The shrinkage of the elastic differential cross section from the multiperipheral model using unitarity

The overlap function has been calculated analytically from a simplified Chan-?oskiewicz-Allison (C?A) model with Regge phase. Hamer and Peierls have shown using the impact parameter variables that in the C?A model with Regge phase the slope of the overlap function increases too rapidly with total energy when compared to experiments. According to Jadach and Turnau this was due to inadequate approximations made for the norm of the C?A amplitude and they showed that in the C?A model with no momentum-dependent phase the shrinkage agrees with experiments but the magnitude of the slope is too small. We show without making the inadequate approximations mentioned by Jadach and Turnau that when the Regge phase is used in the C?A model; it makes the overlap function shrink too rapidly and have a too large slope above 20 GeV/c. Clustering will improve the agreement with experiments, especially when one further assumes that the clusters do not form resonances. Then the trajectories which are exchanged between two clusters are exchange degenerate and have a real contribution to the amplitude. The analytic calculations make it possible to discuss contributions to the overlap function from various properties of the production amplitude.     

The multiperipheral model with constant total cross section

A multiperipheral model is suggested, in which the dependence of the amplitude of production of “n” particles on pair energy and existence of many particles exchanged (?, ω, π, A₂, f) is taken into account.     

Fragmentation and multiperipheral dynamics: A connection through unitarity

A rapidity space decomposition of s-channel unitarity implies interdependence between production mechanisms. The presence of a low multiplicity diffractive production channel shadows the multiperipheral mechanism while the high multiplicity multiperipheral channel shadows the diffractive mechanism in the high produced mass region. The first effect results in negative contributions to the effective two-pomeron cut. Pomeron couplings to elastic and inelastic channels then require a cut structure which evades decoupling theorems. For hard cuts there is a connection between the relative amount of diffractive production and the dip in $\text{d}\text{σ}{}_{\mathrm{<mtext>el</mtext>}}{}^{\mathrm{<mtext>PP</mtext>}}\text{/}\text{d}\text{t}\text{at}\text{?t = 1,}\text{2}\text{GeV}{}^2\text{c}{}^2$ at ISR. The consequent cut to pole strength is 10–20%. It is conjectured that the situation described here resembles the approach to a phase transition in the multiperipheral gas.     

A field theoretic cluster model of multiperipheral production

A field theoretic cluster model of multiproduction process in hadron-hadron collisions at high energy is considered. The multiproduction here is a two-step process. In the first step clusters are produced. We use a field theoretic formalism to describe cluster creation. A validity of the standard approximations, that are usually made in multiperipheral models is discussed. A modified strong ordering hypothesis is proposed. This leads to the Feynman scaling violation. Then cluster decay is considered. Expressions for semi-inclusive pion distributions in rapidity are given and a comparison with experimental data is made.     

Overlap function from the multiperipheral model

Monte Carlo phase space calculations of the overlap function for Chan-Loskiewicz-Allison and Chew-Pignotti models were performed up to laboratory momentum 1500 GeV. Slope of the overlap function was found about four times smaller than the experintal value. Shrinkage of the elastic peak is close to that found in experiment. The qualitative explanation of these results is given, and the discrepancy with the recent estimates obtained by Hamer and Peierls, Hwa, and Henyey is explained. Finally, our analysis shows that the random walk picture of the multiperipheral models is not valid for realistic density of particles in rapidity scale.     

Elastic scattering from the multiperipheral model

Elastic scattering in the Multiperipheral Model (MPM) is examined by use of a new method for simplifying unitary calculations - multiparticle impact parameter. The t dependence of elastic scattering in the MPM is related to the average transverse momentum of produced particles, the average multiplicities (observables), phase variation with transverse momentum, and clustering (not observables, in general). It is shown that MPM's are inconsistent with the combination of elastic and multiparticle data, unless either the cluster size or the phases have rather strong energy dependence.     

Longitudinal momentum transfers in the multiperipheral model

The inclusion of longitudinal momentum transfers in the multiperipheral model is investigated. As recently pointed out by Jadach and Turnau, these longitudinal momentum transfers, if present, have a very large effect on properties of the model. In this paper we find that data rules out such effects. Furthermore, if the longitudinal momentum effects were present, they would in no way solve the serious problem with the multiperipheral model, that average multiplicity and elastic slope ought to be proportional, but experimentally are not. A multiperipheral model using transverse momentum transfers has fewer phenomenological difficulties than one using total momentum transfer.     

Large transverse momenta in the multiperipheral model

A unified picture of small and large transverse momenta is provided by the multiperipheral model in its original version. The large k_T spectrum is k_T^?p times a scaling function. Results are in agreement with ISR data and testable predictions are made.     

Relations in a factorizing multiperipheral cluster model

A multiperipheral cluster model in which the clusters are independently emitted is investigated using the formalism of generating functionals and exact relations between overall correlations and cluster decay spectra are obtained. These relations and the general concept of clusters are subsequently discussed in regard to experimental data.     

Multiplicity distributions in a multiperipheral fireball model

Multiplicity distributions are studied in the thermodynamic model. The approximate Koba, Nielsen, Olesen scaling behaviour of the data and Wroblewski's linear law can be understood in the thermodynamic model with multiperipheral production of fireballs. This production mechanism is also essential to understand two-particle rapidity correlations especially in the ISR energy range. There are contributions from diffractive and non-diffractive production of fireballs in the model, which agrees in this sense with the two-component models used recently to discuss multiplicity distributions. In contrast to other models, however, the non-diffractive component taken separately exhibits approximate KNO-scaling and accounts rather well for the behaviour of the data up to 300 GeV. For the fireball production mechanism choosen the cross section of the diffractive component is expected to be smaller than in other models and can lead to a two-maxima multiplicity distribution only at energies higher than predicted in other models.     

Triple Regge limit in the absorptive multiperipheral model

The x → 1 limit of the inclusive one-particle distribution is studied in the absorptive multiperipheral model: we find a leading behaviour of the type (1−x)⁻¹ 1n⁻³ (1−x), which gives an integrable contribution to the energy conservation sum rule.     

Equivalence between the Mueller Regge model and the multiperipheral model

It is proven that a large class of pionization Mueller Regge models are equivalent to the multiperipheral model. An orthogonal similarity transformation is found which allows one to transform in either direction between equivalent multiperipheral and Mueller models. Models with charge are discussed and the problem of constructing charge conserving Mueller models is solved.     

The Morrison rule in the ABFST multiperipheral model

The validity and consistency of the Morrison rule for the process ππ→πA₂ is considered at asymptotic energy in the context of the ABFST multiperipheral model. The Morrison rule turns out to be inconsistent with the model.     

A model of baryons based on duality and unitarity

A model of “planar” baryons with (10 + 8) ? (1 + 8) exchange degeneracy is proposed, based on duality and unitarity. Dynamical mechanisms for deviation from the “planar” baryons are considered and the consequent pattern of broken exchange degenerate trajectories is compared with observed baryon spectra. Our model suggests a string picture of linear molecule type for baryons.     

Pion and K meson production in the multiperipheral model

A simple multiperipheral model, that utilizes only three parameters, two coupling constants and exponential damping for each momentum transfer is developed and applied to the calculation of inclusive distributions. The pion rapidity and p_⊥² distributions are successfully predicted; as are the energy dependences of strange particle production cross sections. The development of inclusive distributions with increasing energy and possible improvements to the model are discussed.     

Self-consistent diffraction in the multiperipheral model (IV)

Numerical fits to high-energy proton-proton scattering data are made using formulae obtained previously from a self-consistent solution to the multiperipheral model. Agreement with the total cross section and elastic differential cross section is satisfactory.     

Self-consistent diffraction in the multiperipheral model (II)

We present a self-consistent solution to a multi-peripheral model in which the triple pomeron vertex vanishes. This solution possesses all of the good features of our previous model, having naturally diffractive and multiperipheral terms in the total cross section and in particle production. In addition, its region of validity has been increased to include the normal Regge region and a smooth transition from Regge-like behavior to the diffractive limit is obtained.     

Generalization of multiperipheral model with long range correlations; Van Der Waals approximation

Three enhancements are observed in the final state ω^°π⁺π⁺π⁺⁺π^?π^? selected from the channel $\text{p}\text{p → 3π}{}^{\mathrm{+}}\text{3π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{°}}$ at 715 MeV/c: one in ω^°π^± at 1040 MeV (～ ≈ 55MeV) ω^°π⁺π^?, respectively near 1315 MeV (～ ≈ 100 MeV) and 1405 MeV (～ ≈ 40 MeV). The first two effects are strongly correlated and are interpreted in terms of a sequential decay A^°₂ through a new object, the B₁. The second (ωππ) enhancement seems to be an ?^°?^° effect below threshold and is attributed to a pionic decay of the $\text{K}\text{K}\text{)}{}_{\mathrm{I}}\text{=1}$ effect seen around the same mass in other reactions.