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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

A multiperipheral model with continued cross channel unitarity

We derive, by using a spectral representation in momentum transfer, t, an integral equation, similar in structure to a multipheral equation, with continued cross channel unitarity, for the absorptive part for a composite particle scattering amplitude from a Bethe-Salpeter equation describing composite particle scattering in the s channel. At high energy in the t channel, the equation becomes homogeneous and has a Reggeized solution. We indicate how this equation may be solved using determinental techniques. We also show how the composite particle amplitude resulting from the original equation may be used to construct production and three body amplitudes. We also infer the possibility of studying, using the amplitude from the cross channel problem, the effect of extra unitarity on Reggeon-Reggeon-particle vertices.     

Self-consistent quasi-particle model

Here we review the recently developed self-consistent quasi-particle model of QGP and apply it to fit the lattice QCD data on (2+1) flavor QGP.     

Self-consistent random phase approximation within the O(5) model and Fermi transitions

Self-consistent quasiparticle random phase approximation (SCQRPA) is considered in application to the Fermi transitions within the O(5) model. It is demonstrated that SCQRPA improves on renormalized QRPA (RQRPA), a method that has recently become rather popular in this context. The analytical form of the SCQRPA vacuum is used to evaluate all the matrix elements. The SCQRPA results show a general trend similar to the exact solutions. The necessity to change the single particle basis beyond the transition point, and to include the proton-proton and neutron-neutron channels in the QRPA operator, in addition to the proton-neutron one, is pointed out.     

Self-consistent treatment of the Anderson model

TheN-fold degenerate Anderson single impurity model in the infiniteU limit is treated by means of the irreducible Green functions method. In this approach a derivation of an exact Dyson equation and an exact self-energy operator is possible. The necessity of introducing auxiliary fields, such as slave-bosons is avoided.