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The cross-section for Drell-Yan production of a vector boson has beenpreviously calculated at next-to-next-to-leading order, supplemented byenhanced logarithmic terms associated with the threshold region. In this paper,we calculate a large set of enhanced terms associated with the colour structure$C_F^3$ at N$^3$LO, for the double real emission contribution in thequark-antiquark channel, as an expansion around the threshold region up to andincluding the first subleading power. We perform our calculation using themethod of regions, which systematically characterises all contributionsaccording to whether the virtual gluon is (next-to) soft, collinear or hard innature. Our results will prove useful for developing general formalisms forclassifying next-to-leading power (NLP) threshold effects. They are alsointeresting in their own right, given that they constitute a previously unknowncontribution to the Drell-Yan cross-section at ${\cal O}(\alpha_s^3)$.

On next-to-leading power threshold corrections in Drell-Yan production at N$^3$LO