Determination of $\hat{I}{\pm }_s(M_Z)$ via a high-precision effective coupling $\hat{I}{\pm }_s^{g_1}(Q)$

Abstract

We propose a novel method to determine the strong coupling of quantum chromodynamics (QCD) and fix its running behavior at all scales by using the Bjorken sum rules (BSR). The BSR defines an effective coupling $\hat{I}{\pm }_s^{g_1}(Q)$ which includes the nonperturbative high-twist corrections and perturbative QCD (pQCD) corrections to the leading-twist part. For the leading-twist part of $\hat{I}{\pm }_s^{g_1}(Q)$, we adopt the infinite-order scale-setting procedure of the principle of maximum conformality (${\mathrm{PMC}}_{\infty }$) to deal with its pQCD corrections, which reveals the intrinsic conformality of series and eliminates conventional renormalization scheme-and-scale ambiguities. Using the ${\mathrm{PMC}}_{\infty }$ approach, we not only eliminate \textit{the first kind of residual scale dependence} due to uncalculated higher-order terms, but also resolve the previous ``self-consistence problem". The holographic light-front QCD model is used for $\hat{I}{\pm }_s^{g_1}(Q)$ in the infrared region, which also reveals a conformal behavior at $Q\to 0$. As a combination, we obtain a precise $\hat{I}{\pm }_s^{g_1}(Q)$ at all scales, which matches well with the known experimental data with $p$-value $\sim 99\%$, we determine the strong coupling constant at the critical scale $M_Z$, $\hat{I}{\pm }_s(M_Z)=0.1191\pm 0.0012\mp 0.0006$, where the first error comes from $\hat{I}”\hat{I}º$ of LFHQCD model and the second error is from \textit{the second kind of residual scale dependence} that is negligible.

13 pages, 4 figures