F. Henyey

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 MPMs are inconsistent with the combination of elastic and multiparticle data, unless either the duster size or the phases have rather strong energy dependence. Elastic scattering following from the Multiperipheral Model (MPM) by unitarity has been widely studied [1-3]. In this paper a new method, multiparticle impact parameter [4], is applied to this problem. The multiperipheral model shares a number of features with the multiparticle data, such as limited transverse momentum, a spread of longitudinal momenta, etc. We will take these features from the data, so as to use as few details of the model as possible, and also so as not to allow the model to fit elastic scattering by means of a failure to fit multiparticle scattering. There is, however, one feature of the MPM which is somewhat independent of the multiparticle data, and which distinguishes the MPM from other models which fit multiparticle data equally well. This feature is short range order. We will examine the effect short range order has on the elastic scattering.

Double pomeron exchange in the reaction pp → ppπ+π−

Abstract We compute the cross section for pp → pp π + π − in the kinematical region for which two-pomeron exchange is important, assuming dominance of the pion-exchange pole. We include effects due to absorption, final-state interaction, and interference between the two contributing Feynman diagrams. These effects have been ignored in previous calculations. Consequently, our predicted cross section is smaller than previous predictions by a factor of ∼ 3, and is consistent with experimental indications. We calculate the background cross section in the double pomeron exchange region, and find that it is sizable even at s ∼ 3000 GeV 2 . We discuss the two-particle inclusive process pp → ppX.

Impact parameter description of multiparticle and elastic scattering

Abstract Impact parameter variables are defined for a multiparticle production process. The equation of unitarity for elastic scattering is written at high energy in terms of these variables. The overall impact parameter can be expressed in terms of the impact parameters of all the produced particles. The unitarity equation becomes an “optical theorem” at each impact parameter — diffractive scattering is given by beam depletion. These features allow this technique to give a much clearer interpretation of unitarity in any model than has therefore been possible. This technique can be used to study existing models, and to suggest new ones.

Impact parameter study of high energy elastic scattering

The imaginary part of the proton-proton elastic scattering amplitude, as measured at the ISR, is examined in impact parameter. The transformed amplitude has two important properties. First, it is very accurately Gaussian in the impact parameter from the center to two fm with very little flattening near the center. Flattening would be expected from eikonal- ization. Secondly, there is a tail beyong two fm with a much flatter slope. This tail in impact parameter is equivalent to the break of do/d t at t = - 0.15 GeV. We discuss the. physical origin of the tail. It cannot reasonably be diffraction dissociation, since diffraction should be large where absorption is large. We suggest that the tail is due to dissociation which must be distinguished from its diffractive part, and make a physical model which gives the tail and describes do/dt very well. This model predicts the Deck model part of the diffraction inelastic cross section. We discuss the interpretation of elastic scattering in terms of s-channel unitarity rather than a t-channel exchange or the structure of a single hadron.

Unitarity bounds for inelastic diffraction

Unitarity in the s-channel is invoked to derive an upper bound for the inelastic diffractive cross-section as a func- tion of impact parameter. The application of this bound to high-energy proton-proton scattering strongly suggests that inelastic diffraction should be peripheral in the impact parameter space. Introduction. Recent observation of a structure around t = -0.2 GeV 2 in the differential cross-section of the process pp ~ p(n,r +) at the CERN ISR (1 ) sup- ports the assumption that inelastic diffraction, unlike elastic diffraction, is peripheral in the impact param- eter space. This assumption has been made very plaus- ible in the past by many authors (2-6), partially on intuitive grounds, partially on the basis of phenome- nological analyses of experimental data. In this letter we suggest that the previous conclu- sion is in fact a very natural consequence of s-channel unitarity and of the assumption that inelastic, as well as elastic diffraction, is the shadow of non-diffractive particle production. Using these assumptions, Pumplin has recently derived the following bound (7) :

Clusters, correlations and transverse momenta

Abstract We discuss the short range part of two-particle correlations as it results from the phase space available in cluster decay. In such an approach, certain variables emerge which should be useful to organize the data and extract interesting information. We are in particular concerned with tests of large transverse motion of clusters.

Measuring the geometrical size of multiparticle processes

Abstract We examine the possibility of measuring the geometrical size of multiparticle processes. The mean-square impact parameter, 〈 b 2 〉, of a process can be estimated by means of lower bounds which are determined from experiment. A bound of this type, which has been proposed by Webber, is found to be inadequate for the estimate. We propose several alternative bounds. One of them represents a considerable improvement over Webbers bound, with essentially no increase in the difficulty of the measurement. Another is a theoretically optimal bound which, however, requires an extremely high-statistics experiment. We also describe a method of deriving further bounds; and make estimates of the difference between the bounds and the true 〈 b 2 〉.

Longitudinal momentum transfers in the multiperipheral model

Abstract 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.

A model for charged second class currents

A recent experiment [1 ] has reported a non-zero signal for second class currents [2] in the/3-decyas of several nuclear species. Second class currents have not yet, however, been observed in any particle physics experiment. In this paper we investigate some phenomenological consequences for ?article physics of a particular model for the second class current. Remarkably, withir the framework of the model, we are led to a second class current which couples to, the weak interactions with the same strength as the ordinary current, when the normalization is chosen in a particularly simple way. Second class currents do not naturally appear in the quark model. If they are large it could considerably complicate weak interaction theory; in particular, the weak and electromagnetic interactions could no longer generate only an SU(2) X U(1) as they do in the conventional theory. The second class current [3-5] *** by definition has the value -1 for the quant~lm number ((-1)IGp)((-1)J+ I), while the first class current has the value +I for this quantum number. The odd value for this combination is usually described as having the opposite G to the usual current. An ffpair, where fis a spin-½ fermion, has an

Unitarity bounds on diffraction dissociation

Abstract Using s -channel unitarity and the standard picture that diffraction dissociation and elastic scattering are the shadow of non-difractive particle production, we derive rigorous upper bounds for the diffraction dissociation cross section. The bounds are valid at each impact parameter, and are derived for an arbitrary number N of difractive channels. Our results are a generalization of previously derived bounds for the special simple case of N = 2 channels.