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Threshold resummation at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>LL</mml:mi></mml:mrow><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:mrow></mml:math> accuracy and approximate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">…
We advance the threshold resummation formalism for semi-inclusive deep-inelastic scattering (SIDIS) to next-to-next-to-next-to-leading logarithmic (N$^{3}$LL) order, including the three-loop hard factor. We expand the results in the strong coupling to obtain approximate next-to-next-to-next-to-leading order (N$^{3}$LO) corrections for the SIDIS cross section. In Mellin moment space, these corrections include all terms …