AUTHOR=Chishtie Farrukh A. 

TITLE=Achieving Effective Renormalization Scale and Scheme Independence via the Principle of Observable Effective Matching

JOURNAL=Frontiers in Physics

VOLUME=Volume 9 - 2021

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.765960

DOI=10.3389/fphy.2021.765960

ISSN=2296-424X

ABSTRACT=In this work, we explicate a new approach for eliminating renormalization scale and scheme (RSS) dependence in observables. We develop this approach by matching RSS dependent observables such as cross sections and decay rates) to a theory which is independent of both these forms of dependencies. We term the fundamental basis behind this approach as the Principle of Observable Effective Matching (POEM), which entails matching of a scale and scheme dependent observable with the fully physical and dynamical scale (PS) dependent theory at loop orders at which RSS independence is guaranteed. This is aimed towards achieving so-called ``effective" RSS independent expressions, as the resulting dynamical dependence is derived from a particular order in RSS dependent perturbation theory. With this matching at a PS at which the coupling (and masses) are experimentally determined at this scale, and we obtain an ``Effective Theoretical Observable (ETO)'', a finite-order RSS independent version of the RSS dependent observable. We illustrate our approach with a study of the cross section \textcolor{blue}{ratio} $R_{e^{+}e^{-}}$ for $e^{+}e^{-}\rightarrow$ hadrons, which is demonstrated to achieve scale and scheme independence utilizing the 3- and 4-loop order $\overline{MS}$ scheme expression in QCD perturbation theory via matching at both one-loop and two-loop orders for obtaining the ETO. With two-loop matching, we obtain an ETO prediction of $\frac{3}{11}R_{e^{+}e^{-}}^{eff}=1.052431_{-0.0006}^{+0.0006}$ at $Q=31.6 GeV$, which is in excellent agreement with the experimental value of $\frac{3}{11}R_{e^{+}e^{-}}^{exp}=1.0527_{-0.005}^{+0.005}$. Given its new conceptual basis, ease of use and performance, we contend that POEM be explored in its application for obtaining ETOs for predicting RSS independent observables across domains of high energy theory and phenomenology, as well as other areas of fundamental and applied physics, such as cosmology, statistical and condensed matter physics.