goldstone bosons and light vector and axial-vector mesons. Heavy meson weak decay constants, coupling constants and the Isgur-Wise function are predicted in terms of the model parameters partially fixed from the light quark sector. Explicit SU(3) F symmetry breaking effects are estimated and, if possible, confronted with experiment.

Decay constants and masses of octet pseudoscalar mesons.

The masses and decay constants of the octet pseudoscalar mesons are calculated to all orders of quark mass in terms of the effective meson theory. Consequently, the analytic functions of quark masses for the masses and decay constants are obtained. The decay constant ${\mathit{F}}_{\mathrm{\ensuremath{\eta}}}$ has been predicted and the three light quark masses are determined.

Magnetic form factors for a trinucleon system using different meson exchange nucleon–nucleon interactions

The magnetic form factors for the 3He and 3H nuclei have been calculated for different values of momentum transfer. The three-nucleon ground-state wave function is expressed in momentum space and is obtained from the solution of the Faddeev equations with realistic two-body potentials. The potential used is taken from the meson theory to include different meson-exchange contributions satisfying the requirements of current conservation. The different meson-exchange currents and their contributions to the trinucleon magnetic form factors are calculated. The virtual Δ-excitation and the meson–nucleon vertices form factors are included in the 3He and 3H magnetic-form-factors calculations. The present results show the importance of the higher momentum transfer region as being a good source of information to the short-range processes in the nuclear medium. Our results for the 3He and 3H magnetic form factors are in good agreements with the experimental data. The inclusion of the ρ and ω meson exchanges improves the agreement between positions of the minima of the magnetic form factors predicted and the experimental data.

Ghost poles in the nucleon propagator: Vertex corrections and form factors.

Vertex corrections are taken into account in the Schwinger-Dyson equation for the nucleon propagator in a relativistic field theory of fermions and mesons. The usual Hartree-Fock approximation for the nucleon propagator is known to produce the appearance of complex (ghost) poles which violate basic theorems of quantum field theory. In a theory with vector mesons there are vertex corrections that produce a strongly damped vertex function in the ultraviolet. One set of such corrections is known as the Sudakov form factor in quantum electrodynamics. When the Sudakov form factor generated by massive neutral vector mesons is included in the Hartree-Fock approximation to the Schwinger-Dyson equation for the nucleon propagator, the ghost poles disappear and consistency with basic requirements of quantum field theory is recovered.

Chiral theory of mesons in dense baryonic matter (II): Meson propagation

We present the results of meson time-like modes in a dense baryonic medium. The model used is the Nambu-Jona-Lasinio model extended to include vector mesons. We find results for the π-, σ-, ω- and a 1-meson time-like modes. We use the same extrapolation technique we have already used to avoid the impossibility of putting heavy mesons on-shell. Vector-meson modes split into a longitudinal and a transverse mode. The σ-mode mixes with the longitudinal ω-mode.

Relativistic cluster dynamics of nucleons and mesons. I. Kinematics and covariance.

A time-ordered relativistic scattering theory for nucleons and mesons based on clusters rather than individual particles is derived. The S-matrix-type approach provides a recursive hierarchy of Lippmann-Schwinger equations, each describing the dynamical evolution of two-cluster configurations at different levels of the many-body problem. The presentation is restricted to a fixed number of particles; particle absorption and creation are treated in part II. The main concern here are the kinematic aspects of the problem. It is shown that the on-shell results of the formalism are covariant, without requiring negative-energy antiparticle contributions. This is achieved by constructing off-shell T matrices as invariants under a set of energy and momentum transformations which reduce to Lorentz transformations for on-shell energies. The present relativistic formulation is formally equivalent to a previously given nonrelativistic N-body approach.

TWO-DIMENSIONAL BARYONS IN THE LARGE-N LIMIT

We propose a bilocal field theory for mesons in two dimensions obtained as a kind of non-local bosonization of two-dimensional QCD. Its semiclassical expansion is equivalent to the 1/Nc expansion of QCD. Using an ansatz we reduce the classical equation of motion of this theory in the baryon number one sector to a relativistic Hartree equation and solve it numerically. This (non-topological) soliton is identified with the baryon.