Multiperipheral Chain Research Articles

Gravitation interactions at high energies and Reggeon scheme

A parton-Reggeon model that, for basic partons, employs gravitons of virtuality on the order of the Planck scale is proposed to describe inelastic interactions at trans-Planckian energies. A graviton analog of the Pomeron with an intercept of α(0)=3 is introduced on the basis of the structure of the gravitational field of a fast particle. Its unitarization leads to inelastic cross sections growing in proportion to s and corresponds to the pattern of a collision between black disks of radius about E i 1/2 . The inclusive spectra of hard gravitions whose behavior is determined by the size of the region of overlap of colliding black disks at various impact parameters and various energies is found. The graviton system formed in this way proves to be unstable against the gravitational attraction of particles having close momenta. This leads to the emergence of a multiperipheral chain of black holes at the stage of divergence—the structure of such a chain depends greatly on the impact parameters of a collision.

Fireball Emission and Slope of the Overlap Function

The forward slope of the overlap function for the emission of fireballs with a constant mass m and mean decay pion multiplicity ≪k > is calculated with the multiperipheral model. The approximation of equal spacing of the produced fireballs in the rapidity space is used to take account of the effect of the longitudinal part of squared four momentum transfers between adjacent fireballs on the multiperipheral chain. Taking into account the decay properties of fireball, too, the mean squared transverse momentum of final pions is related to that of fireballs, upon which the forward slope of the overlap function is dependent. It results from numerical analyses that the forward slope of the overlap function can be made compatible with the slope of the diffraction peak in p-p elastic scattering in ISR energy region, by adjusting m for a given ≪k > in the range 3 ≲≪k >≲8. The value m ≃2.7 GeV obtained for ≪k >≃6 is consistent with the properties of H-quantum.

The overlap slope and multilink interactions in multiperipherallike impact parameter amplitudes

We investigate the overlap function that results from a general multiperipherallike impact parameter structure for multiparticle production. In particular, we generalize the random-walk model in impact parameter to include interactions that extend over more than one link in the multiperipheral chain. It is found that reasonable values for both the magnitude and the shrinkage of the elastic slope can be easily obtained, due to collective effects in impact parameter space.

Current fragmentation in deep inelastic scattering

It is argued that the current fragmentation products in deep inelastic electron scattering will not be distributed in a “one-dimensional” rapidity plateau as in the parton model picture of Feynman and Bjorken. A reaction mechanism with a multiperipheral topology, by which the above configuration might have been achieved, does not in fact populate the current fragmentation plateau; and unless partons are actually observed in the final state, it cannot lead to Bjorken scaling. The basic reason for this failure is shown to be fact that when a particle is produced in the current fragmentation plateau, the adjacent momentum transfer in the multiperipheral chain becomes large and negative: such processes are inevitably suppressed. Instead, the current fragmentation products are likely to be generated by a fragmentation, or sequential decay process.

Cluster Mass Distribution in Multiperipheral Cluster Emission Model

It is shown that dynamics of the multiperipheral cluster em1ss1on model uniquely determines the cluster mass (M) distribution. In particular, the mass distribution is dynamically suppressed by the output factor (M')-Po(fi,>g'(p.), p.: final hadron mass) in addition to a possible decreasing effect due to the input factors of the cluster emission (g'(M)) and decay (JJ(M)) vertices. A dynamical equation for solving fio is derived. Some quantitative estimates are also presented. Since proposed in 1962 by ABFST,l> a multiperipheral model has been a continuing laboratory of physical interest when the multiple production of hadrons is studied. Incorporation of Regge exchanges 2>·8> along the multiperipheral chain makes the model more suitable for analyzing a high-energy multiparticle production. Quite recently, an idea that hadrons are produced in clusters 4> has provided a popular interpretation of several features of multiparticle production data. In particular, the postulates of (A) independent emission of clusters along th.e multiperipheral chain and (B) their isotropic decay via a Gaussian distribution in rapidity give a facile imitation of data on two-particle inclusive rapidity cor­ relations in the central regioit. 6> It is not clear whether clusters have any intrinsic dynamical significance (e.g., generalized resonances) or whether they are primarily of phenomenological convenience. Experimentally we still have to wajt for eve~t-by-event data on an exclusive rapidity distribution in order to observe directly the cluster formation and its detailed properties. On the other hand, the observed high multiplicity in rapidity space suggests that final hadrons should be produced more preferably through cluster (or resonance) formation along the multiperipheral chain to through factorized Regge exchanges between the final hadrons. It is a reasonable guess that due to a small average spacing of .dy~0.3 to 0.5 between the final hadrons, there will be a strong correlation among the produced particles, which is better represented by the above postulates (A) and (B). The purpose of this paper is to show that the postulates (A) and (B) just mentioned uniquely determine the mass distribution of produced clusters which is usually assumed to take a certain form as a third input. What is important, the predicted mass distribution can be checked experimentally when the exclusive

Multiperipheral operator factorization and the bootstrap idea

We discuss multiparticle production models including important direct channel unitarity effects in the light of the general multiperipheral dynamics proposed by Bassetto, Sertorio and Toller. We first solve the Finkelstein-Zachariasen model by means of the explicit t-channel operator factorization of the exclusive production amplitudes. We show that the absorption, which is introduced in the model according to the Gottfried-Jackson recipe, can be decomposed locally into factors along the multiperipheral chain. The model however does not treat diffraction in a self-consistent way as partial production cross sections and elastic cross sections have different asymptotic behaviour. We then propose a simple model which possesses diffractive contributions in the inelastic channels still exhibiting total cross section and multiplicity fluctuations with the same asymptotic behaviour as the ones of the Finkelstein-Zachariasen model. We solve it again by means of t-channel factorization. Finally we comment upon the relation between exclusive and inclusive factorization in our scheme and argue that it could provide room for a wider realization of the bootstrap idea.

Leakage of quark charge

A sequential model for the fragmentation of a quark into hadrons is constructed with the property that a net charge $2$ "leaks" down the multiperipheral chain. Specifically, for a process initially producing a quark, $2=\frac{1}{3}\frac{(1\ensuremath{-}r)}{(2+r)}$, where $r$ is the ratio of directly produced ${K}^{\ifmmode\pm\else\textpm\fi{}}$ to ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ in the quark fragmentation plateau. This expression corrects an earlier one in which the consequences of such a model were misstated.

Transverse Momenta and Overlap Functions in Multiperipheral Models

The multi-Regge model is studied, with particular emphasis on the predicted slope of the elastic diffraction peak, and the average transverse momentum of the produced particles. The slope of the diffraction peak is proportional to the mean-square impact parameter, and in the multi-Regge model the total impact parameter is built up in a random walk, with each link in the multiperipheral chain corresponding to a step in the walk. A simple Chew-Pignotti model is incapable of fitting the inclusive production data at high energies: It predicts too slow an increase in the multiplicity of produced pions, and too rapid a shrinkage of the diffraction peak. To cure this problem, one must introduce "clustering" effects such as to reduce the over-all spread in impact parameter, and increase the density of produced pions in longitudinal-momentum space. Such effects were to be expected, in fact, because of resonance formation. A multiperipheral cluster model is introduced, in which the decay of the clusters is described via the statistical bootstrap model of Hagedorn and Frautschi. A crude fit to the high-energy data, in which all the clusters are given a common mass, shows that the average cluster mass is at least a couple of GeV, a surprisingly large figure. This provides some a posteriori justification for Hagedorn's thermodynamic model. The calculations are carried out using both approximate analytical methods and a Monte Carlo numerical program.

Slope of the Forward Peak: Ans-Channel Analysis

Starting from the exact multiparticle unitarity relation, we derive the derivative extension of the optical theorem. The slope of the forward peak is then related in a model-independent way to the rotational properties of production amplitudes. A sequential representation is developed for treating an $n$-particle state. The formalism is then applied to the multiperipheral and diffractive models. The analysis makes clear the mechanisms in which the forward slope is built up in those models. In the case of the multiperipheral model the slope is proportional to the number of links in the multiperipheral chain. Quantitatively, the slope of the Pomeranchuk trajectory at $t=0$ is too large. In an oversimplified version of the diffractive model, the predicted slope of the elastic forward peak is one-half the mean slope, the average being taken over all two-cluster production processes; consequently, it is too small. The realistic high-energy model is somewhere between the two extremes considered.

Azimuthal Correlations and the Nature of the Pomeranchuk Singularity in Models Without Short-Range Order

The existence of long-range azimuthal correlations in inclusive data is known to imply that the Pomeranchuk singularity is not a simple pole. A simple independent-emission model, which shares many properties of multiperipheral models except that the produced particles are not ordered along a multiperipheral chain, possesses these long-range correlations. Therefore the leading $J$-plane singularity in this model is seen to be a cut.

Multiperipheral models with charged particles

Techniques are developed to allow the inclusion of many particles with differing quantum numbers in the multiperipheral chain. Within the Chew-Pignotti multi-Regge model these techniques are applied to allow the inclusion of charge in the model. Two proposed models for the isospin structure of the chain, repeated isovector exchange and alternating isoscalar-isovector exchange are discussed; secondary intercepts, charged particle multiplicities, rapidity distributions for charged particles and cross sections for the production of charged prongs are calculated. One immediate result is that an isovector chain predicts that an incoming proton will emerge as a neutron two-thirds of the time (compared to the observed one-third); any realistic model must include isoscalar exchanges in the chain. It is suggested that, if the Pomeranchukon is generated by a simple subset of the available exchanges, then inclusive experiments should spotlight those Regge poles generated simultaneously with it. The utilization of charge correlations to explore this possibility is discussed.

Final state spectra in a multiperipheral model

Using an integral equation technique based on the multiperipheral model, we study various properties of the spectrum of secondaries in high-energy inelastic collisions. From the basic properties of the multiperipheral model, we derive several results about single particle momentum spectra, and multiplicity of secondaries. We initiate an extension of our method to multiparticle correlations by calculating the average invariant mass of neighbors on the multiperipheral chain.

Multiperipheral Theory of Deep-Inelastic Electron-Nucleon Scattering

The Amati-Bertocchi-Fubini-Stanghellini-Tonin multiperipheral model is modified to study deep-inelastic electron-nucleon scattering. The behavior of the structure functions is derived in the limit of large energy and momentum transfer, $\ensuremath{\nu}$ and ${q}^{2}$, with $\ensuremath{\omega}\ensuremath{\equiv}\frac{2m\ensuremath{\nu}}{(\ensuremath{-}{q}^{2})}$ fixed but large. In particular, scaling is derived. To accomplish this derivation it is necessary to introduce a cutoff for the momentum transfer of the exchange nucleon, which directly couples to the photon in the multiperipheral chain. The multiperipheral derivation is compared with derivations that use other models. The generality of our derivation, in the sense of requiring only Regge behavior and a particular asymptotic off-shell dependence, is discussed.

Two-Fireball Phenomenon and the Multiperipheral Model

In the context of the Chew-Snider version of the Amati-Bertocchi-Fubini-Stanghellini-Tonin pion-exchange model, we investigate certain multiperipheral mechanisms that could account for those phenomena that have hitherto motivated the two-fireball model. These mechanisms are (1) double diffractive dissociation, (2) the presence of a sequence of neutral particles on the multiperipheral chain, and (3) statistical fluctuations in the $\mathrm{logtan}\ensuremath{\theta}$ spectrum. At cosmic-ray energies they are of equal importance.

Some Predictions of the Amati-Bertocchi-Fubini-Stanghellini-Tonin Multiperipheral Model

The predictions of the Amati-Bertocchi-Fubini-Stanghellini-Tonin multiperipheral model based on pion pole dominance are calculated quantitatively and compared with experimental data, by using the Veneziano representation for the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ amplitude, with a cutoff at the mass of the $g$ resonance for the input kernel, and neglecting off-shell effects. We find ${\ensuremath{\alpha}}_{P}(0)=0.30$, ${\ensuremath{\alpha}}_{\ensuremath{\rho}}(0)=0.16$, an average multiplicity growing as 0.74 $\mathrm{ln}s$, an elasticity factor of 0.69, an average pion-pair transverse momentum equal to 0.43 $\frac{\mathrm{GeV}}{c}$, and an average invariant mass squared equal to 0.84 Ge${\mathrm{V}}^{2}$. The only serious discrepancies with experiment are the trajectory heights, which correspond to a kernel strength $2\frac{1}{2}\ensuremath{-}5$ times too weak. The inclusion of the high-subenergy contribution and the inclusion of off-shell effects by several methods of off-shell continuation are considered, but none is found to be satisfactory. The importance of interference terms, due to different ways of arranging the final-state particles along the multiperipheral chain, is discussed.

Kinematic Reflections in Multiple-Production Processes

The functional dependence of one subenergy variable of a multiperipheral chain upon another is shown to be extremely strong at fixed, small values of all momentum transfers. A general class of kinematic reflections is therefore likely to occur when Regge asymptotic terms appear in an amplitude. The special case of three final-state particles (the Deck effect) is discussed in relation to a recent conjecture of Chew and Pignotti.