%0 Journal Article %1 Baikov2012Adler %A Baikov, By P. A. %A Chetyrkin, K. G. %A Kühn, J. H. %A Rittinger, J. %D 2012 %K g-2 %T Adler Function, Sum Rules and Crewther Relation of Order O(alpha\_s^4): the Singlet Case %U http://arxiv.org/abs/1206.1288 %X 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 \$O(\alpha\_s^4)\$ expression for the Adler function and, as a direct consequence, at the complete \$O(\alpha\_s^4)\$ correction to the \$e^+ e^-\$ annihilation into hadrons in a general gauge theory.

@article{Baikov2012Adler, 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}(\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.}, added-at = {2019-02-23T22:09:48.000+0100}, archiveprefix = {arXiv}, author = {Baikov, By P. A. and Chetyrkin, K. G. and K\"{u}hn, J. H. and Rittinger, J.}, biburl = {https://www.bibsonomy.org/bibtex/23d6dc6227f726eb3a3ced1c76ec976d2/cmcneile}, citeulike-article-id = {10783841}, citeulike-linkout-0 = {http://arxiv.org/abs/1206.1288}, citeulike-linkout-1 = {http://arxiv.org/pdf/1206.1288}, day = 6, eprint = {1206.1288}, interhash = {d9adab64b72fca0aecc3d96d24bec08a}, intrahash = {3d6dc6227f726eb3a3ced1c76ec976d2}, keywords = {g-2}, month = jun, posted-at = {2012-06-12 16:07:46}, priority = {2}, timestamp = {2019-02-23T22:15:27.000+0100}, title = {{Adler Function, Sum Rules and Crewther Relation of Order O(alpha\_s^4): the Singlet Case}}, url = {http://arxiv.org/abs/1206.1288}, year = 2012 }