<p>We provide state-of-the-art precision QCD predictions for the fiducial <i>W</i> and <i>Z</i> boson transverse momentum spectra at the LHC at N<sup>3</sup>LL<sup><i>′</i></sup> and approximate N<sup>4</sup>LL in resummed perturbation theory, matched to available <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25611_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msubsup> <mi>α</mi> <mi>s</mi> <mn>3</mn> </msubsup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({\alpha}_s^3\right) \)</EquationSource> </InlineEquation> fixed-order results. Our predictions consistently combine all information from across the spectrum in a unified way, ranging from the nonperturbative region of small transverse momenta to the fixed-order tail, with an emphasis on estimating the magnitude of residual perturbative uncertainties, and in particular of those related to the matching. Parametric uncertainties related to the strong coupling, the collinear PDFs, and the nonperturbative transverse momentum-dependent (TMD) dynamics are studied in detail. To assess the latter, we explicitly demonstrate how the full complexity of flavor and Bjorken <i>x</i>-dependent TMD dynamics can be captured by a single, effective nonperturbative function for the resonant production of any given vector boson at a given collider. We point out that the cumulative <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25611_Article_IEq2.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>p</mi> <mi>T</mi> <mi>Z</mi> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {p}_T^Z \)</EquationSource> </InlineEquation> cross section at the level of precision enabled by our predictions provides strong constraining power for PDF determinations at full N<sup>3</sup>LO.</p>

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Drell-Yan transverse-momentum spectra at N3LL and approximate N4LL with SCETlib

  • Georgios Billis,
  • Johannes K. L. Michel,
  • Frank J. Tackmann

摘要

We provide state-of-the-art precision QCD predictions for the fiducial W and Z boson transverse momentum spectra at the LHC at N3LL and approximate N4LL in resummed perturbation theory, matched to available O α s 3 \( \mathcal{O}\left({\alpha}_s^3\right) \) fixed-order results. Our predictions consistently combine all information from across the spectrum in a unified way, ranging from the nonperturbative region of small transverse momenta to the fixed-order tail, with an emphasis on estimating the magnitude of residual perturbative uncertainties, and in particular of those related to the matching. Parametric uncertainties related to the strong coupling, the collinear PDFs, and the nonperturbative transverse momentum-dependent (TMD) dynamics are studied in detail. To assess the latter, we explicitly demonstrate how the full complexity of flavor and Bjorken x-dependent TMD dynamics can be captured by a single, effective nonperturbative function for the resonant production of any given vector boson at a given collider. We point out that the cumulative p T Z \( {p}_T^Z \) cross section at the level of precision enabled by our predictions provides strong constraining power for PDF determinations at full N3LO.