A comprehensive analysis of Drell-Yan production uncertainties and mass effects at moderate and low dilepton masses

TL;DR

The article develops and applies a comprehensive MVFNS framework to Drell-Yan production, delivering differential N$^3$LO predictions for neutral and charged current channels with exact heavy-quark masses up to ${\cal O}(\alpha_s^2)$. It systematically analyzes uncertainties from PDFs (including approximate N$^3$LO sets), scale variations, ${\alpha_s}$, and heavy-quark masses, and extends the MVFNS to differential observables and the CC case. The study finds that PDF uncertainties dominate at low $Q$, especially for aN$^3$LO PDFs, while QCD scale uncertainties remain sub-dominant; mass corrections are small at moderate-to-high $Q$ but can be percent-level at very low $Q$, with charm mass often having larger impact than bottom. These results inform precision tests of SM dynamics, global PDF analyses including small-$x$ regions, and provide input relevant for astrophysical neutrino predictions.

Abstract

We present a thorough investigation of the sources of uncertainties to the Drell-Yan production using state-of-the-art predictions for both neutral and charged current channels, focusing on the low invariant mass region. Differential predictions for the invariant mass spectrum are provided at N$^3$LO supplemented with exact charm and bottom quark mass effects calculated at $\mathcal{O}(α_s^2)$. The impact of PDF choices (including approximate N$^3$LO), scale variations, the variation of the strong coupling constant, and impact heavy quark mass effects on the distributions is studied in detail. We also comment on the correlation of high-energy astrophysical processes with the low-mass DY region.

Figures (11)

• Figure 1: Correlation coefficient between the cross-section rates for the neutral-current DY process at the LHC with ultra-high-energy neutrino-nucleon DIS (left) or inclusive charm production in hadron-hadron collisions (right). In both cases the energy of the projectile neutrino $E_{\nu}$ (left) or proton (right) is varied while the target hadron is considered at rest.
• Figure 2: Power-corrections to the NCDY process up to NNLO accuracy defined in eq. \ref{['eq:Sigma_power_corrections']} for the $Q$-bin (80 GeV, 105 GeV). The bands represent represent the 7-point variation of $\mu_R$ and $\mu_F$ around the central (dynamic) scale $\mu_R=\mu_F=Q$ (see section \ref{['sec:th_uncertainties']}). We observe that the power corrections vanish in the limit $m_Q \rightarrow 0$.
• Figure 3: Power-corrections to the CCDY process up to NLO accuracy for the $Q$-bin (50 GeV, 150 GeV). The bands represent the 7-point variation of $\mu_R$ and $\mu_F$ around the central (dynamic) scale $\mu_R=\mu_F=Q$ (see section \ref{['sec:th_uncertainties']}). We observe that the power corrections vanish in the limit $m_Q \rightarrow 0$.
• Figure 4: The upper panel shows the scale variation of the NCDY cross-section at $\text{N}^3$LO using MSHT20nnlo_as118 PDF sets. In the lower panel we plot the variation of the scale variation w.r.t to the central scale $\mu_R=\mu_F=Q$ and the PDF variation w.r.t to the central PDF set for $\mu_R=\mu_F=Q$.
• Figure 5: The scale dependence of the NCDY process at $\text{N}^3$LO in the 5FS for different PDF sets for the $Q$ in the range (4 GeV, 120 GeV). The uncertainty band was obtained from a 7-point variation around the central scale $\mu_F^0=\mu_R^0=Q$, where $Q$ is integrated between $Q_{\textrm{min}}$ and $Q_{\textrm{max}}$. The $y$-axis corresponds to the ratio of $\delta_\pm(\text{scale})$w.r.t. the central scale.