Crewther Relation and Adler Function: Towards Hadronic Z and tau Decays at Order alpha_s^5

• Applicant: Dr. Konstantin Chetyrkin
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 412091215

• Final Report Year: 2022

Final Report Abstract

We have computed the nonsinglet Adler D-function and the coefficient function for Bjorken polarized sum rules S^Bjp at order O(αs^4 ) in an extended QCD model with arbitrary number of fermion representations. We have found that the Crewther relation is indeed valid in the extended QCD. These results have provided an important input for construction the β-expansion for the Adler D-function and the coefficient function S^Bjp at order O(αs^4 ) and derivation of some useful preductions on the structure of the corresponding β-expansions at hihrer orders. We have investigated in detail the renormalization, Operator Product Expansion and vacuum expectation values of non-local off-light-cone operators of a quark and an antiquark field, and also of two gluon field strength tensors. The results are useful for theoretical studying heavy-light mesons in HQET as well as for for studying parton quasi-distributions. We also have suggested a new approach to compute NNLO anomalous dimensions for twsit-two flavour-singlet operators and have demonstrated its potential by computing NNLO anomalous dimension matrix for flavor-singlet QCD operators for spin N <= 8. We have also provided new results for π-dependent terms in anomalous dimensions and massless 2-point correlatore up to and including unprecedentedly high loop order (7 loops for correlators and 8 loops for anomalous dimensions).

Publications

• Transcendental structure of multiloop massless correlators and anomalous dimensions. Journal of High Energy Physics, 2019(10).
  Baikov, P.A. & Chetyrkin, K.G.
  
• Renormalization of parton quasi-distributions beyond the leading order: spacelike vs. timelike. Journal of High Energy Physics, 2020(7).
  Braun, V. M.; Chetyrkin, K. G. & Kniehl, B. A.
  
• Operator product expansion of the non-local gluon condensate. Journal of High Energy Physics, 2021(5).
  Braun, V. M.; Chetyrkin, K. G. & Kniehl, B. A.
  
• Adler function, Bjorken Sum Rule and Crewther-Broadhurst-Kataev relation with generic fermion representations at orderO(αs). Nuclear Physics B, 985 (2022, 12), 115988.
  Chetyrkin, K.G.
  
• Correlators of heavy–light quark currents in HQET: OPE at three loops. Nuclear Physics B, 976, 115702.
  Chetyrkin, K.G. & Grozin, A.G.
  
• NNLO anomalous dimension matrix for twist-two flavor-singlet operators. Physics Letters B, 834 (2022, 11), 137409.
  Braun, V.M.; Chetyrkin, K.G. & Manashov, A.N.
  
• The {β}-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order O($$ {\alpha}_s^4 $$). Journal of High Energy Physics, 2022(9).
  Baikov, P. A. & Mikhailov, S. V.