Quark-hadron duality and meson-meson scattering amplitudes

We investigate a special concept of quarkhadron duality in meson physics at low and intermediate energies. With a relativistic propagator for confined quarks, we calculated masses and widths of the mesons which areS- andP-wave states ofq¯q (J ^P=0^?, 1^?, 0⁺, 1^+c, 2⁺) as well as meson-meson scattering amplitudes at energies up totrs ≤ 1.3 GeV by including light pseudoscalar and vector mesons into the interaction dynamics. Our investigation shows that the influence of the light meson dynamics resutls in:

1. a contribution to the constituent quark mass of approximately 200 MeV.
2. the appearance of a new soft confinement force barrier responsible for the formation of the highly excited meson states.

     

Pion and kaon electromagnetic form factors in a SUL(3) ⊗ SUR(3) effective Lagrangian

A SU(2) effective Lagrangian is extended to a SU _L(3) ⊗SU _R(3) by including the vector and axial vector meson. With this effective Lagrangian, electromagnetic form factors of charged pion and kaon are calculated in both time- and space-like regions. The pseudoscalar meson loops are taken into account. Good agreement with experimental data is obtained for those form factors and charged pseudoscalar meson radii. Decay widths of ρ→ππ and φ→K ⁺ K ^- are also calculated and shown to agree with experimental data very well. Received: 20 December 1999 / Accepted: 12 October 2000     

Study of X(5568) in a unitary coupled-channel approximation of BK and B_sπ

The potential of the B meson and the pseudoscalar meson is constructed up to the next-to-leading order Lagrangian, and then the BK and B_sπ interaction is studied in the unitary coupled-channel approximation. A resonant state with a mass about 5568 MeV and J~P= 0~+is generated dynamically, which can be associated with the X(5568) state announced by the D0 Collaboration recently. The mass and the decay width of this resonant state depend on the regularization scale in the dimensional regularization scheme, or the maximum momentum in the momentum cutoff regularization scheme. The scattering amplitude of the vector B meson and the pseudoscalar meson is calculated, and an axial-vector state with a mass near 5620 MeV and J~P= 1~+is produced. Their partners in the charm sector are also discussed.     

An su (6)w fit to the negative parity baryon decay rates

We present a least squares fit to the experimental data on decays of negative parity baryon resonances into a pseudoscalar meson and either a J^P = 1/2⁺ stable baryon or a J^P = 3/2⁺ decuplet member. We find that the s-waves and d-waves are separately in good agreement with the predictions of SU (6)_w ⊗ O(2)_Lz. Predictions are given regarding several as yet unobserved decay processes, and for those which concern hitherto undetected resonances, their possible detection is discussed.     

Some New Features in the Pseudoscalar Meson and Vector Meson Photoproductions

We investigate the role of the t-channel meson exchange in various photoproduction processes to discuss features of the respective production mechanism. For the less model-dependent analysis we work with the t-channel meson pole reggeized in the Born approximation amplitude. With the meson–baryon coupling constants chosen consistently with symmetry prediction we show that the Reggeized pole model could reproduce the experimental data to a good degree in the lower energy region. Numerical consequences show the significance of the tensor meson exchange in the γ p → K ⁺Λ, the dominance of the pseudoscalar meson exchange in the πΔ (and KΣ*) processes, and the sizable role of the vector-meson magnetic moment in the charged ρ (and K*) photoproductions, respectively. These new features from the present analyses could provide a useful guide for future study of the N* resonances in the low energy region.     

Spontaneously broken quark helicity symmetry

We discuss the origin of chiral-symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU (N) gauge theory with massless quarks if that theory has a condensate of fermion light-cone zero modes. The symmetry breaking appears as induced interactions in an effective light-cone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1 + 1-dimensional reduced models of gauge theory.     

The kinematic and symmetry structure of e+e−→hadron pairs

The kinematic singularity and constraint free amplitudes for e⁺e^?→two particles which can have arbitrary spins are obtained in a simple closed form. The relationships of these amplitudes with the usual multipole form factors are given. It is noted that SU(6)_W and tests of ideas based on the Melosh transformation are liberated from their γN and πN arena and can be confronted with arbitrary targets and axcitations. The matrix elements or arbitrary meson pairs are then derived, rates are computed for pseudoscalar and vector meson production, and some tests of symmetry breaking mechanisms proposed. Extension to SU(4)[SU(8)_W] broken in the masses enables estimates of charmed particle production rates to be obtained. General features of πR final states suggest that scaling violation at small x may be connected with threshold phenomena as channels open up. A subtle difference between space-like and time-like regions is highted.     

Mass of the up quark and chiral symmetry at infinite momentum

We find here that a very low mass for the X⁰ meson (m_X0=305.5 MeV) is predicted from a study of the pseudoscalar mesons in the framework of chiral symmetry at infinite momentum when the up quark mass vanishes (as an alternative to axion).     

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.     

Resonances Generated by the Vector Meson-Baryon Dynamics

We have recently studied vector meson-octet baryon (VB) interactions with the aim to find dynamical generation of resonances in such systems. For this, we consider the s-, t-, u-channel diagrams along with a contact interaction originating from the hidden local symmetry Lagrangian. We find the contribution from all these sources, except the s-channel, to be important. The amplitudes obtained by solving the coupled channel Bethe–Salpeter equations for the systems with total strangeness zero show generation of one isospin 3/2, spin 1/2 resonance and three isospin 1/2 resonances: two with spin 3/2 and one with spin 1/2. We identify these resonances with Δ (1900) S ₃₁, N*(2080) D ₁₃, N* (1700) D ₁₃, and N*(2090) S ₁₁, respectively. Further, we briefly discuss the results of our investigation of the VB systems when coupled to the pseudoscalar meson-baryon (PB) channels. We find that the low-lying resonances couple strongly to the VB channels, a result which can be useful in studying the reactions involving pseudoscalar and vector meson exchanges. In case of the higher mass resonances (in the 1,800–2,200 MeV region), we find that some of the states claimed as dynamically generated states in the VB system can disappear due to their coupling to the PB channels. We also find that new states can appear from PB–VB coupled channel dynamics; for example, we find that a Σ resonance near 1,400 MeV gets developed due to such an effect.     

Rho meson propagation and dilepton enhancement in hot hadronic matter

A realistic model for the free rho meson with coupling to two-pion states is employed to calculate the rho propagator in a hot and dense hadron gas. The medium modifications are based on hadronic rescattering processes: intermediate two-pion states are renormalized through interactions with surrounding nucleons and deltas, and rho meson scattering is considered off nucleons, deltas, pions and kaons. Constraints from gauge invariance as well as the full off-shell dynamics of the interactions are accounted for. Within the vector dominance model we apply the resulting in-medium rho spectral function to compute e⁺e⁻ production rates from π⁺π⁻ annihilation. The calculation of corresponding e⁺e⁻ spectra as recently measured in central collisions of heavy-ions at CERN/SpS energies gives reasonable agreement with the experimental data.     

Explicit time-reversal violating interactions for nuclear physics

Starting from a T-violating Lagrangian involving the nucleon, meson and electro magnetic fields interacting at a point, we calculate the one meson exchange diagram and obtain the longest range part of a two-nucleon electromagnetic operator. The cases when the meson is scalar, pseudoscalar and vector are considered. For the radiation of a real photon the multipole expansions of the transition operators are obtained. The properties and expected magnitudes of the resulting explicit two-nucleon transition operators are examined and compared to the normal operators. With the interactions at ‘maximal’ strength any contributions from the vector operators are negligible and violations from the other operators are only likely to reach the order of 10^?3 where the normal transitions are strongly inhibited.When the photon is virtual the interactions lead to explicit T-violating three-nucleon potentials. These potentials give practically no contributions to optical model potentials. The best reciprocity experiments appear to be nucleon transfer reactions, and there could be violations of the order of 10^?3 in (d ? p) reactions from the pseudoscalar potential. This potential is shown to give a stripping amplitude with angular properties very different from the normal one.     

Neutral K1(890) and ρ0 meson production in e+e− annihilation at ;s=29GeV

The production of neutral K¹(890) and ρ⁰ mesons was studied in e⁺e^? annihilation at $\text{s}\text{=29}\text{GeV}$ using the High Resolution Spectrometer at PEP. Differential cross sections are presented as a function of the scaled energy variable z and compared to π⁰ and K⁰ production. The measured multiplicities are 0.84±0.08 ?⁰ mesons and $\text{0.57±0.09 K}{}^{10}\text{(890)}$ mesons per event for a meson momentum greater than 725 MeV/c. The ratios of vector meson to pseudoscalar meson production for (u,d), s and c quark are compared to predictions of the Lund model.     

Octet-decuplet baryon mass splittings from self-consistent one-loop perturbation theory

The bag model of confined relativistic quarks in chiral-invariant interaction with scalar, pseudoscalar, vector, and pseudovector mesons, as well as gluons, is used to calculate the masses and wave functions of the spin-1/2 baryon octet and spin-3/2 decuplet, using selfconsistent Brillouin-Wigner bound state perturbation theory. Chiral symmetry breaking is invoked with the sigma model. SU (6) and SU (3) symmetries are broken by the experimental meson spectrum, and a strange quark mass. Mass corrections are calculated to one loop order, limited to the baryons of the octet and decuplet and the lowest lying mesons. Encouraging results are obtained, especially for theΔ — N and theΣ — Λ splittings. Convergence and stability have not been demonstrated, but are evidently improved by the self-consistency requirement. An initial parameter tuning gives a fit to all the octet and decuplet masses within ≦0.02 GeV, at the price of choosing the bag radius, the non-strange baryon input bag mass, and the strange quark mass. Even these small discrepancies can be dramatically reduced by fine-tuning the vector meson coupling and including an instanton contribution peculiar to theΛ.     

Radiative decays and transition form factors of strange mesons in the relativistic constituent quark model

Motivated by the recent lattice QCD results indicating that the topological charge contribution to the flavor singlet axial vector current can be traded off by the constituent quark masses, we investigate the radiative decays of pseudoscalar (π,K, η, η′), vector (ρ,K*, ω, ?) and axial vector (A ₁) mesons using a simple relativistic constituent quark model. For both simplicity and relativity, we take advantage of the distinguished features in the light-cone quantization method: (1) the Fock-state expansion of meson wavefunctions are not contaminated by the vacuum fluctuation, (2) the assignment of meson quantum numbers are given by the Melosh transformation. Except the well-known constituent quark masses of (u,d,s) quarks and the spin-averaged meson masses, the only parameter in the model is the gaussian parameter β which determines the broadness (or sharpness) of radial wavefunction. The computed decay widths and the transition form factors of ρ, ω → π(η)γ*,K* →Kγ* andA ₁ → πγ* at 0≤Q ²≤5 GeV² and π⁰(η) → γ*γ at 0≤Q ²≤3 GeV² are in a remarkably good agreement with the experimental data and the result forA ₁ ⁺ → π₊ γ* transition is quite consistent with the experiments of pion scattering on a nucleus using Primakoff effect. This model is potentially useful in the cocktail analyses of the dilepton productions in proton-proton, proton-nucleus and nucleus-nucleus collisions at SPS energies and a little above.     

Bethe-Salpeter Meson Masses Beyond Ladder Approximation

The effect of quark-gluon vertex dressing on the ground-state masses of the u/d-quark pseudoscalar, vector and axialvector mesons is considered with the Dyson-Schwinger equations. This extends the ladder-rainbow Bethe-Salpeter kernel to two-loops. To render the calculations feasible for this exploratory study, we employ a simple infrared dominant model for the gluon exchange that implements the vertex dressing. The resulting model, involving two distinct representations of the effective gluon exchange kernel, preserves both the axial-vector Ward-Takahashi identity and charge conjugation symmetry. Numerical results confirm that the pseudoscalar meson retains its Goldstone boson character. The vector meson mass, already at a very acceptable value at ladder level, receives only 30MeV of attraction from this vertex dressing. For the axial-vector states, which are about 300MeV too low in ladder approximation, the results are mixed: The 1^+– state receives 290MeV of repulsion, but the 1⁺⁺ state is lowered further by 30MeV. The exotic channels 0^–– and 1^–+ are found to have no states below 1.5GeV in this model.     

Elementary scalar mesons and Regge poles

We show, for the annihilation amplitude of π⁺π^? → two vector mesons, that parity conservation and rotational symmetry demand the existence of a triplet of Regge singularities crossing at t = 0. In the usual scalar-vector field theory, calculations of the leading terms of this amplitude up to the eight order show that these singularities are moving Regge poles. Contrary to common belief, the elementary scalar meson lies on one of them.     

Electromagnetic structure and weak decay of pseudoscalar mesons in a light-front QCD-inspired model

We study the scaling of the ³S₁-¹S₀ meson mass splitting and the pseudoscalar weak-decay constants with the mass of the meson, as seen in the available experimental data. We use an effective light-front QCD-inspired dynamical model regulated at short distances to describe the valence component of the pseudoscalar mesons. The experimentally known values of the mass splitting, decay constants (from global lattice-QCD averages) and the pion charge form factor up to 4 [GeV/c]² are reasonably described by the model.