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

Abstract

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 $\mathcal{O}({\alpha }_s^4)$ expression for the Adler function and, as a direct consequence, at the complete $\mathcal{O}({\alpha }_s^4)$ correction to the $e^{+}{e}^{-}$ annihilation into hadrons in a general gauge theory.

4 pages, 1 figure. Final published version

References in corpus (3)

• Hadronic Z- and tau-Decays in Order alpha_s^4
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Adler Function, DIS sum rules and Crewther Relations

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