Single Particle Distributions from Veneziano Amplitudes I

The single particle distribution for the inclusive reaction A + B → C + anything is calculated from the discontinuity of the Veneziano six point function in the tree approximation and investigated in different kinematical regions. Power series expansions around x = 1 and Barnes‐Mellin integral representations suitable for expansions around x = 0 are presented. For large transverse momenta the single particle distribution shows an exponential decrease in p ⟂ 2 with an x dependent slope assuming the value 4 α′ for x = 0. For small transverse momenta the behaviour of the distribution function in the pionization region is determined by a logarithmic singularity at the unphysical point p ⟂ 2 = − m c 2 . In addition single particle distributions following from two special types of Pomeron‐background modified B 6 functions are studied. Most of the results are similar to those obtained with the unmodified B 6 function. This applies in particular to the pionization region, where the asymptotic p ⟂ 2 ‐slope 4α′ is replaced by a “background slope” 4β′.