String deformations induced by retardation effects in mesons

The rotating-string model is an effective model of mesons, in which the quark and the antiquark are linked by a straight string. We previously developed a method to estimate the retardation effects in this model, but the string was still kept straight. We now go a step further and show that this kind of retardation effects cause a small deviation of the string from the straight line. We first give general arguments constraining the string shape. Then, we find analytical and numerical solutions for the string deformation induced by retardation effects. We finally discuss the influence of the curved string on the energy spectrum of the model.     

Stability of asymmetric tetraquarks in the minimal-path linear potential

The linear potential binding a quark and an antiquark in mesons is generalized to baryons and multiquark configurations as the minimal length of flux tubes neutralizing the color, in units of the string tension. For tetraquark systems, i.e., two quarks and two antiquarks, this involves the two possible quark–antiquark pairings, and the Steiner tree linking the quarks to the antiquarks. A novel inequality for this potential demonstrates rigorously that within this model the tetraquark is stable in the limit of large quark-to-antiquark mass ratio.     

Chiral Lagrangian Treatment of 0^＋＋ Mesons and 0^＋＋ Glueballs

Within the framework of a nonlinear chiral Lagrangian the mass spectra and the decay properties of 0^＋＋ states below 2 GeV are studied. Assuming that f0（980）, a0（980）, K0（1430）, and f0（1500） comprise an SU（3） nonet, we make a detailed prediction about the static properties of the 0^＋＋ mesons. The substructure analysis of these states in terms of two- and four-quark components as well as a glueball component is carried out. We also consider the interaction Lagrangian and provide a preliminary study of the strong and radiative decays of the 0＋＋ mesons. The scalar glueball masses and partial widths are also presented. In view of the fact that few data of 0＋＋ mesons are clearly given in the present PDG （Particle Data Group） list and that the four-quark content of mesons is a hot issue both experimentally and theoretically, the predicted results of the paper may be helpful for upcoming experimental and theoretical studies of these mesons.     

Topologically non-trivial chiral transformations

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu-Jona-Lasinio model the hidden gauge and massive Yang-Mills approaches to vector mesons are linked by a special chiral transformation which removes the chiral field from the scalar-pseudoscalar sector. The chirally rotated axial vector meson field (à _μ ) transforms homogeneously under flavor rotations and may thus be dropped without violating chiral symmetry. The fermion determinant for static meson field configurations is computed by summing the discretized eigenvalues of the Dirac Hamiltonian. It is discussed how the local chiral transformation loses its unitary character in a finite model space. This technical issue proves to be crucial for the construction of the soliton within the Nambu-Jona-Lasinio model when the chirally rotated axial vector field is neglected. In the background of this soliton the valence quark is strongly bound, and its eigenenergy turns out to be negative. This important feature, which usually is generated by non-vanishing axial vector profiles, is thus maintained by the simplificationà _μ = 0.     

Excited flux tube from q¯g hybrid mesons

In the framework of quark models, hybrid mesons are either seen as two-body qˉ systems with an excited flux tube connecting the quark to the antiquark or as three-body qˉg systems including a constituent gluon. In this work we show that, starting from the three-body wave function of the qˉg hybrid meson in which the gluonic degrees of freedom are averaged, the excited flux tube picture emerges as an equivalent qˉ potential. This equivalence between the excited flux tube and the constituent-gluon approach is confirmed for heavy hybrid mesons but, for the first time, it is shown to hold in the light sector too, provided the contribution of the quark dynamics is correctly taken into account.     

About the Casimir scaling hypothesis

A lattice calculation shows that the Casimir scaling hypothesis is well verified in QCD, that is to say that the potential between two opposite colour charges in a colour singlet is proportional to the value of the quadratic Casimir operator. On the other hand, in a bag model calculation for the same system, a scaling of the string tension with the square root of the quadratic Casimir operator is obtained. It is shown that, within the same formalism but with the assumption that the width of the string is independent of the colour charges, the string tension is proportional to value of the quadratic Casimir operator. Some considerations about the colour behaviour of the total interaction are given.     

Is chiral symmetry restored in the excited meson spectrum?

The large degeneracy observed in the excited meson spectrum by the Cristal Barrel Collaboration in the experimental data on proton–antiproton annihilation in flight into mesons in the range 1.9–2.4 GeV has been interpreted as a signal of chiral symmetry restoration. In this work we suggest that such degeneracy may be an indication of the confinement potential modification by color screening. The experimental data can be fairly well reproduced in a constituent quark model with a screened linear confinement potential without changing the dynamical quark mass. Observables that could discriminate our model from those which explicitly restore the chiral symmetry are proposed.     

Rotating QCD string and the meson spectrum

The spectra of light–light and heavy–light mesons are described by spinless Salpeter equation and Dirac equation respectively, which predict linear dependence of the meson mass squared M² on angular momentum J and number of radial nodes n. Both spectra are computed by the WKB method and shown to agree with exact numerical data within few percent even for the lowest levels. The drawback of Salpeter and Dirac equation is that (inverse) Regge slopes do not coincide with the string ones, 2πσ and πσ respectively, because the string dynamics is not taken into account properly. The lacking string rotation is introduced via effective Hamiltonian derived from QCD which generates linear Regge trajectories for light mesons with the correct string slope.     

QCD Coulomb gauge approach to exotic hadrons

The Coulomb gauge Hamiltonian model is used to calculate masses for selected J^PC states consisting of exotic combinations of quarks and gluons: ggg glueballs (oddballs), qˉg hybrid mesons and qˉqˉ tetraquark systems. An odderon Regge trajectory is computed for the J^- glueballs with intercept much smaller than the pomeron, explaining its nonobservation. The lowest 1^-+ hybrid-meson mass is found to be just above 2.2GeV while the lightest tetraquark state mass with these exotic quantum numbers is predicted around 1.4GeV consistent with the observed π(1400).     

Casimir scaling, glueballs, and hybrid gluelumps

Assuming that the Casimir scaling hypothesis is well verified in QCD, masses of glueballs and hybrid gluelumps (gluon attached to a point-like cˉ pair) are computed within the framework of the rotating string formalism. In our model, two gluons are attached by an adjoint string in a glueball, while the gluon and the colour octet cˉ pair are attached by two fundamental strings in a hybrid gluelump. Masses for such exotic hadrons are computed with very few free parameters. These predictions can serve as a guide for experimental searches. In particular, the ground-state glueballs lie on a Regge trajectory and the lightest 2⁺⁺ state has a mass compatible with some experimental candidates.     

Dispersion approach to quark-binding effects in weak decays of heavy mesons

The dispersion approach based on the constituent quark picture and its applications to weak decays of heavy mesons are reviewed. Meson interaction amplitudes are represented within this approach as relativistic spectral integrals over the mass variables in terms of the meson wave functions and spectral densities of the corresponding Feynman diagrams. Various applications of this approach are discussed:Relativistic spectral representations for meson elastic and transition form factors at spacelike momentum transfers are constructed. Form factors at q² > 0 are obtained by the analytical continuation. As a result of this procedure, form factors are given in the full q² range of the weak decay in terms of the wave functions of the participating mesons.The 1/m_Q expansion of the obtained spectral representations for the form factors for the particular limits of the heavy-to-heavy and heavy-to-light transitions are analysed. Their full consistency with the constraints provided by QCD for these limits is demonstrated.Predictions for form factors for B_(s) and D_(s) decays to light mesons are given.The B → γℓν decay and the weak annihilation in rare radiative decays are considered. Nonfactorizable corrections to the B⁰ mixing are calculated.Inclusive weak B decays are analysed and the differential distributions are obtained in terms of the B meson wave function.     

Hadron spectroscopy and structure from AdS/CFT

The AdS/CFT correspondence between conformal field theory and string states in an extended space-time has provided new insights into not only hadron spectra, but also their light-front wave functions. We show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter space z and a specific impact variable ζ which measures the separation of the constituents within the hadron in ordinary space-time. This connection allows one to predict the form of the light-front wave functions of mesons and baryons, the fundamental entities which encode hadron properties and scattering amplitudes. A new relativistic Schr?dinger light-front equation is found which reproduces the results obtained using the fifth-dimensional theory. Since they are complete and orthonormal, the AdS/CFT model wave functions can be used as an initial ansatz for a variational treatment or as a basis for the diagonalization of the light-front QCD Hamiltonian. A number of applications of light-front wave functions are also discussed.     

Light hadron spectra in the constituent quark model with the Kobayashi-Kondo-Maskawa-’t Hooft effective UA (1) symmetry breaking interaction

We make a critical comparison of several versions of instanton-induced interactions present in the literature, all based on ITEP group’s extension to three colours and flavours of ’t Hooft’s effective lagrangian, with the predictions of the phenomenological Kobayashi-Kondo-Maskawa (KKM) chiral quark lagrangian. We analyze the effects of all versions of the effective U_A (1) symmetry breaking interactions on light hadron spectra in the non-relativistic constituent quark model. We show that the KKMT force, when used as a residual hyperfine interaction reproduces the correct ordering of pseudoscalar and vector mesons even without explicitly taking chiral symmetry into account. Moreover, the nucleon spectra are also correctly reproduced, only the Roper resonance remains too high, albeit lower than usual, at 1660 MeV. The latter’s lower than expected mass is not due to a small excitation energy, as in the Glozman-Riska (GR) model, but to a combination of colour, flavour, and spatial wave function properties that enhance the relevant matrix elements. The KKMT interaction explicitly depends on flavour and spin of the quarks, but unlike the GR flavour-spin one it has a firm footing in QCD. In the process we provide several technical advances, in particular we show the first explicit derivation of the three-body Fierz transformation and apply it to the KKM interaction. We also discuss the ambiguities associated with the colour degree of freedom.     

夸克和弦模型中非奇异轻介子的类雷吉谱(英文)

本工作重新考察了相对论弦模型和准相对论夸克模型中轻介子的类雷吉谱。基于辅助场技术,提出了非奇异轻介子的一个解析质量公式,由此推导出了一个准线性的Regge-Chew-Frautschi轨迹关系,并将此关系用相应介子的实验数据（PDG）进行了检验。检验结果表明,和实验观测数据比较,夸克模型对介子质量的预言与弦模型的相符,但在角动量较大时,夸克模型的预言稍微优于弦模型。We revisit the Regge-like spectra of light mesons in the relativistic string model and the simirelativistic quark model. An analytical mass formula is proposed for light mesons based on the auxiliary field technique, and a quasi-linear Regge-Chew-Frautschi plot with flavor dependence is derived and verified with the experimental data(PDG) for light mesons.The results show that the quark model predictions for meson masses agree with those of the string model, but are slightly better when the angular momentum is relatively large as compared with the observed data.     

Axial resonances in the open and hidden charm sectors

A SU(4) flavor symmetrical Lagrangian is constructed for the interaction of the pseudo-scalar mesons with the vector mesons. SU(4) symmetry is broken to SU(3) by suppression of terms in the Lagrangian where the interaction should be driven by charmed mesons. Chiral symmetry can be restored by setting this new SU(4) symmetry-breaking parameters to zero. Unitarization in coupled channels leads to the dynamical generation of resonances. Many known axial resonances can be identified including the new controversial X(3872) and the structure found recently by Belle around 3875MeV in the hidden charm sector. Also new resonances are predicted, some of them with exotic quantum numbers.     

Semileptonic decays of baryons in a relativistic quark model

We calculate semileptonic decays of light and heavy baryons in a relativistically covariant constituent quark model. The model is based on the Bethe-Salpeter equation in instantaneous approximation. It generates satisfactory mass spectra for mesons and baryons up to the highest observable energies. Without introducing additional free parameters we compute on this basis helicity amplitudes of electronic and muonic semileptonic decays of baryons. We thus obtain form factor ratios and decay rates in good agreement with experiment.     

Scalar mesons in a chiral quark model with glueball

Ground-state scalar isoscalar mesons and a scalar glueball are described in a U(3)×U(3) chiral quark model of the Nambu-Jona-Lasinio (NJL) type with 't Hooft interaction. The latter interaction produces singlet-octet mixing in the scalar and pseudoscalar sectors. The glueball is introduced into the effective meson Lagrangian as a dilaton on the base of scale invariance. The mixing of the glueball with scalar isoscalar quarkonia and amplitudes of their decays into two pseudoscalar mesons are shown to be proportional to current quark masses, vanishing in the chiral limit. Mass spectra of the scalar mesons and the glueball and their main modes of strong decay are described. Received: 14 July 2000 / Accepted: 31 July 2000     

Complex-mass renormalization in chiral effective field theory

We consider a low-energy effective field theory of vector mesons and Goldstone bosons using the complex-mass renormalization. As an application we calculate the mass and the width of the ρ meson.