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

The strong-coupling constant alpha_s is one of the three fundamental gauge coupling constants of the Standard Model of particle physics.  Its precise determination is one of the most important goals of particle physics. Experiments at different energies allow us to test the predictions for the energy dependence of alpha_s based on the renormalization group equations; comparisons of the results obtained from different processes lead to critical tests of the theory. Theoretically, the cross section of electron-positron annihilation into hadrons R(s) and its variants, like the Z boson decay rate into hadrons or the semileptonic branching ratio of the tau lepton into hadrons, can be reliably predicted in perturbative QCD and thus lead to the "gold-plated" alpha_s  determinations at M_Z and M_tau, respectively. To extract the fundamental parameters of the theory and to relate the large number of experimental results, knowledge of higher-order perturbative corrections is crucial. Significant advances in this direction have been made during the past years. However, the present theoretical accuracy will not be enough once future colliders will start to operate. This includes the International Linear Collider ILC running in the Giga-Z mode or a new circular electron-positron collider TLEP hosted in a 80- to 100-km tunnel. The big challenge here is to construct a reliable estimation of the next-to-next-to-next-to-next-to-order correction to R(s), at the fifth order in alpha_s, unless a genuine calculation is feasible. The latter problem is currently prohibitively difficult: after the calculation of the third-order correction (1991), it took more than 15 years until the forth-order one was found (2008).In our research project, we want to tackle theoretical investigations of both challenges. The aim of the project is threefold. First, to construct the best currently possible estimations of the influence on the predictions for R(s) and the Adler function of both unknown higher-order corrections, especially those of the fifth order in alpha_s, and of the best choices of the renormalization scheme and scale.  This includes a critical analysis and careful comparison of two currently popular methods, namely the Principle of Maximal Conformality and the Sequential Extended Brodsky-Lepage-Mackenzie Criterion. Second, to find a constructive proof of the so-called Crewther relation. This will be an important contribution to quantum field theory in its own right. Third, to use this for an analytical evaluation of the corresponding Crewther coefficient K_4 of the fourth order in alpha_s. The usefulness of the knowledge of K_4 is that, via the Crewther relation, it will significantly simplify, at least by one order of magnitude, a future calculation of the Adler function and, thus, of the very ratio R(s).

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Bernd A. Kniehl