Five-loop accuracy in perturbative QCD

• Applicants: Dr. Konstantin Chetyrkin; Professor Dr. Johann Kühn
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2014 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 262491569

Precise determinations of parameters of the Standard Model (SM) andprecise predictions for observables measured at present and futureexperiments are critical in testing the SM and may hint towardsphysics beyond the SM. Increasingly precise results from high energyexperiments at LEP, LHC or a future electron-positron collider havebeen obtained during the past years or are expected for the comingdecade, with production and decay rates or masses of gauge or Higgsbosons or of the top quark as characteristic examples. These are complementedby measurements at low energies, which lead to precise values of the strong coupling from tau-lepton decay or the masses of strange, charm and bottom quarks.To extract the fundamental parameters of the theory and relate thelarge number of experimental results, the knowledge of higher orderperturbative corrections is crucial. Significant advances in thisdirection have been made during the past years, in particular in theframework of the collaborative research center ``ComputationalParticle physics'' (SFB/TR-9).The results have been presented in a number of publications and havebeen used for the improved extraction of the strong coupling  or the quark masses. To relate the parameters measured at lowand high energies, respectively, renormalization group (RG) equationsand corresponding anomalous dimensions are crucial.It is the aim of the present project to evaluate thebeta-function in five-loop approximation for a generic SU(N) gaugetheory with arbitrary number of fermion species, building onongoing work within project A1 of SFB/TR-9.This result will be used for an improved analysis of the strong coupling for lowand high energies and could become a crucial ingredient once theprecision of the strong coupling as determined from experiments or latticecalculations will be improved even further.Using the recent five-loop evaluation of the quark mass anomalousdimension in combination with the beta-function, the running bottom andcharm quark masses could be improved, leading to improved predictionsfor the Higgs branching ratios into bottom and charmed quarks.A closely related topic, to be addressed in this project, aims at a deeperunderstanding of the so-called generalized Crewther relation. The results will leadto an additional check of our results for the five-loop current-current correlator and mightpave the path to the corresponding six-loop result.

• DFG Programme: Research Grants