Order $α_s(Q^2)$ QCD corrections to the polarised $e^+~e^- \to Λ~X$

The importance of polarised gluons fragmenting into $Λ$ in the polarised $e^+ e^-$ annihilation is discussed using the Altarelli-Parisi evolution equations satisfied by the quark and gluon fragmentation functions. In this context, the polarised fragmentaion function $\hat g_1^Λ(x,Q^2)$ appearing in the cross section is discussed within the parton model. We relate this fragmentation function to the quark, anti-quark and gluon fragmentation functions and also find the QCD corrections to order $α_s$.

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