Regge-pole Exchange Research Articles

On the breakdown of eikonal approximation and survival of Reggeization in presence of dimension-5 Higgs-gluon coupling

We consider the one-loop effective vertex for the interaction of a gluon with a Reggeized gluon and a Higgs boson in the infinite-top-mass limit, which is described by a dimension-5 non-renormalizable operator. This vertex enters the calculation of differential cross sections for the forward inclusive production of a Higgs boson in high-energy proton-proton collisions, possibly in association with a backward jet or identified hadron, in a framework where next-to-leading logarithms of the energy are resummed to all orders. The effective vertex is extracted from the high-energy behavior of two-to-two amplitudes for the Higgs production in parton-parton collisions and relies on the validity of the Regge form for these amplitudes. We find that the usual eikonal approximation (Gribov prescription) for the Regge limit and the known region-expansion technique in this limit lead to an incomplete result for the amplitude. The discrepancy is traced back to the non-renormalizable nature of the involved operator. However, the Regge limit of the exact QCD amplitude agrees with the Regge-pole exchange form at one loop, nontrivially supporting the Reggeization hypothesis.

Regge Phenomenology of Photoproduction of π−Δ++ and Scaling with Saturation of Trajectory

In this work we investigate the reaction $\gamma p\to\pi^-\Delta^{++}$ in the Reggeized model for $\pi(138)+\rho(775)+a_2(1320)$ exchanges in the $t$-channel. For a convergence of the reaction cross section at high energies the minimal forms of proton and $\Delta^{++}$ exchanges are introduced in the direct and crossed channels for gauge invariance of $\pi$ Regge-pole exchange. The role of spin-2 tensor meson $a_2$ is found to be crucial to agree with existing data at high energies. Electromagnetic multipoles of $\Delta^{++}$ baryon are analyzed in the $\Delta$ resonance region. Based on the constituents counting rule the scaled differential cross section at $E_\gamma=4$ GeV is reproduced with the Regge trajectory saturated at large momentum transfer $-t$.

Nondiffractive feature of γN → ρ ± N with ρ -meson electromagnetic multipole moments

We investigate photoproduction of charged $\rho$ off the nucleon using $\rho(770)+\pi(140)$ Regge pole exchanges by considering the $\rho$-meson electromagnetic multipole moments. The significance of the Ward identity at the $\gamma\rho\rho$ vertex is emphasized for current conservation in the process. Given $\pi$ exchange with the well-known coupling constants for $\gamma\pi\rho$ and $\pi NN$, we analyze the role of the $\rho$ exchange in the $\gamma p\to \rho^+n$ and $\gamma n\to\rho^-p$ processes without model-dependences except for the magnetic moment $\mu_{\rho^\pm}=\pm2.01$ and electric quadrupole moment ${\cal Q}_{\rho^\pm}=\pm0.027$ fm$^2$ taken from theoretical estimates. The nondiffractive feature of both cross sections is reproduced with a rapid decrease beyond the resonance region by the dominance of $\pi$ exchange over the $\rho$\,. % Cross sections for differential and density matrix elements are presented to compare with existing data. The parity and photon polarization asymmetries are predicted to demonstrate the apparent roles of the $\rho$-meson electromagnetic multipole moments.

Glueball Regge trajectories in (2+1)-dimensional gauge theories

We compute glueball masses for even spins ranging from 0 to 6, in the D=2+1 SU(2) lattice gauge theory. We do so over a wide range of lattice spacings, and this allows a well-controlled extrapolation to the continuum limit. When the resulting spectrum is presented in the form of a Chew–Frautschi plot we find that we can draw a straight Regge trajectory going through the lightest glueballs of spin 0, 2, 4 and 6. The slope of this trajectory is small and turns out to lie between the predictions of the adjoint-string and flux-tube glueball models. The intercept we find, α 0∼−1, is much lower than is needed for this leading trajectory to play a ‘Pomeron-like’ role of the kind it is often believed to play in D=3+1. We elaborate the Regge theory of high-energy scattering in 2 space dimensions, and we conclude, from the observed low intercept, that high-energy glueball scattering is not dominated by the leading Regge pole exchange, but rather by a more complex singularity structure in the region 0⩽Re λ⩽1/2 of the complex angular momentum λ plane. We show that these conclusions do not change if we go to larger groups, SU( N>2), and indeed to SU(∞), and we contrast all this with our very preliminary calculations in the D=3+1 SU(3) gauge theory.

Mechanisms of the reactionπ−p→a00(980)n→π0ηnat high energies

The main dynamical mechanisms of the reaction $\pi^-p \rightarrow a^0_0 (980)n \rightarrow \pi^0\eta n$ at high energies, currently investigated at Serpukhov and Brookhaven, are considered in detail. It is shown that the observed forward peak in its differential cross section can be explained within the framework of the Regge pole model only by the conspiring $\rho_2$ Regge pole exchange. The tentative estimates of the absolute $\pi^-p \rightarrow a^0_0(980)n \rightarrow \pi^0\eta n$ reaction cross section at $P_{lab}^{\pi^-} = 18$ GeV/c are obtained: $\sigma\approx200$ nb and, in the forward direction, $d\sigma/dt\approx940$ nb/GeV$^2$. The contribution of the one pion exchange, which is forbidden by $G$-parity and which can rise owing to the $f^0_0(980)-a^0_0(980)$ mixing, is also estimate. A role of the Regge cuts in the non-flip helicity amplitude is briefly examined and a conclusion is made that the contributions of the cuts have to be inessential in comparison with the conspiring $\rho_2$ Regge pole exchange.

Production processes

In this historical review, covering roughly the years from 1960 to 1980, some contributions are presented in an exemplary selection that bubble chambers have made to our understanding of particle production processes within the framework of the following phenomenological models: one-particle exchange (in particular one-pion exchange); Regge-pole exchange; duality, finite-energy sum rules and Veneziano models; multiperipheral model, multi-Regge exchange, longitudinal phase space and diffraction dissociation.

Distribution of valence quarks in hadrons at small x in QCD

Valence u- and d-quark distributions in nucleons and pions at small x corresponding to ϱ and ω Regge pole exchanges have been obtained on the basis of the QCD sum rule method.

Spin-Dependent Forces in Elastic pp Scattering at 6 GeV/c

The data on differential cross sections, polarizations and spin-correlation parameters eNN, eLL, ess and esL of elastic proton-proton scattering at 6GeV/c are analyzed in the eikonal model with spin-dependent eikonals of spin-orbit, spin-spin and tensor couplings in addition to the spin-independent central eikonal. The behavior of the measured values of eLL and ess is shown to require a certain magnitude of spin-spin and tensor forces. These forces have turned out to have two components of short-range (0.8~1.2 fm) and long-range (1.5~ 2 fm). The long-range one is interpreted as due to one-pion exchange, since it reproduces the so-called spike in neutron-proton charge-exchange scattering cross sections. § l. Introduction Recent measurements of spin-correlation parameters of elastic proton-proton scattering at 6 Ge VIc with Argonne ZGS polarized beams and polarized targets have exhibited a remarkable feature that the correlation parameters have unexpec­ tedly large valUes, for example, eLL~- 0.3 at momentum-transfer squared t=- 2.5 (GeVIc) 2 and C88~-0.2 at t~-1.5(GeVIc) 2 .n' 2l The absolute magnitude of these values is comparable to or even a little larger than the polarization value of 0.15~0.20 around t = -1.5 (Ge VI c) 2 of the same process. 3l This behavior of experiments leads us to expect that spin-dependent part of the interaction in PP scattering is stronger than was expected before. Phenomeno­ logically, there has not yet appeared any overall good fit to the data on all these observables over wide t range in the Regge model even with an enormous number of poles!l As an alternative to Regge approach, it would be interesting to see behavior of the spin-dependent interaction in the impact parameter plane. In the low energy region below 1 Ge VIc, dynamics of one-pion and one-boson exchanges have played a major role in the nucleon-nucleon scattering. 5l On the contrary, in the high energy region above about 10 Ge VIc, Regge pole exchange mechanism works well and has been able to explain especially the energy-dependence of the peripheral scattering. 6l But, it is not yet known so well how the dynamics undergoes transi­ tion between the two mechanisms in the energy region of 1~ 10 Ge VI c. For the analysis of this region, eikonal model based on the impact parameter representation for scattering amplitude seems to be applicable for the following reasons ;'l (i) *l Present address: Osaka Prefectural Higashi-Neyagawa High School, Neyagawa, Osaka 572.

Reggeon exchange in the quark model

A formalism is presented for obtaining Regge-pole exchange amplitudes in the quark model. The Reggeon-quark couplings are determined by the electromagnetic and weak couplings of the quarks, through the vector dominance of the quark currents, exchange degeneracy and, for diffractive processes, f dominance of the pomeron coupling. The magnitudes of the Reggeon couplings are thus fixed by the vector-meson-photon coupling constant fomega gamma . It is shown that given fomega gamma a wide variety of successful predictions can be made, both of particle decay rates and of hadronic scattering amplitudes. The theoretical implications of the success of the scheme are examined briefly.

The production properties of [formula omitted] from 3.6 to 12 GeV/ c

Cross sections and decay distribution moments are presented for the reaction p p → Δ ++ Δ ++ at 3.6 GeV/ c, and compared with previously published data at 9.1 and 12 GeV/ c. With the aid of the quark model, we have isolated the natural and unnatural parity exchange contributions and shown them to accord with expectations based on simple Regge-pole exchanges.

Study of the reaction p̄p → p̄ωp at 9.1 GeV/c

The reaction p̄p → p̄pπ +π −π 0 has been studied at 9.1 GeV/ c. The cross section is 2.04 ± 0.04 mb based on 3062 events. The cross section for p̄p→ p̄ωp is 0.17 ± 0.02mb. The p lab dependence on this cross section is p lab −0.9 ± 0.2. This rules out a double Regge pole exchange model with a pomeron trajectory.

The role of A 1 exchange in the reaction π−p → ( π+π−n

Data have recently become available, at 17.2 GeV/ c, which show strong target polarization effects for the reaction π −p → ( π + π −)n. These data require the presence of an exchange with the quantum numbers of the A 1. A simple model based on π, A 2, and A 1 Regge pole exchange together with parametrized n = 0 cuts is found to provide an excellent description of both the polarized and unpolarized data. The resulting structure of the A 1 dominated amplitudes is discussed and the results are compared with earlier models which neglected A 1 exchange effects.

Eikonal description of nucleon-nucleon polarizations

Nucleon-nucleon elastic polarization data are analyzed within an eikonal framework in the range 6⩽ plab⩽45 GeV/ c and | t| 2.5 GeV/ V 2. The isovector component is found to be dominated by a nearly exchange degenerate ρ-A 2 contribution while the isoscalar part requires both a lower lying Regge-pole exchange and an asymptotic pomeron contribution.

Analysis of single pion photoproduction at high and low energies

Fixed- t dispersion relations are used in a combined analysis of single pion photoproduction in the resonance and high-energy regions. Data are fitted from threshold to a centre-of-mass energy W of 2 GeV and for W from 2.6 to 5.6 GeV. In the resonance region, a partial-wave analysis is performed and 44 resonance couplings are evaluated. In the high-energy region, the imaginary parts of the amplitudes are parametrized in terms of Regge-pole exchanges and their trajectories and couplings are evaluated.

A comparison of reactions of the type PB → VOΔ

A comparison of the reactions π +p → ϱ 0 Δ ++, π +p → ωΔ ++, and K + p → K ∗o Δ ++ is made using data near 7 GeV/ c. Particular attention is paid to the question of relative normalization for each of the reactions. Using an SU(3) sum rule, predictions are made for the reaction K − n → K ∗0 Δ − . A phenomenological model is presented which is based on Regge pole exchange modified by Regge cuts in those amplitudes with zero net helicity. Excellent fits to the ϱ 0 Δ ++ and ωΔ ++ observables are obtained. The resulting amplitudes are then used to predict the observables in K + p → K ∗0 Δ ++ .

The radius of the Pomeron and absorptive cuts

It is pointed out that absorption in quantum number exchange two-body reactions with a Pomeron whose radius in impact parameter is proportional to log s, and whose opacity is not totally black, yields singularities which, asymptotically, are dominated for all t by the original Regge pole. Thus for such Pomerons, in the limit of infinite energy, the simple phenomenology associated with pure Regge pole exchange should be valid.

Tests of Higher Symmetries

Model-independent cross-section relations predicted by unbroken SU(3) symmetry, and some predicted by $\mathrm{SU}{(6)}_{W,\mathrm{strong}}$, are compared with experiment. The relations are found to be satisfied, apart from deviations which follow, in every case, the pattern and rough size of symmetry breaking expected from Regge-pole exchange. Interestingly, this Regge symmetry breaking diverges with increasing energy. It is argued that this behavior, though contrary to intuition, is reasonable.

Exchange structure of N, Δ backward peaks

The I u = 1 2 and I u = 3 2 cross sections and interference term in πN backward scattering are separated from data for p lab > 3 GeV/ c. The separated cross sections and recent 6 GeV/ c polarization data imply restrictions on the structure of N and Δ exchange amplitudes near the dip location in π +p backward scattering. The possibility of an amplitude analysis is discussed and the importance of polarization experiments in KN → Λπ stressed. The determinations of π N → Nπ I u = 1 2 and 3 2 contributions permit unambiguous studies of SU(3) for the exchanges in π N → Nπ and KN → Yπ reactions. Finally we show how isospin regularities observed in 180° scattering at low energies are implied by duality of N α, Δ δ Regge pole exchanges.

A new Regge absorption model

The weak-cut Regge absorption model is generalized to allow for unequal absorption of the rotating (e − iπα ) and non-rotating (1) parts of the Regge-pole exchange amplitude. Some justification for this procedure is given in terms of duality and peripheral resonance dominance. Fits to data for πN charge-exchange cross section and polarization and cross sections for the line-reversed hypercharge-exchange reactions K N→πΣ and π N→ KΣ are obtained.

The kinematics of the coupling of Regge poles to photons

We examine two problems which arise in understanding Regge-pole exchange in amplitudes which include photons; namely how there can be a pion-exchange pole in pion photoproduction, and a finite pomeron coupling in forward Compton scattering. We try to resolve these problems by noting that the usual sense-nonsense zeros, which might seem to make the couplings vanish, can in fact be replaced in the partialwave amplitudes by zeros in the kinematical factors. Since the zeros are absent from the total amplitudes, we are left with finite couplings. This replacement is a peculiarity of photon couplings. It has the disadvantage of changing the threshold behaviour of the partial-wave amplitudes, but seems to be the only plausible way out of the dilemma. There are no other special requirements of gauge invariance, so that these photon-induced processes may be Reggeized in exactly the same way as purely hadronic reactions.