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Single Particle Distributions from Veneziano Amplitudes I
Author(s) -
Biebl K. J.,
Bebel D.,
Ebert D.
Publication year - 1972
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19720200903
Subject(s) - logarithm , exponential function , gamma function , physics , singularity , pomeron , amplitude , distribution (mathematics) , mellin transform , mathematical analysis , series (stratigraphy) , power series , mathematical physics , discontinuity (linguistics) , function (biology) , distribution function , transverse plane , mathematics , laplace transform , quantum mechanics , scattering , paleontology , structural engineering , evolutionary biology , engineering , biology
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′.