Proton-proton scattering and the pomeron

We describe various attempts to fit the data on pp and $\text{p}\text{p}$ elastic scattering and total cross sections, including the recent ISR data, with a variety of Regge pole and cut models. Only two types of model are able to explain the data over the whole energy range satisfactorily. The simplest of these has no cuts, but a pomeron pole with trajectory αp(0) = 1.06 + 0.25 t, and a non-shrinking “core” term at large |t|. The other has a flat trajectory, αp(t) = 1.06 for all t, and strong eikonal-model cuts which explain both the shrinkage at low |t|, and the lack of it at larger |t|. We also briefly review various speculations which relate the fact that αp(0) > 1 to the small triple-pomeron coupling.     

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.     

K−p elastic scattering at 14.3 GeV/c

Results are presented of a bubble chamber experiment on K^?p elastic scattering at 14.3 GeV/c, in four-momentum transfer range 0.04 < |t| < 2.74 GeV² using an initial set of 40 000 events. The total elastic cross section is (2.96 ± 0.10) mb. The results are compared with K⁺p elastic scattering data at 13.8 GeV/c, and the effective Regge trajectory is calculated using K^?p data from 5 to 100 GeV/c.     

Impact parameter analysis of KN and πN scattering in the intermediate energy region

We have evaluated the s-channel-helicity partial-wave amplitudes for $\text{K}\text{N and πN}$ scattering as functions of the impact parameter using partial-wave data in the energy range P_L≈1.0–2.0 GeV/c. We find that the $\text{K}\text{N}$ background and resonance amplitudes exhibit features consistent with the dual absorptive picture for pomeron and f + ω and A₂ + ? exchanges. Comparison of the πN low-energy amplitude with the partial-wave decomposition of a quantitative Regge model gives evidence for local duality between the s-channel resonance and t- and u-channel Regge exchanges.     

Differential cross sections of elastic pp scattering in the energy range 8–70 GeV

In this paper we present tables of absolute differential cross sections of elastic pp scattering together with the values of the slope parameter B and the real-part parameter α, where $\text{B=}\text{d}\text{d}\text{t}\text{In}\text{dσ}\text{d}\text{t}\text{α=}\text{Re A(0)}\text{Im A(0)}$ and A(0) is the amplitude of elastic pp scattering at t = 0. The cross-section data have been obtained at the Serpukhov accelerator from 8 to 70 GeV in the |t|-range 0.0007 ? 0.12 (GeV/c)².     

Experimental limits on the lowest possible mass horizontal gauge boson in SU(2) H

A unified picture of both soft and hard hadronic collisions is suggested. The basis idea is to use Regge trajectories of the type $$\alpha (t) = \alpha (0) - \gamma ln (1 + \beta \sqrt {t_0 - t} )$$ in dual models with Mandelstam analyticity. The idea is applied to elastic proton-proton scattering to derive kinematical boundaries of the asymptotic (Regge-t _R and scaling-S _sc.,t _sc.) regimes, to fix the angular dependence in the scaling-and thet-dependence in the Regge domain of the scattering amplitude and to interpolate between the two asymptotic domains.     

最大解析性原理与Regge轨迹的若干性质

根据最大解析性原理,本文研究了Regge轨迹的某些性质。证明了与各粒子对应的Regge轨迹在阈能以下是能量的单调增加函数,当t→±∞时,每一轨迹的渐近极限是相同的。特别当-t₀p (0)应满足不等式1/t₀<α′_p(0)<1/4,其中t₀由α_p(t=-t₀)=0决定。     

A model for Regge cuts with pole enhancement

It is argued that, since hadronic processes show Regge shrinkage even at large ∣t∣, Regge-cut discontinuities must be enhanced in the region of J near the Regge poles (as suggested by some recent theoretical work on the weak-coupling solution to the “infrared problem” in the reggeon calculus) so that the dominant Regge-cut contribution (at current energies) does not come from the region of the discontinuity near the branch point (as it does in eikonal and absorption models). In particular we show that this hypothesis works well for π^?p→π⁰n. However, there is less shrinkage in photoproduction processes at large ∣t∣, and we find that in γp→π⁰p (and related processes) there is no pole enhancement of the cuts. We connect this fact with the absence of t-channel unitarity constraints for electromagnetic processes and more speculatively with the possibility that a scaling behaviour due to Regge cuts develops at large ∣t∣ as the mass of the external particle is decreased.     

Reggeon phases and the dual bootstrap program

Analyticity requirements lead to complex Regge vertices in multiparticle production amplitudes. Their effect is discussed within a dual, unitary and exchange-degenerate multi-Regge model. A resulting complex Regge vertex is incorporated in fixed-t model calculations of the reggeon bootstrap and the topological pomeron. The bootstrap condition for particle-particle scattering is unaffected but new j-plane singularities appear in Regge-Regge scattering amplitudes. The pomeron and reggeon intercepts determine the two parameters of our Regge vertex and admit two possible solutions: one is close to the naive phase rule (real vertex) and the other is complex and leads to a high lying non-leading pole in the pomeron channel.     

Elastic pp scattering in the cern sps energy region

The pronounced dip-bump structure with a sharp minimum at |t| = 1.5 (GeV/c)², recently observed in elastic $\text{p}$p scattering at P_L = 50 GeV/c at the CERN SPS, is explained by the quark multiple scattering model with a realistic wavefunction for the proton and the antiproton. It is predicted that a second dip will appear around |t| = 7 (GeV/c)² at P_L = 50 GeV/ c and at higher energies.     

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.     

The polarised beam asymmetry in photoproduction of eta mesons from protons at 2.5 GeV and 3.0 GeV

Measurements of the polarised beam asymmetry parameter Σ for eta photoproduction from protons, have been carried out at incident energies of 2.5 GeV and 3.0 GeV, and for various t-values between ?0.2 (GeV/c)² and ?1.2 (GeV/c)². The values of Σ are close to +1 for values of |t| less than 0.7 (GeV/c)², showing that there can be little contribution from unnatural parity exchange in any Regge exchange model of the process, in disagreement with present theories. Differential cross sections for the process werre also measured, and are consistent with those from other experiments.     

Measurements of elastic scattering in alpha-alpha and alpha-proton collisions at the CERN intersecting storage rings

We measured the elastic scattering of $\text{αα}\text{at}\text{s}\text{= 126}\text{GeV}$ and of αp at $\text{s}\text{= 89}\text{GeV}$. For αα, the differential cross section dσ/dt has a diffractive pattern minima at |t| = 0.10 and 0.38 GeV². At small |t| = 0.05?0.07 GeV², this cross section behaves like exp[(100 ± 10) t]. Extrapolating a fit to the data to the optical point, we obtained for the total cross section α_tot(αα) = 250 ± 50 mb and an integrated elastic cross section σ_e1(αα) = 45 ± mb. Another method of estimating σ_tot(αα), based on measuring the interaction rate, yielded 295 ± 40 mb. For αp, dσ/dt has aminimum at |t| = 0.20 GeV², and for 0.05 < |t| < 0.18 GeV² behaves like exp[(41 ± 2) t]. Extrapolating this slope to |t| = 0, we found σ_tot(αp) = 130 ± 20 and σ_e1(αp) = 20 ± 4mb. Results on pp elastic scattering at $\text{s}\text{= 63}\text{GeV}$ agree with previous ISR experiments.     

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.     

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.     

Measurement of the polarization parameter in pp elastic scattering at 150 GeV/c

The polarization parameter in pp elastic scattering at 150 GeV/c, and in the momentum transfer interval 0.4 ? ?t ? 3.0 GeV², has been measured in an MWPC and scintillation counter experiment at the CERN SPS using a polarized proton target. The polarization is decreasing steadily from zero to ≈ ? 10% in the range 0.4 < ?t < 1.3 GeV²; for higher |t| the data suggests a change of sign. Results are also given for the differential cross section, which exhibits a small dip at ?t = (1.46 ± 0.01) GeV.     

Upper bound on the slope parameter

We find the axiomatic upper bound on the slope parameter of the scattering amplitude, which is logarithmically divergent with respect to energies in the region 0 < t < 4m²_π. This upper bound is realized in Regge-pole theory. We also obtain explicitly the numerical upper bound on the slope parameter of the linear Regge trajectory.