Jet Veto Resummation with Jet Rapidity Cuts

TL;DR

The paper develops a systematic SCET-based framework to incorporate finite jet rapidity cuts into jet-veto resummation for color-singlet processes at the LHC. It identifies and analyzes four parametric regimes, deriving factorization theorems and computing the $\eta_{cut}$-dependence of resummation ingredients up to the order currently known, while showing that the phenomenologically relevant regimes are free of large nonglobal logarithms. The authors provide numerical results at NLL$'+$NLO for representative processes (Drell-Yan and gluon-fusion Higgs production), demonstrating that a forward rapidity cut at $\eta_{cut}=4.5$ has little effect, whereas a sharp cut at $\eta_{cut}=2.5$ can significantly inflate uncertainties unless a stepped veto is used. They also generalize the formalism to stepped vetoes and outline how to extend to NNLL$'$ with further finite terms or numerical extraction, offering practical guidance for applying rapidity cuts in jet-veto analyses.

Abstract

Jet vetoes are widely used in experimental analyses at the LHC to distinguish different hard-interaction processes. Experimental jet selections require a cut on the (pseudo)rapidity of reconstructed jets, $|η_{\rm jet}| \leq η_{\rm cut}$. We extend the standard jet-$p_T$ (jet-veto) resummation, which implicitly works in the limit $η_{\rm cut}\to\infty$, by incorporating a finite jet rapidity cut. We also consider the case of a step in the required $p_T^{\rm cut}$ at an intermediate value of $|η| \simeq 2.5$, which is of experimental relevance to avoid the increased pile-up contamination beyond the reach of the tracking detectors. We identify all relevant parametric regimes, discuss their factorization and resummation as well as the relations between them, and show that the phenomenologically relevant regimes are free of large nonglobal logarithms. The $η_{\rm cut}$ dependence of all resummation ingredients is computed to the same order to which they are currently known for $η_{\rm cut}\to\infty$. Our results pave the way for carrying out the jet-veto resummation including a sharp cut or a step at $η_{\rm cut}$ to the same order as is currently available in the $η_{\rm cut}\to\infty$ limit. The numerical impact of the jet rapidity cut is illustrated for benchmark $q\bar q$ and $gg$ initiated color-singlet processes at NLL$'+$NLO. We find that a rapidity cut at high $η_{\rm cut} = 4.5$ is safe to use and has little effect on the cross section. A sharp cut at $η_{\rm cut} = 2.5$ can in some cases lead to a substantial increase in the perturbative uncertainties, which can be mitigated by instead using a step in the veto.

Figures (16)

• Figure 1: Cartoon of possible strategies to avoid contamination from unsuppressed pile up in jet-binned analyses. The pile-up suppression is much better in the pseudorapidity range $\lvert\eta\rvert \lesssim 2.5$, where it can use information from the tracking detectors. To avoid the higher pile-up contamination in the forward region, one can raise the jet threshold (left panel), only consider central jets (middle panel), or combine both approaches by using a step-like jet selection (right panel).
• Figure 2: Illustration of the parametric regimes for a jet veto with a jet rapidity cut. Emissions above the black solid lines are vetoed as $p_T > p_T^{\rm cut}$ up to $\lvert\eta\rvert < \eta_{\rm cut} = 2.5$. The thick gray line corresponds to $p_T/Q = e^{-\lvert\eta\rvert}$, and emissions above and to the right of it are power suppressed. The colored circles indicate the relevant modes in the effective theory for a given hierarchy between $p_T^{\rm cut}/Q$ and $e^{-\eta_{\rm cut}}$. For $p_T^{\rm cut} = 25 \,\mathrm{GeV}$, the given examples for $p_T^{\rm cut}/Q$ correspond to $Q = 125 \,\mathrm{GeV}$ (left panel, upper case), $Q = 300 \,\mathrm{GeV}$ (left panel, lower case), $Q = 1\,\mathrm{TeV}$ (right panel).
• Figure 3: Comparison of the singular contributions to the fixed $\mathcal{O}(\alpha_s)$ (LO$_1$) $p_T^{\rm jet}$ spectrum for $gg\to H$ (left) and Drell-Yan (right). The orange solid lines show the singular contributions in regime 2 with $\eta_{\rm cut}$ dependent beam functions. The dashed blue lines show the singular contributions in regime 1 in the limit $\eta_{\rm cut} = \infty$, $p_T^{\rm cut} \gg Q e ^{-\eta_{\rm cut}}$. Their difference, shown by the dotted green lines, correctly scales as a power in $Q e^{-\eta_{\rm cut}} / p_T^{\rm jet}$. The vertical lines indicate the point $p_T^{\rm jet} = Q e^{-\eta_{\rm cut}}$.
• Figure 4: Comparison of singular and nonsingular contributions to the fixed $\mathcal{O}(\alpha_s)$ (LO$_1$) $p_T^{\rm jet}$ spectrum with rapidity cut $\lvert\eta_{\rm jet}\rvert < \eta_{\rm cut}$ for $gg\to H$ (top row) and $gg\to X$ (bottom row), $\eta_{\rm cut} = 2.5$ (left) and $\eta_{\rm cut} = 4.5$ (right). The orange solid lines show the full results, the dashed blue lines the regime 2 results with $\eta_{\rm cut}$ dependent beam functions, and the dotted green lines their difference. The dashed and dotted gray lines show the corresponding regime 1 results, which do not describe the singular behavior of the full cross section for finite $\eta_{\rm cut}$.
• Figure 5: Comparison of singular and nonsingular contributions to the fixed $\mathcal{O}(\alpha_s)$ (LO$_1$) $p_T^{\rm jet}$ spectrum with rapidity cut $\lvert\eta_{\rm jet}\rvert < \eta_{\rm cut}$ for Drell-Yan at $Q = m_Z$ (top row) and $Q = 1\,\mathrm{TeV}$ (bottom row), $\eta_{\rm cut} = 2.5$ (left) and $\eta_{\rm cut} = 4.5$ (right). The meaning of the curves are as in \ref{['fig:sing_nons_ggHX']}.