Regge Residues Research Articles

Global analysis of charge exchange meson production at high energies

Many experiments that are conducted to study the hadron spectrum rely on peripheral resonance production. Hereby, the rapidity gap allows the process to be viewed as an independent fragmen- tation of the beam and the target, with the beam fragmentation dominated by production and decays of meson resonances. We test this separation by determining the kinematic regimes that are dominated by factorizable contributions, indicating the most favorable regions to perform this kind of experiments. In doing so, we use a Regge model to analyze the available world data of charge exchange meson production with beam momentum above 5 GeV in the laboratory frame, that are not dominated by either pion or Pomeron exchanges. We determine the Regge residues and point out the kinematic regimes which are dominated by factorizable contributions.

Shape of proton and the pion cloud

Proton-proton differential and total cross sections provide information on the energy dependence of proton shape and size. We show that the deviation from exponential behavior of the diffraction cone observed near $t=-0.1$ GeV$^2$, (so-called break), both at the ISR and the LHC follows from the $t$-channel two-pion loop contributions, imposed by unitarity. By using a simple Regge-pole model, we extrapolate the "break" from the ISR energy region to that of the LHC. This allows us to answer two important questions: 1) To what extent is the "break" observed recently at the LHC a "recurrence" of that seen at the ISR (universality)? 2) What is the relative weight of two-pion effect to the vertex coupling (Regge residue) compared to expanding size (pomeron propagator) in producing the "break"? We find that the effect comes both from the Regge residue (proton-pomeron coupling) and from the Regge propagator. A detail analyses of their balance, including the correlation between the relevant parameters is presented.

Finite-energy sum rules in eta photoproduction off a nucleon

The reaction ${\gamma}N \to {\eta}N$ is studied in the high-energy regime (with photon lab energies $E_{\gamma}^{\textrm{lab}} > 4$ GeV) using information from the resonance region through the use of finite-energy sum rules (FESR). We illustrate how analyticity allows one to map the t-dependence of the unknown Regge residue functions. We provide predictions for the energy dependence of the beam asymmetry at high energies.

Q 2 dependence of diffractive ρ meson electroproduction

The Q2 dependence of diffractive ρ meson electroproduction has been analyzed in the present paper. This dependence arises from the virtual photon–vector meson–reggeon vertex that is represented by a triangle of a quark loop. Integration over the quark loop produces a form involving a Spence function that is symmetric in the external masses connected to the triangle. In the Regge model, the vertex is considered a residue of the Regge pole. As the parameterization of the Regge residue is given by an exponential function of t times the residue at t=0 then, the vertex is reduced to an elementary function. Two pomeron models have also been adopted in the analysis. A reasonable agreement with the data has been achieved.

Exclusive and semi-inclusive strangeness and charm production in $\pi N$ and NN reactions

Using the Quark-Gluon Strings Model (QGSM) combined with Regge phenomenology we consider the reactions $\pi^- p \to K^0 \Lambda$ and $\pi^- p \to D^- \Lambda_c^+$ which are dominated by the contributions of the $K^*$ and $D^*$ Regge trajectories, respectively. The spin structure of the amplitudes is described by introducing Reggeized Born terms. It is found that the existing data for the reaction $\pi^- p \to K^0 \Lambda$ are in reasonable agreement with the model predictions. To describe the absolute values of the cross sections it is necessary to introduce also suppression factors which can be related to absorption corrections. Furthermore, assuming the SU(4) symmetry to hold for Regge residues and the universality of absorption corrections we calculate the cross section of the reaction $\pi^- p \to D^- \Lambda_c^+$. Employing the latter results from $\pi^- p$ reactions we then estimate the contributions of the pion exchange mechanism to the cross sections of the reactions $NN \to NK\Lambda$ and $NN \to N\bar D \Lambda_c$ and compare them with the contributions of the $K$ and $D$ exchanges. We find that the $NN$ reactions are dominated not by pion exchange but by $K$ and $D$ exchanges, respectively. Moreover, assuming the SU(4) symmetry to hold approximately for the coupling constants $g_{ND \Lambda_c}$ = $g_{NK \Lambda}$ we analyze also the production of leading $\Lambda_c$ hyperons in the reaction $NN \to \Lambda_c X$. It is shown that the non-perturbative mechanism should give an essential contribution to the $\Lambda_c$ yield for $x \geq 0.5$.

Regge poles as complex eigenvalues

We report a new direct method for calculating Regge pole positions and residues. Upon introduction of an absorbing optical potential sufficiently far in the asymptotic region, the problem reduces to several iterative diagonalizations of a symmetric complex matrix. The method is tested on well-studied cases of potential scattering.

Uniform semiclassical and quantum calculations of Regge pole positions and residues for complex optical nuclear heavy-ion potentials

The first uniform semiclassical (SC) calculations of Regge pole positions and residues have been carried out for four complex optical potentials, which have been used to fit [sup 16]O+[sup 28]Si elastic-scattering data at [ital E][sub lab]=55 MeV. In particular, we have extended a SC formalism developed for atomic and molecular scatterings to allow for the presence of a long-range Coulomb potential. The SC Regge poles and residues are compared with quantum results of Takemasa and Tamura [Phys. Rev. C 18, 1282 (1978)], who numerically integrated the radial Schroedinger equation. The SC computations show that Takemasa and Tamura missed ten poles. Using a modified version of the quantum computer code REGGE, due to Takemasa, Tamura, and Wolter [Comput. Phys. Commun. 18, 427 (1979)] we have located five of these poles---the remaining poles have residues of modulus [lt]10[sup [minus]8]. For low values of the Regge pole quantum number, [ital n], the SC and quantum pole positions are in close agreement, with larger differences for the residues. As [ital n] increases, the SC results become less accurate. However at high values of [ital n], the quantum results also lose accuracy due to numerical instabilities in the REGGE code. It is demonstrated that themore » choice of Coulomb interaction---charged sphere or pure Coulomb---can significantly effect the properties of the Regge pole positions and residues.« less

Accurate Regge pole positions and residues determined by phase-amplitude formulae

Formulae determining Regge pole positions and residues are derived within the phase-amplitude method. Numerical calculations are performed for an optical Lennard-Jones (12,6) potential using parameters approximating elastic scattering of K, and Li, by HBr. Comparison with previous investigations shows that the phase-amplitude results are very accurate. Hence, the phase-amplitude method provides an important alternative to other methods used to investigate scattering problems in the complex angular momentum representation.

Energy and Regge residues in quantum-mechanical "QCD" sum rules.

It was shown recently by Fishbane, Kaus, and Gasiorowicz that the residues at the poles of quantum-mechanical two-point functions for arbitrary angular momenta l have an incorrect l dependence when calculated by the sum-rule method used for the analogous problem in QCD. Knowledge of the residues is of interest since they are directly related to particle couplings and decay widths. We develop reliable expressions for the energy and Regge residues using semiclassical methods.

Nucleon-nucleon potentials and regge poles. II. Reggeon exchange potentials

We derive and discuss in detail a connection between the low-energy nucleon-nucleon potentials and reggeon exchanges. In particular explicit relations between coupling constants and form factors of one-boson-exchange amplitudes and Regge residues are given. Besides the traditional one-boson-exchange potentials we also obtain new contributions to the potentials which come from the J = 0 components of the Pomeron and tensor meson trajectories. In the central potential these extra contributions are repulsive and this could provide a partial explanation for the need of soft or hard cores in semi-phenomenological and some of the one-boson-exchange models.

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.

The energy dependence of Regge pole positions and residues for singular interatomic potentials

A detailed investigation of the energy dependence of Regge pole positions and residues has been carried out for r-12 and Lennard-Jones (12,6) singular interatomic potentials. Semiclassical calculations are used to show that the pole positions can vary relatively slowly with wavenumber, whereas the residues can show a much faster variation. In addition, the semiclassical results are compared with the predictions of some simple formulae due to Brander (1966) and Tiktopoulos (1969) and one that arises from a complex harmonic oscillator formalism. It is found that these formulae, together with the criteria for their validity, are a useful way of understanding and predicting the energy dependence of pole positions and residues for singular interatomic potentials.

A possible pomeron building mechanism in the fragmentation region

By the use of a Regge parametrization of the one-particle inclusive cross section in the fragmentation region, an integral equation is obtained for the high-energy hadron–hadron inelastic cross section. The main assumptions used in the derivation of this integral equation are: (i) When two hadrons collide with sufficiently high energy, the elastic, inelastic, and total cross sections have the same energy dependence and (ii) Unitarity and factorization of Regge residues hold also for Reggeon–hadron 'amplitudes'. The solution of the integral equation, i.e., the function σinel(s) can be made constant or slowly increasing. For 'reasonable' values of all the parameters involved, it is in very good agreement with the high energy pp data.

Connection between fixed-angle and fixed-momentum-transfer scattering in the framework of the double phase representation

The double phase representation of Sugawara and Nambu, which assumes some simple analytical properties with respect to momentum transfer for the phase of the amplitude, is applied to the discussion of large-angle scattering. From the assumptions of Regge behavior and finite asymptotic Regge trajectories, one derives the fixed-angle scaling laws $F(s,\ensuremath{\theta})\ensuremath{\simeq}{s}^{\ensuremath{\Delta}}F(\ensuremath{\theta})$, and the extrapolation to the large-angle region of the Regge formula; the high-momentum-transfer behavior of Regge residues is thereby obtained. As a byproduct, we get the general form of the amplitude (including its phase) in the large-angle region for given values of $\ensuremath{\Delta}$ and of the three asymptotic leading Regge trajectories in the $s$, $t$, and $u$ channels. The angular dependence of various scattering processes is determined, using as input the values of $\ensuremath{\Delta}$ and of the asymptotic trajectories given by the constituent-interchange model. A strong correlation between the forward-backward asymmetry of the angular distribution in a given channel and the ratio of the 90\ifmmode^\circ\else\textdegree\fi{} cross sections in the other two channels is shown to be present in a simple case. Applied to ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ scattering the double phase representation shows, together with positivity and the Froissart bound, that the angular distribution can take only two possible forms for each choice of the fixed-angle power $\ensuremath{\Delta}$; in this case one also finds, using the Kinoshita-Loeffel-Martin upper bound, that the asymptotic Pomeron trajectory is bounded from above either by 0 or by 2/3.

On the parametrization of the Δ residue function

The complex residues at the Δ(1236) and Δ(1950) poles in the relevant partial-wave amplitudes provide information on the behaviour of the Δ Regge residue function in the resonance region u > 0. Attempts to incorporate this information in parametrizations of the residue by functions that are real on the real u-axis result in residues which have unsatisfactory behaviour in the region u < 1 GeV 2. The choice of complex functions for the trajectory and residue removes this undesirable feature and provides a better representation of the residue in the resonance region, suggesting that complex parametrizations would be better suited to Regge analyses of near-backward scattering.

Nucleon representation of the algebra of Regge residues and chiral symmetry

A nucleon saturation scheme for the algebra of Regge residues and chiral symmetry is studied. A representation of this extended algebra of SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) \ifmmode\times\else\texttimes\fi{} O(5) includes the nucleon $N(940)$, the $\ensuremath{\Delta}(1236)$, and two other nucleon resonances. The masses for the resonances, the low-energy pionic coupling, and the Regge coupling of the $\ensuremath{\rho}$, $f$, $\ensuremath{\pi}$, and ${A}_{1}$ trajectories to the particles present in the scheme are predicted and the results are compared with experimental numbers.

Fixed mass and scaling sum rules: Generalized truncation and current algebra constraints on Regge residues

Using the correspondence principle (continuity in dynamics), we extend the approach of Keppel-Jones-Ward-Taha to fixed mass and scaling current algebraic sum rules so as to consider explicitly the contributions of all classes of intermediate states. A natural, generalized formulation of the truncation ideas of Cornwall, Corrigan, and Norton is introduced as a by-product of this extension. The formalism is illustrated in the familiar case of the spin independent Schwinger term sum rule. New sum rules are derived which relate the Regge residue functions of the respective structure functions to their fixed hadronic mass limits for q 2 → ∞.

Residue sum rules for inelastic (anti) neutrino nucleon scattering

We discuss the complete set of current algebra sum rules for the Regge residues and asymptotic constant S limits of the structure functions of inelastic (anti) neutrino nucleon scattering.

A formula for Regge residues in terms of trajectories and phase shifts

The asymptotic behavior for largez = cos θ is derived for a recent analytic continuation of the scattering amplitude in potential theory and is shown to be consistent with Eegge behavior. This leads to a new formula for the Regge residues in terms of trajectories with Re αn > -1/2 and real physical phase shifts. The residues are approximately compared with exact results in potential theory and asymptotic limits discussed.

Resonance spins and thetdependence of Regge residues in multiperipheral models

We argue that the $t$ dependence of Regge residues for small $t$ can be understood within the context of multiperipheral cluster models if the clusters are identified with the resonance spectrum and the correct spin structure is included for the resonances. The difference between the slopes of the $pp$ and $\ensuremath{\pi}p$ differential cross sections is ascribed to the average shift of resonance spin by 1/2 between the baryon and meson resonances. An illustrative calculation is performed which leads to qualitative agreement with experiment, including the energy dependence of diffractive slopes, multiplicities, and transverse momentum distributions for energies below 30 GeV. Longitudinal components of momentum transfer are correctly treated.