Drell-Yan lepton-pair production: $q_T$ resummation at N$^3$LL accuracy and fiducial cross sections at N$^3$LO

We present high-accuracy QCD predictions for the transverse-momentum (<math display="inline"><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math>) distribution and fiducial cross sections of Drell–Yan lepton pairs produced in hadronic collisions. At small values of <math display="inline"><msub><mi>q</mi><mi>T</mi></msub></math> we resum to all perturbative orders the logarithmically enhanced contributions up to next-to-next-to-next-to-leading logarithmic (<math display="inline"><mrow><msup><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LL</mi></mrow></math>) accuracy, including all the next-to-next-to-next-to-leading order (<math display="inline"><mrow><msup><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>) [i.e., <math display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>S</mi><mn>3</mn></msubsup><mo stretchy="false">)</mo></math>] 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 <math display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>S</mi><mn>3</mn></msubsup><mo stretchy="false">)</mo></math> fixed-order predictions at large values of <math display="inline"><msub><mi>q</mi><mi>T</mi></msub></math> thus also obtaining full <math display="inline"><mrow><msup><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math> 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.