We identify a property of renormalizable SU(N)/U(1) gauge theories, intrinsic conformality (iCF), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in perturbative QCD (pQCD): the ${\mathrm{PMC}}_{\infty }$. This new method reflects the underlying conformal properties displayed by pQCD at next-to-next-to-leading order, eliminates the scheme dependence of pQCD predictions, and is consistent with the general properties of the principle of maximum conformality (PMC). We introduce a new method to identify conformal and $\beta$-terms which can be applied from either a numerical or an analytical calculations. We illustrate the ${\mathrm{PMC}}_{\infty }$ for the thrust and C-parameter distributions in $e^{+}{e}^{-}$ annihilation and then show how to apply this new method to general observables in QCD. We point out how the implementation of the ${\mathrm{PMC}}_{\infty }$ can significantly improve the precision of pQCD predictions; its implementation in a multiloop analysis also simplifies the calculation of higher order corrections in a general renormalizable gauge theory.

• Received 5 February 2020
• Accepted 23 June 2020

DOI:https://doi.org/10.1103/PhysRevD.102.014015

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Published by the American Physical Society