Spectrum and Regge trajectories in QCD

Starting in the 1960s, an active group of physicists under the guidance of Prof. K.A. Ter-Martirosyan began creating the theory of high-energy processes in QCD. From the beginning, the key element of this theory is the notion of Regge trajectories and, in particular, of the Pomeron trajectory, which have been introduced phenomenologically. In this talk, I review the problem of the spectrum and Regge trajectories as it can be derived from nonperturbative QCD dynamics.     

Deuteron photodisintegration within the Quark-Gluon Strings Model and QCD motivated nonlinear Regge trajectories

We investigate deuteron two-body photodisintegration within the framework of the Quark-Gluon Strings Model with nonlinear baryon Regge trajectories. Special attention is paid to the use of QCD motivated Regge trajectories of the logarithmic and square-root form. We find that the recent experimental data from TJNAF in the few-GeV region can be reasonably described by the model. Angular distributions at different γ-energies are presented and the effect of a forward-backward asymmetry is discussed. Predictions for the energy dependence of dσ/dt at higher energies and different Θ_c.m. are presented, too. Received: 12 March 2001 / Accepted: 19 March 2001     

The spatial string tension and dimensional reduction in QCD

The spatial string tension is calculated in 2+1 flavor QCD with a physical strange quark mass and almost physical light quark masses on lattices with N_t=4,6 and 8. The results are compared with predictions of dimensionally reduced QCD. They suggest that dimensional reduction works also in the presence of light dynamical quarks down to temperatures of about 1.5T_c.     

Couplings of the rho meson in a holographic dual of QCD with Regge trajectories

The couplings g_ρHH of the ρ meson with a scalar meson H are calculated in a holographic dual of QCD in which the Regge trajectories for the mesons are manifest. In contrast to the conclusion in general AdS/QCD models, the resulting couplings grow linearly with the quantum number of excited H; thus they are far from universal. This non-universality seems to result from the disappearance of an explicit cutoff in the holographic dimension in this model. Correspondingly, the ρ-dominance for the electromagnetic form factors of H does not hold any more, even in an apparent sign-alternating manner. With these couplings at hand, the asymptotic behavior of the form factors can easily be calculated. The form factor exhibits the 1/Q^(2Δ-2) behavior, which is in accordance with the scaling behavior of the fixed-angle scattering amplitude based on the AdS/CFT correspondence. It is also pointed out that the asymptotic behavior can be matched to the results of perturbative QCD, if the conformal dimension Δ of the operator is replaced by the combination τ+L of the meson. PACS  11.25.Tq; 12.40.Vv; 14.40.Cs     

Scaling in lattice QCD: Glueball masses and string tension

We study the scaling behaviour of lattice quantum chromodynamics by comparing the β dependence of the string tension and the 0⁺⁺ glueball mass. We use a source method at β=5.7, β=5.9 and β=6.1, on lattices from 9³· 24 to 16³· 32. Assuming a string tension of about (420 MeV)², the lattice spacing ranges from 0.16 to 0.08 fm. In order to separate finite volume from scaling violation effects we have compared data from lattices having approximately the same overall physical size at the different values of β. We find deviations from scaling to be very small.     

Higher order corrections and the scale parameter in QCD

I estimate the influence of the higher order corrections on the determination of the scale parameter Λ². I find a sizeable effect (a reduction of Λ² by a factor 3 to 4). This factor can be relevant in the comparison of Λ² with the characteristic confinement parameters.     

Astrophysical determination of the scale parameter in QCD

We consider the phase transition to quark matter in a system of high density matter, taking into account the spin-2 interaction among nucleons. We find that the transition is possible only if the spin-2 coupling constant is ten times smaller than its value at low energies. From this we are able to determine the scale parameter of QCD.     

Regge trajectories in the quark model

We prove that the large angular momentum behaviour of the leading Regge trajectory of a meson (q \(\bar q\) ) or a baryon (qqq) can be obtained by minimizing the classical energy of the system for given angular momentum. A two-body quark-antiquark linear potential plus relativistic kinematics produces asymptotically linear Regge trajectories for mesons. For baryons we take either a sum of two-body potentials with half strength or a string of minimum length connecting the quarks, and find in both cases that the favoured configuration is a quark-diquark system and that the baryon and meson trajectories have the same slope. Short-distance singularities of the potential are shown to be unimportant.     

QCD and the string model

Infinitisimal variations of the path-dependent phase factor P exp(i∫_σA_μdz_μ) in gauge theory are studied. They are shown to satisfy differential equations which are equivalent to those for a quantized string if the gauge fields meet certain constraints.     

Connection between perturbation theory and lattice QCD

The problems associated with comparing perturbation theory and lattice Monte Carlo techniques when applied to QCD matter at zero net baryon number are discussed. In particular, the importance of next-to-leading order corrections to optimising the magnitude of the leading corrections to the equation of state and screening lenghts is emphasised.     

Regge theory and QCD in large-angle scattering

We argue that exclusive processes whose cross-sections are determined by Regge pole trajectory exchanges, α(t), at small momentum transfers (t), are controlled by these same exchanges at very large |t| too. The analysis is based on a Reggeized version of the constituent interchange model (CIM), which predicts that α(t)→?1 ast→?∞, and that the asymptotic form of the Regge residues is fixed by the dimensional counting rules and CIM constraints. Between the two regimes of soft and hard scattering there is an intermediate region where Regge cuts are important, but these higher-twist effects die away as |t| is increased. We show that this hypothesis is consistent with high energy nucleon-nucleon and pion-nucleon scattering at all angles.     

Magnetic Symmetry,Regge Trajectories,and the Linear Confinement in Dual QCD

Using the magnetic symmetry structure of non-Abelian gauge theories, we analyze the flux tube formulation and its implications on the hadronic Regge trajectories and the confinement of color isocharges in magnetically condensed (with as well as without the electric excitations) QCD vacuum. Starting with the fiber bundle structure of QCD, the dual potentials are used to construct the QCD Lagrangian which has been shown to develop a unique flux tube configuration in its dynamically broken phase. The vector mass mode of the condensed vacuum has been shown to play a leading role in flux tube energy and other confinement parameters. Using the flux tube energy and the angular momentum, the Regge trajectories for hadrons have been obtained and the linear confining properties of dual QCD have been established. The dyonic flux tube structure of the condensed QCD vacuum has been obtained by inducing the electric excitation of QCD monopoles and the confining nature along with the linearity of Regge trajectories in dyonically condensed QCD vacuum are shown to remain intact. Implications of the modification in Regge slope parameter, on improving the confining properties of dual QCD vacuum are also discussed. PACS: 12.38.Aw; 11.30.-j; 14.80.Hv; 12.39.Mk An erratum to this article is available at .     

Chiral-symmetry breaking and the QCD string

The Lorentz nature of the effective interquark interaction is investigated in a heavy-light quarkonium. The approach of the Dyson-Schwinger-type equation and the quantum-mechanical Hamiltonian method of the QCD string with quarks at the ends are employed to demonstrate that the effective scalar interaction, which appears owing to chiral-symmetry breaking, is responsible for the QCD-string formation. The Hamiltonian of the QCD string with quarks at the ends arises naturally if this effective scalar interaction dominates. If, on the contrary, chiral symmetry is manifest, the effective interquark interaction remains vectorial, and the corresponding bound-state equation is incompatible with the QCD-string Hamiltonian.We conclude therefore that the genuine Lorentz nature of the QCD string is scalar. The text was submitted by the authors in English.     

Vibration of the QCD string

The large-distance behavior of adiabatic hybrid potentials is studied on the basis of the QCD string model. The calculated spectra are shown to result from the interplay of potential-type longitudinal and string-type transverse vibrations.     

Two new Regge trajectories in the Neveu-Schwarz model

The existence of two new families of Regge trajectories at the tree diagram level of the Neveu-Schwarz dual pion model is pointed out. They both have odd G-parity but are of opposite naturality. The highest lying new trajectory is related to the usual unnatural parity pion trajectory $\text{α}{}_{\mathrm{\pi }}\text{by}\text{β}{}_{\mathrm{\pi }}\text{=}\text{1}\text{2}\text{α}{}_{\mathrm{\pi }}\text{+}\text{1}\text{2}$. It factorizes and has positive signature. The parent of the new natural parity trajectories is related to the usual trajectory α_ω by $\text{β}{}_{\mathrm{\omega }}\text{=}\text{1}\text{2}\text{α}{}_{\mathrm{\omega }}$.     

A comparative analysis of Mesonic, Baryonic and Glueball Regge trajectories

We present a comparative analysis of mesonic, baryonic and Glueball Regge trajectories based on different parameters. The different inbuilt compositions of the three seem to serve as a basis for their individual identities. We discuss features such as crossed channel forces, signature, string models and also the dependence of the slope of the mesons and baryons on the fine structure constant. We infer that inspite of various inherent similarities, these three Regge trajectories have some distinctive features which serve as a basis for their identification.