Drell-Yan production at ${\mathrm{NNLL}}^{\prime }+\mathrm{NNLO}$ matched to parton showers

We present results for Drell-Yan production from the geneva Monte-Carlo framework. We combine the fully differential next-to-next-to leading order (NNLO) calculation with higher-order resummation in the 0-jettiness resolution variable. The resulting parton-level events are further combined with parton showering and hadronization provided by pythia8. The 0-jettiness resummation is carried out to ${\mathrm{NNLL}}^{\prime }$, which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment of perturbative uncertainties. In this way, inclusive observables are correct to NNLO, up to small power corrections in the resolution cutoff. Furthermore, the perturbative accuracy of zero-jet-like resummation variables is significantly improved beyond the parton shower approximation. We provide comparisons with LHC measurements of Drell-Yan production at 7 TeV from ATLAS, CMS, and LHCb. As already observed in $e^{+}{e}^{-}$ collisions, for resummation-sensitive observables, the agreement with data is noticeably improved by using a lower value of ${\alpha }_s(M_Z)=0.1135$.

Figure 1

Comparison of the full, singular, and nonsingular ${\mathcal{T}}_0$ distribution at ${\mathrm{NNLO}}_0$.

Figure 2

The nonsingular cumulant for 0-jettiness, as a function of ${\mathcal{T}}_0^{\text{cut}}$. The black (blue) curve shows the NLO (pure NNLO) nonsingular cumulant, coming from the $f_1$ and $f_2$ terms in Eq. (35).

Figure 3

Validation of the ${\mathcal{T}}_0$ spectrum in geneva. The analytic ${\mathrm{NNLL}}^{\prime }+\mathrm{NNLO}$ ${\mathcal{T}}_0$ resummation is compared to the partonic and showered results of geneva, but before the addition of nonperturbative effects.

Figure 4

Comparison of the showered and hadronized ${\mathcal{T}}_0$ spectra in geneva.

Figure 5

Comparison of geneva with the NNLO rapidity distribution of the vector boson. The orange curve shows the results from dynnlo, while the black histogram shows the geneva result. For geneva, the uncertainties shown are the FO uncertainties as described in the text.

Figure 6

Comparison of geneva with the NNLO rapidity distribution of the negatively charged lepton. The orange curve shows the results from dynnlo, while the black histogram shows the geneva result. For geneva, the uncertainties shown are the FO uncertainties as described in the text.

Figure 7

Comparison of geneva with NNLO transverse-momentum distribution of the negatively charged lepton. The orange curve shows the results from dynnlo, while the black histogram shows the genevaresult. For geneva, the uncertainties shown are the FO uncertainties as described in the text.

Figure 8

Comparison of geneva with the $q_T$ distribution from dyqt. The $\mathrm{NNLL}+{\mathrm{NLO}}_1$ ($\mathrm{NLL}+{\mathrm{LO}}_1$) results from dyqt are shown in blue (green), and the geneva results are shown in black. The geneva results are much closer to dyqt’s NNLL results than NLL results.

Figure 9

Comparison of geneva with the analytic $q_T$ distribution at $\mathrm{NNLL}+{\mathrm{NLO}}_1$ from Ref. [88]. The analytic results are shown in blue, and the geneva results are shown in black.

Figure 10

Comparison of geneva with the analytic ${\varphi }^{*}$ distribution at $\mathrm{NNLL}+{\mathrm{NLO}}_1$ from Ref. [88]. The analytic results are shown in blue, and the geneva results are shown in black.

Figure 11

Comparison of geneva with the zero-jet cross section as a function of $p_T^{\text{cut}}$ from jetvheto [92] at $\mathrm{NNLL}+\mathrm{NNLO}$. The analytic results are shown in blue, and the geneva results are shown in black. For geneva, the uncertainties are the FO uncertainties only; see the text for details.

Figure 12

Comparison of geneva with the rapidity of the vector boson from the ATLAS study in [98]. The geneva results with default values of ${\alpha }_{\mathrm{s}}(M_Z)$ and with ${\alpha }_{\mathrm{s}}(M_Z)=0.1135$ are shown in orange and green, respectively, while the ATLAS points are shown in black.

Figure 13

Comparison of geneva with the rapidity of the vector boson from the CMS study in [99]. The geneva results with default values of ${\alpha }_{\mathrm{s}}(M_Z)$ and with ${\alpha }_{\mathrm{s}}(M_Z)=0.1135$ are shown in orange and green, respectively, while the CMS points are shown in black.

Figure 14

Comparison of geneva with the rapidity of the vector boson from the LHCb study in [100]. The geneva results with default values of ${\alpha }_{\mathrm{s}}(M_Z)$ and with ${\alpha }_{\mathrm{s}}(M_Z)=0.1135$ are shown in orange and green, respectively, while the LHCb points are shown in black.

Figure 15

Comparison of geneva with data on inclusive and exclusive jet cross sections from the ATLAS study in [102]. The geneva results with default values of ${\alpha }_{\mathrm{s}}(M_Z)$ and with ${\alpha }_{\mathrm{s}}(M_Z)=0.1135$ are shown in orange and green, respectively, while the ATLAS points are shown in black.

Figure 16

Comparison of geneva with the transverse momentum of the leading jet from the ATLAS study in [102]. The geneva results with default values of ${\alpha }_{\mathrm{s}}(M_Z)$ and with ${\alpha }_{\mathrm{s}}(M_Z)=0.1135$ are shown in orange and green, respectively, while the ATLAS points are shown in black.

Figure 17

Comparison of geneva with the ${\varphi }^{*}$ distribution from the ATLAS study in [103]. The geneva results with default values of ${\alpha }_{\mathrm{s}}(M_Z)$ and with ${\alpha }_{\mathrm{s}}(M_Z)=0.1135$ are shown in orange and green, respectively, while the ATLAS points are shown in black.

Figure 18

Comparison of geneva with the ${\varphi }^{*}$ distribution from the LHCb study in [100]. The geneva results with default values of ${\alpha }_{\mathrm{s}}(M_Z)$ and with ${\alpha }_{\mathrm{s}}(M_Z)=0.1135$ are shown in orange and green, respectively, while the LHCb points are shown in black.

Figure 19

Comparison of geneva with the transverse momentum of the vector boson from the CMS study in [99]. The geneva results with default values of ${\alpha }_{\mathrm{s}}(M_Z)$ and with ${\alpha }_{\mathrm{s}}(M_Z)=0.1135$ are shown in orange and green, respectively, while the CMS points are shown in black.

Figure 20

Comparison of geneva with the transverse momentum of the vector boson both inclusive (top-left) and in different bins of vector-boson rapidity $Y$ from the ATLAS study in [104]. The geneva results with default values of ${\alpha }_{\mathrm{s}}(M_Z)$ and with ${\alpha }_{\mathrm{s}}(M_Z)=0.1135$ are shown in orange and green, respectively, while the ATLAS points are shown in black.