Explanation of Rising Multiplicity with Increasing Perpendicular Momentum Transferred to the Leading Proton, Using the Quark Multiple-Scattering Model

Abstract

It is shown that the rise in multiplicity with increasing perpendicular momentum transferred to the leading proton seen in recent experiments can be simply explained as due to double quark-quark scattering in the Glauber quark multiple-scattering model. The quark-quark inelastic-scattering amplitude is entirely consistent with the quark-quark elastic amplitudes obtained previously for elastic proton-proton scattering.In a recent experiment, Ramanauskas et aL 1 have studied multiplicity as a function of p ± , the perpendicular momentum transferred to the leading proton. The reaction specifically studied was p+p-~p+ particles, where the leading proton was detected and its momentum determined. All other charged particles were observed and their momenta measured as well. The results, over a range of values for the effective mass of the particles other than the leading proton, show that the multiplicity is roughly constant with/> x till a value of p L~ 0,65 GeV/c at which point it rises sharply by ~ 0.6, followed by indications for a leveling off at p ± ~ 1.0. We present here an explanation for this in terms of the multiple-quark-scattering model.Both the low-and high-energy proton-proton elastic scattering data are found to be fitted well using the Glauber model by considering the proton as a composite particle of three quarks. The first calculations for low-energy data were done by Harrington and Pagnamenta, 2 and calculations on data from the CERN intersecting storage rings were done by the authors. 3 In this model, the behavior in the small-momentum-transfer region \t\<Q.l (GeV/c) 2 (i.e., the forward slope region) is dominated by the process of a single quark in one proton scattering off of a single quark in the other proton. The behavior in the higher-momentum-transfer regions is determined by higherorder quark scatterings. The various scattering processes to all orders for elastic scattering are shown schematically in Fig. 1(a) where the dots represent quarks and the lines represent quark-quark scatters. Figure 1(b) shows the contributions to the elastic differential cross section da/dt due to first-, second-, third-, etc. order scattering. It is seen that second-order scattering is equal to first-order scattering at Ul^0.7 (GeV/c) 2 and exceeds it for larger It I Higher-order quark-quark scattering terms become predominant at even larger It I values.We may now consider inelastic scattering to occur in the same way as elastic. Inelastic scattering resulting in single-particle production has previously been treated formally in the Glauber model by Dean. 4 Instead of a line we draw an oval to represent an inelastic process in Fig. 1(a) resulting in pions in the final state. The amplitude for producing pions due to a single quark-quark collision depends primarily on the cm. energy and not the momentum transfer, since we may think of most of the energy of collision of the quarks as due to motion along the beam direction.The various lower-order diagrams that contribute to inelastic processes along with a schematic ...