Strong Coupling Constant Determination from the new CTEQ-TEA Global QCD Analysis

TL;DR

This paper reports a new NNLO global QCD determination of the strong coupling constant $α_s(M_Z)$ from the CT25 CT20-era PDF analysis, incorporating high-precision Run-2 LHC measurements and a broad data set. It develops and employs multiple uncertainty frameworks—global and dynamic tolerances, Bayesian hierarchical models, and Gaussian mixture models—to explore the robustness of $α_s(M_Z)$ against PDF parametrizations, correlated systematics, and data tensions. A key contribution is the introduction of data-clustering safety to ensure replicable uncertainty estimates across clustering schemes. The final result is $α_s(M_Z)=0.1183^{+0.0023}_{-0.0020}$ (68% CL), with a careful synthesis of several methodologies, highlighting the role of systematic error modeling in precision QCD determinations and offering a path toward more reliable uncertainty quantification in future global fits.

Abstract

We present a new determination of the strong coupling constant $α_s$ from a global QCD analysis CT25 of parton distribution functions (PDFs) that incorporates high-precision experimental measurements from the Run-2 of the Large Hadron Collider together with a large sample of other measurements over a wide interval of energies. This work addresses two objectives: providing an up-to-date determination of $α_s$ using NNLO calculations and a sensitive nucleon data set within a self-consistent framework, and critically assessing the robustness of the $α_s(M_Z)$ extraction in light of systematic uncertainties as well as correlations of $α_s(M_Z)$ with the functional forms of PDFs and other model parameters. In regard to the uncertainty assessment, we demonstrate that some commonly used criteria, including the dynamical tolerance and Bayesian hierarchical models, may produce significantly different or even unstable estimates for the net $α_s$ uncertainty, and we introduce a concept of \textit{data-clustering safety} that the replicable uncertainty estimates must satisfy. Based on this in-depth examination of the CT25 global hadronic data set using a combination of analysis methods, and after demonstrating a weak correlation between $α_s$ and the functional forms of CT25 PDF parametrizations, we find $α_s(M_Z)=0.1183^{+0.0023}_{-0.0020}$ at the 68\% credibility level.

Figures (15)

• Figure 1: $\chi^2$ of the data versus $\alpha_s(M_Z)$ from the scan of the nominal CT25 PDF parametrization form and PDF+$\alpha_s$ fits with 287 alternative parametrizations.
• Figure 2: $\chi^2$ profiles for different ksys settings: $\{\texttt{ksys}_{DIS},\texttt{ksys}_{DY},\texttt{ksys}_{\textrm{Jet} + t{\bar{t}}} \}$ = $\{1,1,1\}$, $\{1,1,2\}$, $\{1,2,2\}$, and $\{2,2,2\}$. These are obtained with a fixed CT25 PDF set determined with the default ksys=1 setting.
• Figure 3: Separate contributions to $\chi^2_{R}/N_\textrm{pt}$ from the best-fit summed data residuals and nuisance parameters, as exemplified in Eq. \ref{['minchi2']}, for the four ksys combinations shown in Fig. \ref{['fig:chi2_for_ksysXYZ']}. The theory predictions are obtained with the CT25NNLO PDFs determined using ksys={1,1,1}.
• Figure 4: $\Delta\chi^2$ profiles vs. $\alpha_s(M_Z)$ for the ksys=1 (left) and ksys=2 (right) prescriptions. Curves are shown for the full-baseline global fit (black), DIS (purple), DY (green), jets (blue), $t\bar{t}$ (red), and jet+$t\bar{t}$ (dashed magenta). Each parabola is obtained from the same global fit result, projected onto the corresponding data subset.
• Figure 5: $\Delta\chi^2$ profiles for individual jet-production measurements only in the $\alpha_s$ scans with the ksys=1 (left) and ksys=2 (right) prescriptions for jet data sets. The $\alpha_s(M_Z)$ values in the plot headers are for the jet data subset only.