Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-03-24
Phys.Rev. D58 (1998) 076002
Physics
High Energy Physics
High Energy Physics - Phenomenology
25 pages, Phys. Rev. Tex, no figures
Scientific paper
10.1103/PhysRevD.58.076002
We present the two-loop corrected operator matrix elements contributing to the scale evolution of the longitudinal spin structure function $g_1(x,Q^2)$ calculated up to finite terms which survive in the limit $\epsilon = N - 4 \to 0$. These terms are needed to renormalize the local operators up to third order in the strong coupling constant $\alpha_s$. Further the expressions for the two-loop corrected operator matrix elements can be inserted into one loop graphs to obtain a part of the third order contributions to these matrix elements. This work is a first step in obtaining the third order anomalous dimensions so that a complete next-to-next-to-leading order (NNLO) analysis of the above mentioned structure function can be carried out. In our calculation particular attention is paid to the renormalization constant which is needed to restore the Ward-identities violated by the HVBM prescription for the $\gamma_5$-matrix in $N$-dimensional regularization.
Matiounine Y.
Smith Jeffrey J.
van Neerven W. L.
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