The strong coupling from the IR to the UV extremes: Determination of $α_s$ and prospects from EIC and JLab at 22 GeV

TL;DR

The paper demonstrates that the Bjorken sum rule can be exploited to determine the strong coupling $α_s$ across a broad range of scales, including the nonperturbative infrared, by defining an effective charge $α_{g_1}$ from the isovector moment $Γ_1^{p-n}$. By combining existing data with future measurements at the Electron-Ion Collider (EIC) and Jefferson Lab at 22 GeV (JLab@22), it maps $α_s(Q)$ over four to five orders of magnitude and forecasts high-precision determinations of $α_s(M_Z)$, with about 1.3% relative precision from EIC and ~0.6% from JLab@22. The approach leverages simple $Q^2$ evolution, minimal nonperturbative inputs, and the effective-charge framework to provide RS-independent results that agree with AdS/QCD and Schwinger-Dyson/Lattice QCD predictions at low $Q^2$ while remaining consistent with pQCD at high $Q^2$. This work underscores the Bjorken sum rule as a powerful, model-insensitive probe of QCD dynamics and a route to testing higher-loop running and potential new physics through precise, complementary measurements.

Abstract

We discuss how the Bjorken sum rule allows access to the QCD running coupling $α_s$ at any scale, including in the deep infrared IR domain. The Bjorken sum data from Jefferson Lab, together with the world data on $α_s$ reported by the Particle Data Group, allow us to determine the running of $α_s(Q)$ over five orders of magnitude in four-momentum $Q$. We present two possible future measurements of the running of $α_s(Q)$ using the Bjorken sum rule: the first at the EIC, covering the range $1.5 < Q < 8.7$ GeV, and the second at Jefferson Lab at 22 GeV, covering the range $1.0 < Q < 4.7$ GeV.

Figures (3)

• Figure 1: $\alpha_{g_1}/\pi$ at all scales. The low $Q$ data (light blue) are from CERN, DESY, JLab and SLAC Deur:2021klh, while the large $Q$ dataset (dark blue) is the PDG compilation ParticleDataGroup:2024cfk transformed to the $g_1$ scheme. The red line is the prediction deTeramond:2024ikl incorporating AdS/QCD constraints at low $Q$ and pQCD ones at large $Q$. The blue line is the simple fit form $aT_r/\ln([Q^2+Q^2_r]/\Lambda^2)$ with $a$=1.56, $T_r$=$(1+(\pi-1)/(e^{(Q-f)/g}+1))$, $Q_r$=$b/(e^{(Q^2-c)/d} +1)$, $\Lambda$=0.246 GeV, $b=$0.808 GeV, $c$=0.11 GeV$^2$, $d$=0.20 GeV$^2$, $f$=1.29 GeV and $g$=0.59 GeV Deur:2025rjo.
• Figure 2: Expected accuracy for $\alpha_s(M^2_z)$ from EIC and JLab@22 compared to the three most precise world data ParticleDataGroup:2024cfk.
• Figure 3: Contributions from higher loops on the running of $\alpha_s$: red ($\beta_1$, i.e., NLO), blue ($\beta_2$, N$^2$LO) and magenta ($\beta_3$, N$^2$LO) lines. The black error bars centered on the horizontal 0-line show the uncertainties on $\alpha_s$ from the world data (Ref. ParticleDataGroup:2024cfk). The uncertainties expected from EIC and JLab@22GeV are shown by the blue and red error bars, respectively. JLab@22GeV+EIC can for the first time separate multi-loop effects, where non-QCD physics, including possible contributions of physics beyond the Standard Model, arise.