$O(α_s^2)$ Contributions to the longitudinal fragmentation function in $e^+\,e^-$ annihilation

Physics – High Energy Physics – High Energy Physics - Phenomenology

Scientific paper

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11 pages, uses 'mcite', and 'amsfonts', dvi-file available at http://rulgm4.leidenuniv.nl/preprints/longfrag.dvi

Scientific paper

10.1016/0370-2693(96)00898-2

We present the order $\alpha_s^2$ contributions to the coefficient functions corresponding to the longitudinal fragmentation function $F_L(x,Q^2)$. A comparison with the leading order $\alpha_s$ result for $F_L(x,Q^2)$ shows that the corrections are large and vary from 44\% to 67\% in the region $0.01 < x < 0.9$ at $Q^2=M_Z^2$. Our calculations also reveal that the ratio of the longitudinal and total cross section $\sigma_L/\sigma_{\rm tot}$ amounts to 0.054. This number is very close to the most recent value obtained by the OPAL collaboration which obtained $0.057\pm 0.005$.

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