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

TL;DR

The paper computes the order $\alpha_s^2$ contributions to the asymmetric fragmentation function coefficient functions in $e^+e^-$ annihilation, addressing the $\gamma_5$ treatment in dimensional regularization and the axial current renormalization. It shows the first moment of the non-singlet coefficient function is corrected by $-12\beta_0C_F\zeta(3)$ at order $(\alpha_s/4\pi)^2$, modifying the flavour asymmetry sum rule. It then assesses the impact of higher-order QCD corrections on $F_A(x,Q^2)$ and compares with OPAL data, finding NNLO effects to be negligible and that the data constrain the valence fragmentation densities, prompting adjustments to the NLL Bin95 parametrizations. Overall, the work links perturbative coefficient functions to observed asymmetries in hadron fragmentation and provides constraints on valence fragmentation functions for identified hadrons.

Abstract

The order α_s^2 contributions to the coefficient functions corresponding to the asymmetric fragmentation function $F_A(x,Q^2)$ in $e^+e^-$ annihilation are calculated. From this calculation we infer that the order $(α_s/4π)^2$ correction to the flavour asymmetry sum rule is non vanishing and amounts to $-12β_0C_Fζ(3)$. We also study the effect of the higher order QCD corrections on $F_A(x,Q^2)$ and compare them with the OPAL data. The latter put a strong constraint on the valence part of the fragmentation densities $D_q^H(x,μ^2)$.

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