The Zγ transverse-momentum spectrum at NNLO+N3LL

Abstract

We consider the transverse-momentum ($p_T$) distribution of $Zγ$ pairs produced in hadronic collisions. Logarithmically enhanced contributions at small $p_T$ are resummed to all orders in QCD perturbation theory and combined with the fixed-order prediction. We achieve the most advanced prediction for the $Zγ$ $p_T$ spectrum by matching next-to-next-to-next-to-leading logarithmic (N$^3$LL) resummation to the integrated cross section at next-to-next-to-leading order (NNLO). By considering $\ell^+\ell^-γ$ production at the fully differential level, including spin correlations, interferences and off-shell effects, arbitrary cuts can be applied to the leptons and the photon. We present results at the LHC in presence of fiducial cuts and find agreement with the $13$\,TeV ATLAS data at the few-percent level.

Figures (7)

• Figure 1: Feynman diagrams for the production of two charged leptons and a photon: (a-b) sample tree-level diagrams in the quark-annihilation channel contributing at LO; (c) sample loop-induced diagram in the gluon-fusion channel contributing at NNLO.
• Figure 2: Panel (a) and (c): transverse-momentum spectrum of the $Z\gamma$ pair at NLO (purple, dot-dashed) and NNLO (orange, dashed), and the expansion of the NLL (blue, dotted) and N$^3$LL (red, solid) cross section. The lower frame shows the relative difference between the fixed-order cross section and the expansion, normalized to the latter. Panel (b) and (d): the upper frame shows the difference at the cumulative level between NLO and NLL expansion (blue, dotted), and between NNLO and N$^3$LL expansion (red, solid). The lower frame shows the same results for the derivative of the cumulative cross section with respect to $\ln(p_{T,\ell\ell\gamma}/{\rm GeV})$.
• Figure 3: Panel (a) and (b): $p_{T,\ell\ell\gamma}$ spectrum at NLO (black, dotted), NLL (brown, dash-double-dotted), and NLO+NLL (magenta, dash-dotted) in the small-$p_{T,\ell\ell\gamma}$ (panel (a)) and large-$p_{T,\ell\ell\gamma}$ (panel (b)) region. The lower frames show the ratio to the central NLO+NLL prediction. Panel (c) and (d): $p_{T,\ell\ell\gamma}$ spectrum at NNLO (red, dashed), N$^3$LL (green, double-dash-dotted), and NNLO+N$^3$LL (blue, solid) in the small-$p_{T,\ell\ell\gamma}$ (panel (a)) and large-$p_{T,\ell\ell\gamma}$ (panel (b)) region. The lower frames show the ratio to the central NNLO+N$^3$LL prediction.
• Figure 4: $p_{T,\ell\ell\gamma}$ spectrum at NLO+NLL (magenta, dash-dotted) and NNLO+N$^3$LL (blue, solid) in the inclusive (panel (a)) and fiducial (panel (b)) setup. The lower frames show the ratio to the central NNLO+N$^3$LL prediction.
• Figure 5: $p_{T,\ell\ell\gamma}$ spectrum at NNLO+N$^3$LL in the additive matching scheme (blue, solid) and in the multiplicative matching scheme (green, long-dashed) in the inclusive (panel (a) and (b)) and fiducial (panel (c) and (d)) setup, showing the small-$p_{T,\ell\ell\gamma}$ (panel (a) and (c)) and large-$p_{T,\ell\ell\gamma}$ (panel (b) and (d)) region. The lower frames show the ratio to the central prediction in the additive scheme.