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On the infrared sensitivity of the longitudinal cross section in $e^+ e^-$ annihilation

M. Beneke·V. M. Braun·L. Magnea
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Abstract

We have calculated the contributions proportional to $β_0^nα_s^{n+1}$ to the longitudinal fragmentation function in $e^+e^-$ annihilation to all orders of perturbation theory. We use this result to estimate higher-order perturbative corrections and nonperturbative corrections to the longitudinal cross section $σ_L$ and discuss the prospects of determining $α_s$ from $σ_L$. The structure of infrared renormalons in the perturbative expansion suggests that the longitudinal cross section for hadron production with fixed momentum fraction $x$ receives nonperturbative contributions of order $1/(x^2Q^2)$, whereas the total cross section has a larger, $1/Q$ correction. This correction arises from very large longitudinal distances and is related to the behaviour of the Borel integral for the cross section with fixed $x$ at large values of the Borel parameter.

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M. Beneke, V. M. Braun, L. Magnea. 1996-09-05. On the infrared sensitivity of the longitudinal cross section in $e^+ e^-$ annihilation. https://doi.org/10.1016/s0920-5632(97)00037-6

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