Frontiers in Physics (Jan 2022)
Achieving Effective Renormalization Scale and Scheme Independence via the Principle of Observable Effective Matching
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 scale (PS) and dynamical scale-dependent theory at loop orders at which RSS independence is guaranteed. This is aimed toward 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) is experimentally determined at this scale, 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 ratio Re+e− for e+e− → hadrons, which is demonstrated to achieve scale and scheme independence utilizing the three- and four-loop order MS̄ 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 311Re+e−eff=1.052431−0.0006+0.0006 at Q = 31.6GeV, which is in excellent agreement with the experimental value of 311Re+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 and statistical and condensed matter physics.
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