A first determination of the strong coupling $$\alpha _S$$ at approximate $$\textrm{N}^3$$LO order in a global PDF fit

We present the first determination of the value of the strong coupling via a simultaneous global fit of the proton parton distribution functions (PDFs) at approximate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mtext>N</mml:mtext> <mml:mn>3</mml:mn></mml:msup> </mml:math> LO (a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mtext>N</mml:mtext> <mml:mn>3</mml:mn></mml:msup> </mml:math> LO) order in QCD. This makes use of the MSHT global PDF fitting framework, and in particular the recent theoretical advances t l;;mhat allow a PDF fit to now be performed at this order. The value of the strong coupling is found to be <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:mo>(</mml:mo> <mml:mrow><mml:msup><mml:mi>aN</mml:mi> <mml:mn>3</mml:mn></mml:msup> <mml:mi>LO</mml:mi></mml:mrow> <mml:mo>)</mml:mo></mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0.1170</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.0016</mml:mn></mml:mrow> </mml:math> . This is in excellent agreement with the NNLO value of <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:mo>(</mml:mo> <mml:mtext>NNLO</mml:mtext> <mml:mo>)</mml:mo></mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0.1171</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.0014</mml:mn></mml:mrow> </mml:math> , indicating that good perturbative convergence has been found. The resulting uncertainties, calculated using the MSHT dynamic tolerance procedure, are somewhat larger, but more accurate, at a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mtext>N</mml:mtext> <mml:mn>3</mml:mn></mml:msup> </mml:math> LO, due to the missing higher order theoretical uncertainties that are included at this order, but not at NNLO. We in addition present a detailed breakdown of the individual dataset sensitivity to the value of the strong coupling, with special focus on the impact of fitting dijet rather than inclusive jet data. This choice is found to have a non-negligible impact, but with overall good consistency found, especially at a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mtext>N</mml:mtext> <mml:mn>3</mml:mn></mml:msup> </mml:math> LO.