The calculation of the two-loop spin splitting functions $P_{ij}^{(1)}(x)$ |
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Authors: | R Mertig W L van Neerven |
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Institution: | 1. NIKHEF-H, P.O. Box 41882, 1009, DB Amsterdam, The Netherlands 2. Instituut-Lorentz, University of Leiden, P.O. Box 9506, 2300, RA Leiden, The Netherlands
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Abstract: | We present the calculation of the two-loop spin splitting functions $P_{ij}^{(1)}(x)(i,j=q,g)$ contributing to the next-to-leading order corrected spin structure function g 1 (x, Q2). These splitting functions, which are presented in the ${?erline {? MS}}$ scheme, are derived from the order $←pha_{s}^{2}$ contribution to the anomalous dimensions $αmma_{ij}^{m}(i,j=q,g)$. The latter correspond to the local operators which appear in the operator product expansion of two electromagnetic currents. Some of the properties of the anomalous dimensions will be discussed. In particular our findings are in agreement with the supersymmetric relation $αmma_{qq}^{m}+αmma_{gq}^{m}-αmma_{qg}^{m}-αmma_{gg}^{m}=0$ up to order $←pha_{s}^{2}$. |
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