1206.1288 (by P. A. Baikov et al.)

Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4):
the Singlet Case    [PDF]

by P. A. Baikov, K. G. Chetyrkin, J. H. Kühn, J. Rittinger

The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function [2,3] we arrive at the complete ${\cal O}(\alpha_s^4)$ expression for the Adler function and, as a direct consequence, at the complete ${\cal O}(\alpha_s^4)$ correction to the $e^+ e^-$ annihilation into hadrons in a general gauge theory.

View original: http://arxiv.org/abs/1206.1288