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.     

Properties of vector and axial-vector mesons from a generalized Nambu-Jona-Lasinio model

We construct a generalized Nambu-Jona-Lasinio lagrangian including scalar, pseudoscalar, vector and axial-vector mesons. We specialize to the two-flavor case. The properties of the structured vacuum as well as meson masses and coupling constants are calculated giving an overall agreement within 20% of the experimental data. We investigate the meson properties at finite density. In contrast to the mass of the scalar σ-meson, which decreases sharply with increasing density, the vector meson masses are almost independent of density. Furthermore, the vector-meson-quark coupling constants are also stable against density changes. We point out that these results imply a softening of the nuclear equation of state at high densities. Furthermore, we discuss the breakdown of the KFSR relation on the quark level as well as other deviations from phenomenological concepts such as universality and vector meson dominance.     

Extended skyrmion model from quark flavour dynamics

From the effective chiral meson lagrangian derived recently from Nambu-Jona-Lasinio type of quark flavour dynamics, an extended skyrmion model is extracted. This model contains besides the usual Skyrme term further fourth-order derivative terms of the chiral field and in addition the ω meson field. It is shown that the net effect of all fourth-order derivative terms is to destabilize the soliton and to provide the desired medium-range attraction of the nucleon-nucleon interaction, which is responsible for nuclear binding but missing in the original Skyrme model. The soliton is stabilized by the coupling to the ω meson which produces a short-range repulsion. The corresponding equation of state of skyrmion matter is constructed and found to be in qualitative agreement with the equation of state of nuclear matter obtained from effective density-dependent forces.     

Effective chiral meson lagrangian with Weinberg and KSFR relations from microscopic four-quark interactions

An effective chiral meson lagrangian is derived from a microscopic quark lagrangian. It contains a partial Higgs mechanism for ϱ-A₁ mass splitting reproducing Weinberg and KSFR relations, and includes quartic derivative “Skyrme” terms and the gauges Wess-Zumino term. The connection to previous approaches deriving the effective lagrangian exclusively from the chiral anomaly including “normal-parity” terms is established.     

Instanton induced flavour mixing in the presence of vector mesons

An extended version of the Nambu-Jona-Lasinio model is supplemented with the 't Hooft determinant and bosonized for an arbitrary number of flavours. The resulting effective meson lagrangian is in good agreement with the experimental low-energy mesonic data. The presence of the 't Hooft determinant leads to a flavour mixing of the scalar and pseudoscalar mesons with diagonal flavour content. This instanton induced flavour mixing in the scalar and pseudoscalar channel is noticeably effected by the coupling to the vector and axial-vector meson sector. If the latter is taken into account the η?η′ mixing angle is shifted from ?31° to ?22° in good agreement with the experimental value.     

Stabilization of skyrmions via ϱ-mesons

It is shown that a skyrion can be stabilized by introducing ?-mesons into the chiral SU(2)_L × SU(2)_R lagrangian without higher-derivative terms like the Skyrme term. The ?-mesons are considered as dynamical gauge bosons associated with a hidden local symmetry of the non-linear sigma model. The lagrangian reduces to the Skyrme model in a limit of parameters. The Skyrmion mass M is found to be M = 1058 MeV when the parameters are fixed so as to satisfy the KSRF relation. It is also shown that a solition solution in a model with Ω-meson coupled with the baryonic current is a saddle-point solution.     

Derivation of the skyrme lagrangian

The form as well as the strength of the quartic term in the Skyrme lagrangian are obtained from the general nonlinear chiral SU₂ × SU₂ invariant π-N-ϱ lagrangian suggested earlier. The agreement with experiment is excellent.     

Saturating chiral field theory for the study of nuclear matter in the relativistic Hartree approximation

The bulk properties of nuclear matter are studied by considering a chirally invariant lagrangian which contains an interaction term involving scalar and vector mesons, of the form (apart from a numerical factor) used by Boguta. The calculation is performed in the relativistic Hartree approximation which includes the baryon vacuum fluctuation correction.     

The energy levels of the heavy flavour baryons in the topological soliton model

The energy levels of the charm and bottom as well as the mixed flavour hyperons are calculated with the model in which the hyperons are described as bound states of a topologicalSU (2) soliton andK-, D- andB-mesons. The spectra are obtained in a modified version of the Skyrme model where the chiral symmetry breaking term in the Lagrangian density is modified so as to incorporate the different values of the decay constants of the mesons of different flavour. The predicted strange and charmed hyperon spectra are in very good agreement with the empirical values, while the bottom hyperon energies that are more sensitive to the short range dynamics are somewhat below the empirical values. The predicted hyperfine spectra are remarkably close to those obtained with the constituent quark model, more or less independently of the short-distance properties of the effective Lagrangian. We suggest that this feature reflects the presence of an induced nonabelian gauge potential generated by the interplay between “fast” and “slow” degrees of freedom in the meson-soliton system.     

Electromagnetic interactions in a chiral effective lagrangian for nuclei

Electromagnetic (EM) interactions are incorporated in a recently proposed effective field theory of the nuclear many-body problem. Earlier work with this effective theory exhibited EM couplings that are correct only to lowest order in both the pion fields and the electric charge. The Lorentz-invariant effective field theory contains nucleons, pions, isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields. The theory exhibits a nonlinear realization of SU(2)_L × SU(2)_R chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying QCD, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. It has been verified that for normal nuclear systems, the effective lagrangian can be expanded systematically in powers of the meson fields (and their derivatives) and can be truncated reliably after the first few orders. The complete EM lagrangian arising from minimal substitution is derived and shown to possess the residual chiral symmetry of massless, two-flavor QCD with EM interactions. The uniqueness of the minimal EM current is proved, and the properties of the isovector vector and axial-vector currents are discussed, generalizing earlier work. The residual chiral symmetry is maintained in additional (non-minimal) EM couplings expressed as a derivative expansion and in implementing vector meson dominance. The role of chiral anomalies in the EM lagrangian is briefly discussed.     

Low-energy limit of chiral meson theory

Based on a phenomenologically successful effective chiral theory of pseudoscalar, vector, and axial-vector mesons, all the coefficients of the chiral perturbation theory are predicted. There is no new adjustable parameter in these predictions. Up to O(m ² _q) the formulas of the masses of the pseudoscalar mesons are the same as the ones obtained by ChPT. Received: 31 August 2000 / Accepted: 16 March 2001     

Confront holographic QCD with Regge trajectories of vectors and axial-vectors

By matching the predictions of the Dp–Dq soft-wall model in type II superstring theory with the spectra of vector and axial-vector mesons, we show the dependence of the Regge trajectories parameters on the metric parameters of the model. From the experimental results of Regge parameters for vector mesons, it is found that the D3 background brane with both q=5 and q=7 probe brane and D4 background brane with q=4 probe brane are close to the realistic holographic QCD. We also discuss how to realize chiral symmetry breaking in the vacuum and asymptotic chiral symmetry restoration in high excitation states. We find that the constant component of the 5-dimension mass square of axial-vector mesons plays an efficient role to realize the chiral symmetry breaking, and a small negative z ⁴ correction in the 5-dimension mass square is helpful to realize the chiral symmetry restoration in high excitation states.     

Vector dominance and radiative meson decays

The vector dominance model is reexamined in a semi-empirical approach. Vector-meson-photon couplings are determined from leptonic decays, and the vector-meson mixing angle and a single vector-vector-pseudoscalar coupling constant for an effective VVP lagrangian, which is constrained by Zweig's rule, is calculated from the V→πλ decay widths. The lagrangian is observed to be the same as that obtained by gauging the U(3)_L × U(3)_R hidden symmetry of the nonlinear pseudoscalar chiral lagrangian. The results are in reasonably good agreement with the data. Discrepancies are isolated and found to be substantially cured by a small symmetry breaking mass factor in the coupling constant.     

Chiral model of N and Δ with vector mesons

Vector mesons ?, A and ω are introduced in a chiral model for N and Δ, in which three valence quarks interact via meson exchange. In the phenomenological lagrangian, used here, the ? and ω are coupled to appropriate conserved currents. This reduces the number of coupling constants and fixes g_? and g_ω directly in terms of corresponding meson-nucleon coupling constants. The calculations are done fully self-consistently in the mean field theory using the hedgehog ansatz. The vector mesons play a significant role in the dynamics and allow us to obtain very good results for physical observables.     

Effective lagrangians with U(1) axial anomaly (I)

The effective lagrangian which includes the U(1) axial anomaly is discussed. The lagrangian describes the interaction of physical mesons of spin-zero and spin-one fields and an effective Kogut-Susskind four-vector anomaly field. The interactions are constructed which satisfy all the anomalous Ward identities for vertices which accommodate arbitrary amounts of chiral and SU(3) symmetry breaking consistent with U(3) × U(3) current algebra.     

An effective lagrangian with no U(1) problem in CPn−1 models and QCD

We write an effective lagrangian which gives two-point Green's functions satisfying the anomalous Ward identities for the U(1) axial vector current with a singlet particle that has a non-vanishing mass in the chiral limit. We show that the mechanism that has been postulated by Witten and Veneziano for solving the U(1) problem in the framework of the 1/n expansion in QCD is fully active in the two-dimensional CP^n? model where the 1/n expansion can be explicitly performed.     

Vector mesons and magnetic moments of hyperons

We calculate hyperon magnetic moments by using the bound-state approach to the SU(3) Skyrme model. We analyze the role of the vector mesons as ω and meson in the calculation of the magnetic moment. Inclusion of an ω vector meson, instead of the Skyrme term, shows a net improvement of the nonstrange part of the isoscalar current. Taking account of the vector meson, although only treated approximately in the SU(2) sector, does not give a meaningful improvement in isoscalar or isovector current, if we fix the physical input of the model to fit the hyperon masses. Importance of the heavy vector mesons is argued, not only in the hyperfine mass splitting but also in the magnetic moment. It is also argued that the treatment of the gauged Wess-Zumino action in the SU(2) sector is crucial in reproducing the experimental results.     

Evaluation of the Skyrme parameter from QCD sum rules

The dimensionless parameter of the Skyrme lagrangian is evaluated by two methods. In one a combination of sum rules for the nucleon and the pion is used, in the other only baryonic sum rules. e = 5−8 and e = 5−7 is found, respectively, in agreement with the phenomenological value e = 5.45. To leading order in the operator-product expansion the analytical expression of e does not depend on the chiral-symmetry-breaking parameters.     

Vector meson dominance and the KSRF relation as consequences of the interplay between the standard electroweak model and hidden local symmetry

The old concept of vector meson dominance and the KSRF relation are shown to be natural consequences (i.e. without the choice of any arbitrary parameter) of the assumption that ϱ mesons are dynamical gauge bosons of a hidden local symmetry in the non-linear chiral lagrangian and of SU(2)_L × U(1)_Y gauge invariance. This result intrinsically links the standard electroweak model to the strong isospin group.