Drell-Yan lepton-pair production: $q_T$ resummation at approximate N$^4$LL+N$^4$LO accuracy

We consider Drell–Yan lepton pairs produced in hadronic collisions. We present high-accuracy QCD predictions for the transverse-momentum (<math altimg="si1.svg"><msub><mrow><mi>q</mi></mrow><mrow><mi>T</mi></mrow></msub></math>) distribution and fiducial cross sections in the small <math altimg="si1.svg"><msub><mrow><mi>q</mi></mrow><mrow><mi>T</mi></mrow></msub></math> region. We resum to all perturbative orders the logarithmically enhanced contributions up to the next-to-next-to-next-to-next-to-leading logarithmic (N<sup loc="post">4</sup>LL) accuracy and we include the hard-virtual coefficient at the next-to-next-to-next-to-leading order (N<sup loc="post">3</sup>LO) (i.e. <math altimg="si11.svg"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo stretchy="false">)</mo></math>) with an approximation of the N<sup loc="post">4</sup>LO coefficients. The massive axial-vector and vector contributions up to three loops have also been consistently included. The resummed partonic cross section is convoluted with approximate N<sup loc="post">3</sup>LO parton distribution functions. We show numerical results at LHC energies of resummed <math altimg="si1.svg"><msub><mrow><mi>q</mi></mrow><mrow><mi>T</mi></mrow></msub></math> distributions for <math altimg="si3.svg"><mi>Z</mi><mo stretchy="false">/</mo><msup><mrow><mi>γ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>,</mo><msup><mrow><mi>W</mi></mrow><mrow><mo>±</mo></mrow></msup></math> production and decay, including the <math altimg="si15.svg"><msup><mrow><mi>W</mi></mrow><mrow><mo>±</mo></mrow></msup></math> and <math altimg="si5.svg"><mi>Z</mi><mo stretchy="false">/</mo><msup><mrow><mi>γ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> ratio, estimating the corresponding uncertainties from missing higher orders corrections and from incomplete or missing perturbative information coefficients at N<sup loc="post">4</sup>LL and N<sup loc="post">4</sup>LO. Our resummed calculation has been encoded in the public numerical program DYTurbo.