Perturbative fragmentation

Abstract

The Berger model of perturbative fragmentation of quarks to pions is improved by providing an absolute normalization and keeping all terms in a ($1\ensuremath{-}z$) expansion, which makes the calculation valid at all values of fractional pion momentum $z$. We also replace the nonrelativistic wave function of a loosely bound pion by the more realistic procedure of projecting to the light-cone pion wave function, which in turn is taken from well known models. The full calculation does not confirm the $(1\ensuremath{-}z{)}^{2}$ behavior of the fragmentation function (FF) predicted in [E. L. Berger, Z. Phys. C 4, 289 (1980); Phys. Lett. 89B, 241 (1980] for $z>0.5$, and only works at very large $z>0.95$, where it is in reasonable agreement with phenomenological FFs. Otherwise, we observe quite a different $z$-dependence which grossly underestimates data at smaller $z$. The disagreement is reduced after the addition of pions from decays of light vector mesons, but still remains considerable. The process dependent higher twist terms are also calculated exactly and found to be important at large $z$ and/or ${p}_{T}$.