Drell–Yan lepton-pair production: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>q</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math> resummation at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mi>LL</mml:mi></mml:mrow></mml:math> accuracy and fiducial cross sections at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mi>LO</mml:mi></mml:mrow></mml:math>

We present high-accuracy QCD predictions for the transverse-momentum (${q}_{T}$) distribution and fiducial cross sections of Drell--Yan lepton pairs produced in hadronic collisions. At small values of ${q}_{T}$ we resum to all perturbative orders the logarithmically enhanced contributions up to next-to-next-to-next-to-leading logarithmic (${\mathrm{N}}^{3}\mathrm{LL}$) accuracy, including all the next-to-next-to-next-to-leading order (${\mathrm{N}}^{3}\mathrm{LO}$) [i.e., $\mathcal{O}({\ensuremath{\alpha}}_{S}^{3})$] terms. Our resummed calculation has been implemented in the public numerical program DYTurbo, which produces fast and precise predictions with the full dependence on the final-state lepton kinematics. We consistently combine our resummed results with the known $\mathcal{O}({\ensuremath{\alpha}}_{S}^{3})$ fixed-order predictions at large values of ${q}_{T}$ thus also obtaining full ${\mathrm{N}}^{3}\mathrm{LO}$ accuracy for fiducial cross sections. We show numerical results at LHC energies discussing the reduction of the perturbative uncertainty with respect to lower-order calculations.

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