The transverse momentum spectrum of weak gauge bosons at N 3 LL + NNLO

Abstract

We present accurate QCD predictions for the transverse momentum ( $p_{\perp }$ ) spectrum of electroweak gauge bosons at the LHC for $13\mathrm{TeV}$ collisions, based on a consistent combination of a NNLO calculation at large $p_{\perp }$ and N ${}^3$ LL resummation in the small $p_{\perp }$ limit. The inclusion of higher order corrections leads to substantial changes in the shape of the differential distributions, and the residual perturbative uncertainties are reduced to the few percent level across the whole transverse momentum spectrum. We examine the ratio of $p_{\perp }$ distributions in charged- and neutral-current Drell-Yan production, and study different prescriptions for the estimate of perturbative uncertainties that rely on different degrees of correlation between these processes. We observe an excellent stability of the ratios with respect to the perturbative order, indicating a strong correlation between the corresponding QCD corrections.

Fig. 1

Comparison of the normalised transverse momentum distribution for neutral and charged Drell–Yan pair production at NLL+LO (green, dotted), NNLL + NLO (blue, dashed) and N${}^3$LL + NNLO (red, solid) at $\sqrt{s}=13\mathrm{TeV}$ for the fiducial volume defined in the text. The lower panel shows the ratio to the NNLL + NLO result

Fig. 2

Comparison of the normalised transverse momentum distribution for neutral and charged Drell–Yan pair production at NNLO (green, dotted), NNLL + NLO (blue, dashed) and N${}^3$LL + NNLO (red, solid) at $\sqrt{s}=13\mathrm{TeV}$ for the fiducial volume defined in the text. For reference, the Pythia8 prediction in the AZ tune is also shown, and the lower panel shows the ratio of each prediction to the Pythia8 result

Fig. 3

Difference Eq. (13) between the matched and the resummed predictions for the Z (green, dotted), $W^{+}$ (blue, dashed) and $W^{-}$ (red, solid) normalised distributions. The lower panel shows the ratio of ${\Delta }^{{\mathrm{N}}^3\mathrm{LL}}$ to the N${}^3$LL + NNLO matched result

Fig. 4

Ratios of $Z/W^{+}$ and $W^{-}/W^{+}$ normalised differential distributions at NLL + LO (green, dotted), NNLL+NLO (blue, dashed) and N${}^3$LL + NNLO (red, solid) at $\sqrt{s}=13\mathrm{TeV}$. The three lower panels show three different prescriptions for the theory uncertainty, as described in the text

Fig. 5

Ratios of $Z/W^{+}$ and $W^{-}/W^{+}$ normalised differential distributions at NNLO (green, dotted), NNLL+NLO (blue, dashed) and N${}^3$LL + NNLO (red, solid) at $\sqrt{s}=13\mathrm{TeV}$. For reference, the Pythia8 prediction in the AZ tune is also shown, and the lower panels show the ratio of each prediction to the latter