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We present the results for the associated production of Higgs boson withvector boson computed at threshold N$^3$LO in QCD. We use the recentlyavailable result on the threshold contributions to the inclusive Drell-Yanproduction cross-section at third order in strong coupling constant. We haveimplemented it in the publicly available computer package vh@nnlo, therebyobtaining the numerical impact of threshold N$^3$LO contributions for the firsttime. We find that the inclusion of such corrections do reduce theoreticaluncertainties resulting from the renormalization scale.

Associated production of Higgs boson with vector boson at threshold N$^3$LO in QCD