Extraction of the strong coupling with HERA and EIC inclusive data

Abstract Sensitivity to the strong coupling $$\alpha _S(M^2_Z)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>S</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> is investigated using existing Deep Inelastic Scattering data from HERA in combination with projected future measurements from the Electron Ion Collider (EIC) in a next-to-next-to-leading order QCD analysis. A potentially world-leading level of precision is achievable when combining simulated inclusive neutral current EIC data with inclusive charged and neutral current measurements from HERA, with or without the addition of HERA inclusive jet and dijet data. The result can be obtained with substantially less than one year of projected EIC data at the lower end of the EIC centre-of-mass energy range. Some questions remain over the magnitude of uncertainties due to missing higher orders in the theoretical framework.