The derivative rule for helicity-flip amplitudes

Consequences of the derivative relation $\text{f}{}_{\mathrm{+-}}\text{=}\text{λ?f}{}_{\mathrm{++}}\text{?√?t}$, proposed empirically and also in various models for s-channel helicity amplitudes, are explored. A comparison with π^?p→π⁰n charge-exchange data is made, imposing the usual Regge pole form on f_+-. The assumptions are seen to conflict with the s-dependence of the cross-section dip and the polarization structure. There are also difficulties with finite energy sum rules and with-experimental data on some other reactions.     

Double Regge exchange phenomenology

We construct a double Regge exchange amplitude which has the proper analytic structure and which is phenomenologically viable. The various couplings involved can be estimated using pole extrapolation techniques which are successful in two-body scattering. We explicitly calculate the double Regge exchange contributions to the well-measured, and related, processes K^±p → K⁰π^±p and π^?p → K^?K⁰p. In this way the observed features of the dimeson partial-wave production amplitudes are used to text the double-exchange approach.     

Elementary scalar mesons and Regge poles

We show, for the annihilation amplitude of π⁺π^? → two vector mesons, that parity conservation and rotational symmetry demand the existence of a triplet of Regge singularities crossing at t = 0. In the usual scalar-vector field theory, calculations of the leading terms of this amplitude up to the eight order show that these singularities are moving Regge poles. Contrary to common belief, the elementary scalar meson lies on one of them.     

Regge analysis and dual absorptive model for γN → πN, γN → ηN and related processes

We present a combined Regge-pole Regge-cut analysis of γN → π^oN, γN → ηN and of certain processes related by vector dominance. The magnitude of Regge cuts is constrained to satisfy the requirements of the dual absorptive model. Calculations in terms of the weak cut model are also presented and ways to experimentally distinguish between these two models are discussed. The structure of the real and imaginary parts of the amplitudes is also analyzed.     

Axial vector meson production

Recently available differential cross section and density matrix information on π^?p → B^?p at 4 GeV/c are successfully described in terms of t channel exchanges and s channel absorptive effects. The s channel helicity amplitude which is dominant at small |t| (zero net helicity flip ω exchange) is found to have a zero at ?t = 0.2 GeV². SU(3) and higher symmetries are used to predict cross sections for further axial vector meson production processes, in particular non-diffractive A₁ production. The importance of these processes with regard to Regge phenomenology and meson spectroscopy is emphasized.     

On the behavior of the πN partial wave amplitudes ats=0

The behavior of theπN partial wave amplitudes in the limitss→+0 ands→? 0 is related to backward scattering in thes- andt-channel, respectively. Assuming Mandelstam analyticity we prove with the aid of the Phragmen-Lindelöf theorem that the amplitudes for high energy backward scattering inπN→πN andππ→N¯N are equal and therefore dominated by the same exchange mechanism, namely Reggeized Fermion exchange. The dominating Regge trajectory is the Δ_δ-trajectory, and it is shown that theπN partial wave amplitudes diverge fors→±0 as \(s^{ - \alpha \Delta _\delta (0) - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) . — Reduced amplitudes are defined which are regular ats=0. — Using recent results ofπN backward scattering real and imaginary part of thes-wave amplitudef ₀₊ ^(?) are calculated in the interval 0≦s≦7.     

Application of K-matrix CMSR'S to single charged pion photoproduction

The background terms, required in addition to Regge poles with some definite properties, in order to describe the high energy behavior of the t-channel single pion photoproduction amplitudes F_t^(?)(v, t), i = 1, …, 4, are investigated in the framework of a reggeized K-matrix model. To this end continuous moment sum rules (CMSR's) are applied, not to the full amplitudes, but just to the two-particle K-matrix amplitudes assumed to show pure Regge pole asymptotic behavior. The K-matrix amplitudes are defined by taking into account in the Heitler equation the elastic (πN) intermediate state alone. Such a definition corresponds to a weak-cut model with only final-state interactions included. It turns out that strong background contributions are still present on the high energy side of the K-matrix CMSR's. The Regge cut contributions generated within our formalism are found to be too weak to account for the background terms in the full amplitudes. This is presumably to a great extent due to the neglect of the (?N) diffraction-dissociation intermediate state in the definition of the K-matrix amplitudes.     

Regge pole and cut behaviour at Fermilab energies

Prompted by some unusual features of the np charge-exchange cross sections recently measured at Fermilab, we study this process over the entire energy range in an attempt to clarify its exchange amplitude structure. Comparison with all the other two-body processes so far measured at Fermilab (π^?p → π⁰n, νn, ω⁰n and elastic scattering) allows one to draw useful conclusions concerning the required J-plane structure of Regge cut models. We show that the shrinkage properties and helicity dependence of Regge cuts must be more complicated than current models suggest. We also present evidence that the Williams (or “poor man's absorption”) model for π exchange is incorrect at high energies.     

Discrepancies between πN charge exchange forward scattering data and the dispersion relation prediction

The πN charge-exchange forward scattering amplitude has been recalculated, using the most recent total cross section data, charge independence and the forward dispersion relation. In general the prediction agrees rather well with the data, but there are several discrepancies which are considerably larger than the errors. Some of these discrepancies follow from the fact that a structure at small ¦t¦ has been ignored in the extrapolation. — The new fit gives an accurate value for the subtraction constant of the integral. It agrees with the evaluation of the unsubtracted integral at threshold, if, at high energies, the Regge behaviour for σ(π^? p)—σ(π⁺ p) is inserted. This result favours the validity of Pomeranchuk's theorem. — An improved value forf ² cannot be obtained at present because of the uncertainty following from charge-dependent effects at low energies.     

Two body reactions and the quark model

A simple quark model for two-body hadronic amplitudes is presented and applied to pp ($\text{p}\text{p}$) and K^±p elastic scattering. Hadronic processes are described in terms of quark-quark scattering, using Glauber theory to take into account the effects of multiple scattering. Exchange degenerate Regge poles are introduced at the quark level. A predictive model for Regge cuts is obtained. It has some features in common with the dual absorption model in its correlation of dip structure and shrinkage in elastic processes with the exoticity of the s-channel but also significant differences, for example in the interpretation of the $\text{p}\text{p}$ dip. The qualitatively different structure in the pp differential cross section is also reproduced. It breaks exchange degeneracy in a well-defined way and in doing so offers an explanation of the differences between pp and K⁺p total cross sections. The difference in their differential cross sections is a natural consequence of the model and structure similar to the pp structure is predicted to appear in the K⁺p differential cross section in the region t ≈ ?2(GeV/c)².     

Comparison between γN→π and πN→ϱN in the resonance region up to s=1.75 GeV via the vector-dominance-model

We display the helicity amplitudes for the N_? system for each J^P state of the N_π system in the reaction Nπ→N?. These amplitudes are obtained from a K-matrix fit to amplitudes of the reaction Nπ→Nπ and Nπ→Nππ (via the isobar model). We then take either these amplitudes or the resonance couplings estimated from these amplitudes and compare them to the photoproduction amplitudes via the V.D.M. Two possible kinematics are considered for the N_? system below its threshold. These four methods give a range in which the V.D.M. can be accomodated even at this low energy.     

Study of the reaction ¯pd→p s π+2π−π0 at 5.5 GeV/c incident momentum

A study of a 150000-picture exposure of ¯pd at 5.5 GeV/c yielded 152 events satisfying the hypothesis ¯pd→p _s π⁺2π^?π⁰. For the events with proton spectator in the momentum range 100–280 MeV/c we obtained the cross section of 0.11±0.02 mb. Assuming the validity of the impulse approximation we estimate a cross section of 0.43±0.06 mb for the reaction ¯pn→ π⁺2π^?π⁰. The rate for single ? meson production and an upper limit for double ? production are given. A modified multiperipheral Regge model was used in order to describe the general features of the data.     

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.     

Experimental tests of the factorisation of Regge trajectories in the proton fragmentation region

We present double differential cross sections for the reactions K^? + p → π^± + anything at 8.25 GeV/c. Using published data for reactions K⁺ + p→ π^? + anything and p + p → π⁺ anything we predict the differential cross sections for γ + p → π^? + anything, π^? + p → π^? + anything and π^? + p → π⁺ + anything in the target fragmentation region based on factorisation of the pomeron and Regge trajectories. Our predictions agree with the experimental data and support the hypothesis of factorisation of the Regge trajectories in the target fragmentation region.     

Pomeron dominance in a triple-Regge representation of inclusive Δ++ production in K−p and π−p reactions

Data are presented on the reactions K^?p → Δ⁺⁺ + anything at 10 and 16 GeV/c and π^?p → Δ⁺⁺ + anything at 16 GeV/c. In the K^?p reaction, scaling is observed between 10 and 16 GeV/c in the variable M²/s. The scaling occurs at relatively low values of M in marked contrast to the reaction π⁺p → Δ⁺⁺ + anything. This result can be explained by duality arguments on a triple Regge picture, since the exchanged reggeon-incident particle scattering is exotic. Comparison of the π^?p reaction, which is similarly exotic, with the K^?p reaction at the same energy gives further evidence for factorization in pomeron-dominated inclusive reactions.     

On the calculation of spin dependence in the absorption model for π-exchange

A generalization of the absorption model of Williams done for the reaction π^?p → π^?π⁺n is presented for arbitrary π⁺B final states in the reaction Bp → Bπ⁺n. For small values of the π⁺B crossing angle we can express the results in terms of the π⁺B scattering amplitude instead of the π⁺B partial-wave amplitudes. By this a considerable simplification of the general formalism is achieved. Some of the predictions which can be made turn out to be independent of the π⁺B amplitudes. This allows a sensitive test also in the case of B = π or K, where the πB amplitudes are unknown.