Extractions of the strong coupling from collider data without PDF refitting are biased

Abstract

We present an explicit demonstration that a determination of the strong coupling constant $α_s(m_Z)$ from deep-inelastic scattering and hadron collider data without a simultaneous determination of the parton distribution functions (PDFs) leads to a biased result for both the central value and the uncertainty, even in the ideal scenario (closure test) where there are no internal tensions between datasets and where theoretical calculations describe perfectly the experimental measurements. Specifically, we show that a determination of $α_s(m_Z)$ from a single process leads in general to a result that differs from the global best fit more than the value of $α_s(m_Z)$ that is actually favoured by this process.

Figures (3)

• Figure 1: Comparison between the standard deviation of a pair of correlated variables $(\alpha_s,\theta)$ and the one-sigma range for the variable $\alpha_s$ along the best-fit line of $\theta$. The true uncertainty on $\alpha_s$ is denoted by $\sigma_\alpha$ and the uncertainty obtained by not simultaneously fitting $\theta$ is denoted by $\sigma_{\rm old}$. (Figure taken from Ref. Ball:2018iqk).
• Figure 2: Left: values of $\alpha_s(m_z)$ extracted from the partial $\chi^2$ (real data) evaluated for separate groups of processes for the determination of Ref. Ball:2025xgq. The vertical dashed line indicates the best fit value from the global fit. Right: same, now for the $\alpha_s(m_z)$ values extracted from closure test artificial data generated with $\alpha_s^{\rm true}=0.118$ (vertical dashed line).
• Figure 3: Contours of $\chi^2$ contours in (PDF, $\alpha_s$) space (see text) (Figure taken from Ref. Forte:2020pyp).