The impact of inclusive electron ion collider data on the strong coupling determination in a global PDF fit

TL;DR

This paper evaluates how inclusive DIS data from the future Electron Ion Collider can influence the determination of the strong coupling $\alpha_S(M_Z^2)$ within the MSHT global PDF framework, using pseudodata generated under conservative and optimistic uncertainty scenarios. The authors perform simultaneous fits of proton PDFs and $\alpha_S(M_Z^2)$ at NNLO and $a{\rm N}^3{\rm LO}$, update theory ingredients, and explore three tension scenarios to model potential inconsistencies with existing data. They find that EIC data can modestly improve the precision of $\alpha_S(M_Z^2)$ at NNLO, with a more substantial impact in the optimistic scenario, while at $a{\rm N}^3{\rm LO}$ the potential gains are even larger; however, explicit inconsistencies between EIC pseudodata and the baseline fit can bias the extracted coupling by roughly $1$–$2\sigma$, depending on the scenario and highlighting the need for conservative error treatment. Overall, the study underscores the promising potential of the EIC to constrain the strong coupling within a global QCD analysis, while also illustrating the importance of accounting for theoretical uncertainties and possible data tensions in precision PDF fits.

Abstract

We present a study of the impact of data from the upcoming Electron Ion Collider (EIC) on the determination of the strong coupling within the context of the global MSHT fitting framework. To achieve this, we generate EIC electron-proton scattering pseudodata according to both conservative and optimistic experimental uncertainty projections and perform a simultaneous fit to obtain the proton PDFs and the value of the strong coupling. In the conservative case the impact is found to be moderate, but non-negligible, while in the optimistic case it is observed to be rather significant. These results therefore underline the promising potential for the EIC in the determination of the strong coupling. We in addition explore the impact of any potential tensions between the EIC data and the rest of the data in the global fit by injecting explicit inconsistencies into the pseudodata generation. This can lead to a noticeable bias in the extracted value of the strong coupling, highlighting the importance of accounting for all sources of theoretical uncertainty in the fit as well as the relevance of an enlarged, conservative, error definition in the determination of the strong coupling.

Figures (5)

• Figure 1: Best fit value of the strong coupling $\alpha_S(M_Z^2)$ for a range of NNLO fits, including ('w. EIC') or excluding EIC ('no EIC') pseudodata ('pd'), in the conservative scenario. The inner (outer) limits correspond to $\Delta \chi^2=1 (9)$, and are intended to be indicative of the relative uncertainty on $\alpha_S(M_Z^2)$ in different fits, rather than indicating the actual size of the uncertainty that would result from the dynamic tolerance procedure. The top (bottom) plots show the result of the globally and locally (EIC NC) preferred values.
• Figure 2: $\chi^2$ profiles corresponding to the 'w. EIC' and 'w. EIC (pd a${\rm N}^3$LO)' cases in Fig. \ref{['fig:as_NNLO']}.
• Figure 3: Best fit value of the strong coupling $\alpha_S(M_Z^2)$ for a range of a${\rm N}^3$LO fits, including or excluding EIC pseudodata. The inner (outer) limits correspond to $\Delta \chi^2=1$ (9) that result from a quadratic fit about the minimum to the corresponding global profile, and are intended to be indicative of the relative uncertainty on $\alpha_S(M_Z^2)$ in different fits, rather than indicating the actual size of the uncertainty that would result from the dynamic tolerance procedure. The left (right) plots show the result of the globally and locally (EIC NC) preferred values. Unless otherwise specified, the pseudodata correspond to the conservative scenario
• Figure 4: $\chi^2$ profiles corresponding to the 'No EIC' and 'w. EIC' cases in Fig. \ref{['fig:as_N3LO']}.
• Figure 5: Ratio of the MSHT20a${\rm N}^3$LO to NNPDF4.0a${\rm N}^3$LO charge weighted quark singlet PDFs at $Q^2=10^4\,{\rm GeV}^2$.