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arXiv · 1206.1288

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

P. A. Baikov·K. G. Chetyrkin·J. H. Kühn·J. Rittinger
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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 ${\cal O}(α_s^4)$ expression for the Adler function and, as a direct consequence, at the complete ${\cal O}(α_s^4)$ correction to the $e^+ e^-$ annihilation into hadrons in a general gauge theory.

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P. A. Baikov, K. G. Chetyrkin, J. H. Kühn, J. Rittinger. 2012-10-10. Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case. https://doi.org/10.1016/j.physletb.2012.06.052

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