Multiplicities in Deep Hadron - Hadron Scattering

We derive, an expression for the average multiplicity for an inclusive experiment a + b +c + X, where a, b, and c are hadrons and c is detected with a large transverse momentum. If EC is the energy of c in the center-of-mass of aandb, wefind &/4, the last term is absent. C e+eand Ch are related to the average multiplicities in annihi lation and small angle hadron-hadron scattering respectively, while Cx is determined by the final hadron density in the hole plateau region. We also apply our method to the semi-inclusive reaction a+b-tc+d+X where c and d both have large pI 0 Finally, we speculate about the value of Cx, and about nonasymptotic relations between multiplicities in various reactions. (Submitted to Phys, Rev.) work supported by the U. S. Atomic Energy Commission. The idea that hadrons are, in some sense, composed of point-like constituents has motivated a number of recent speculations about the average multiplicities, , in various high energy reactions. In efeannihilation, 1 the massive photon is assumed to decay into a parton-antiparton pair, each of which then decays into hadrons. In h-h scattering ” ” 3 (where h is a hadron), the major contribution to the multiplicity is supposed to come from pionization which populates the low energy region in the center-of-mass of the colliding hadrons. In deep inelastic e-h or v-h scattering, a number of authors 1,394 have used the ideas of the parton model to picture the virtual y or W knocking a parton to a distant region of phase space where it turns into hadrons, while the original hadron, which is now missing one constituent, evolves into the final state for which it is destined. For large energies and photon (or W) masses, Cahn, Cleymans, and Colglazier4 have derived relationships between the average multiplicities in these reactions by making two further assumptions. These are (1) partons which are widely separated in phase space do not strongly affect each other, 5 and (2) most produced hadrons are distributed in energy as dE/E, typical of a bremsstrahlung process. With these additional assumptions, it is also possible to conjecture about the dependence of on the relevant kinematic variables. In this note, we wish to apply these intuitive ideas to study the average multiplicities in hadron-hadron scattering where at least one particle is observed in the final state with a large transverse momentum. Except in certain limits, large will generally mean I p, I > l-2 GeV, However, we can further divide this range of I p, I. A A’ The two subdivisions are N -22 I pI I 2 1, and I pl I 2 NT , where N is some reasonable fraction. Now, it is entirely possible that different