Adler function, sum rules and Crewther relation of order O(αs4): The singlet case

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 (Baikov et al., 2010 [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 (Baikov et al., 2008 [2], Baikov et al., 2010 [3]) we arrive at the complete O(αs4) expression for the Adler function and, as a direct consequence, at the complete O(αs4) correction to the e⁺e^- annihilation into hadrons in a general gauge theory.