Extrapolating parton fragmentation to low $Q^2$ in $e^{+}$-$e^{-}$ collisions

Abstract

We analyze the energy scale dependence of fragmentation functions from $e^{+}$-$e^{-}$ collisions using conventional momentum measures $x_p$ and ${\xi }_p$ and rapidity $y$. We find that replotting fragmentation functions on a normalized rapidity variable results in a compact form precisely represented by the beta distribution, its two parameters varying slowly and simply with parton energy scale $Q$. The resulting parameterization enables extrapolation of fragmentation functions to low $Q$ in order to describe fragment distributions at low transverse momentum $p_t$ in heavy ion collisions at RHIC.

19 pages, 20 figures

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