Self-intersecting Regge trajectories in multi-channel scattering

We present a simple direct method for calculating Regge trajectories for a multichannel scattering problem. The approach is applied to the case of two coupled Thomas-Fermi type potentials, used as a crude model for electron-atom scattering below the second excitation threshold. It is shown that non-adiabatic interaction may cause formation of loops in Regge trajectories. The accuracy of the method is tested by evaluating resonance contributions to elastic and inelastic integral cross sections.     

Analytic model of Regge trajectories

A model for a Regge trajectory compatible with the threshold behavior required by unitarity and asymptotics in agreement with analyticity constraints is given in explicit form. The model is confronted in the time-like region with widths and masses of the mesonic resonances and, in the space-like region, the ρ trajectory is compared with predictions derived from the π-N charge-exchange reaction. Breaking of the exchange degeneracy is studied in the model and its effect on both the masses and widths is determined. Received: 23 January 2001 / Accepted: 9 February 2001     

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.     

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 possibility of a pion-pion scattering experiment

A possibility of a pion-pion collision experiment is discussed. This experiment permits one to perform very precise measurements of the s-wave scattering lengths at isospin state of I = 0 and 2 and a pion energy of 200 MeV-1 GeV. Quark-antiquark condensate, effective Lagrangian theory, and some features of the QCD lattice approach can be tested with very high precision. The text was submitted by the authors in English.     

A generalized interference model with indefinitely rising Regge trajectories

A class of analytic crossing-symmetric amplitudes is constructed which is compatible with any Regge trajectory bounded by ¦α(s)¦q, q<1/2. There are examples with an infinite number of Regge poles and without cuts. The model shows that the restrictions on the Regge trajectory and the residue function by analyticity and crossing symmetry are extremely weak.     

Regge trajectories of the bethe-salpeter equation of the wick-cutkosky model

A low-energy perturbation method is used for solving the Bethe-Salpeter equation of the Wick-Cutkosky model in the case of unequal masses. Explicit expansions are obtained for the solutions and Regge parent and daughter trajectories.     

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.     

Exchange-degenerate Regge trajectories: A fresh look from resonance and forward scattering regions

The exchange degeneracy of the mesonic and Regge trajectories, dominant at moderate and high energies in hadron elastic scattering, is analyzed from two viewpoints. The first one concerns the masses of the resonances lying on these trajectories; the second one deals with the total cross sections and the ratios of the real to the imaginary parts of the forward amplitudes of hadron and photon induced reactions. Neither set of data supports exact exchange degeneracy. Received: 23 June 2000 / Revised version: 13 November 2000 / Published online: 23 January 2001     

Spectroscopy and Regge trajectories of heavy quarkonia in the relativistic quark model

The mass spectra of charmonia and bottomonia are calculated in the framework of the relativistic quark model up to high orbital and radial excitations. The Regge trajectories of heavy quarkonia are constructed both in the (J,M ²) and (n _r ,M ²) planes, where J is the total angular momentum and nr is the radial quantum number. All daughter trajectories turn out to be almost linear and parallel, while parent trajectories exhibit some nonlinearity. Such nonlinearity occurs only in the vicinity of ground states and few lowest excitations and is more pronounced for bottomonia, while it is only marginal for charmonia. The obtained results are compared with available experimental data, and a possible interpretation of the new charmonium-like states above open charm production threshold is discussed.     

Classification of resonance Regge trajectories and a modified Mulholland formula

We employ a simple potential model to analyze the effects which a Regge trajectory, correlating with a bound or a metastable state at zero angular momentum, has on an integral cross section. A straightforward modification of the Mulholland formula of Macek et al. (2004, 2009) [2] is proposed for more efficient separation of the resonance contribution.     

Regge poles in multiparticle scattering amplitudes

A study is made of the high-energy limits of multi-particle scattering amplitudes in a φ³ theory. A limited set of chekerboard diagrams dominate the asymptotic behavior .The diagrams sum to produce Regge poles. If N is the number of particles bound together, the trajectory functions of the leading Regge poles are given by α(N)=? (2N ? 3) +g²8π²m². Comparison is made with the generalized multiperipheral model of Auerbach, Aviv, Sugar and Blankenbecler in which the corresponding trajectories have the form α(N)=a?bN+cN².     

Ambiguities in Regge analyses of backward scattering

Ambiguities in Regge analyses of backward scattering due to the possibility of $\text{u}$ dependence in trajectory and residue functions of fermion Regge poles are investigated. Experiments to clarify the ambiguities are suggested. Also an intrinsic difficulty in separating exchanges of opposite parity is discussed.     

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.