Scheme Variations of the QCD Coupling and Hadronic τ Decays.

Area of Science:

• High-energy physics
• Quantum field theory
• Quantum chromodynamics

Background:

• The strong force coupling (QCD coupling α_{s}) is not a physical observable due to renormalization scheme dependence.
• Perturbative predictions in QCD are sensitive to the choice of renormalization scheme.

Purpose of the Study:

• To define a new QCD coupling, denoted α[over ^]_{s}, that is explicitly invariant under renormalization scheme transformations.
• To demonstrate that this new coupling can improve perturbative predictions for physical observables.

Main Methods:

• Introduced a novel definition for the QCD coupling (α[over ^]_{s}) with inherent scheme invariance.
• Parametrized the residual scheme dependence using a single parameter C, linked to QCD scale Λ transformations.
• Applied the new coupling to phenomenological studies of e^{+}e^{-} scattering and τ lepton decays.

Main Results:

• The new coupling α[over ^]_{s} exhibits explicit renormalization scheme invariance.
• The scheme dependence is controlled by a single parameter C.
• Appropriate choices of C significantly improve perturbative predictions for physical observables.

Conclusions:

• The developed invariant QCD coupling offers a more robust framework for theoretical calculations.
• This approach enhances the reliability of perturbative predictions in quantum chromodynamics.
• The method shows promise for refining analyses of particle physics processes like e^{+}e^{-} scattering and τ decays.