Factorization for Jet Radius Logarithms in Jet Mass Spectra at the LHC

TL;DR

The paper develops a comprehensive factorization framework for jet mass spectra at the LHC that accounts for jet radius effects and jet-veto measurements. By extending Soft-Collinear Effective Theory to SCET$_+$, it systematically resums logarithms of the jet mass, jet radius, and veto scales across multiple regimes, and provides explicit definitions and one-loop results for the jet and soft functions. It clarifies the connections between large-$R$ and small-$R$ setups, demonstrates RG consistency to NNLL for global vetoes, and discusses nonperturbative effects and jet-based vetoes. The work enables a unified, higher-order treatment of jet mass observables with realistic jet algorithms, offering improved precision and control over nonglobal logarithms across the full spectrum.

Abstract

To predict the jet mass spectrum at a hadron collider it is crucial to account for the resummation of logarithms between the transverse momentum of the jet and its invariant mass $m_J$. For small jet areas there are additional large logarithms of the jet radius $R$, which affect the convergence of the perturbative series. We present an analytic framework for exclusive jet production at the LHC which gives a complete description of the jet mass spectrum including realistic jet algorithms and jet vetoes. It factorizes the scales associated with $m_J$, $R$, and the jet veto, enabling in addition the systematic resummation of jet radius logarithms in the jet mass spectrum beyond leading logarithmic order. We discuss the factorization formulae for the peak and tail region of the jet mass spectrum and for small and large $R$, and the relations between the different regimes and how to combine them. Regions of experimental interest are classified which do not involve large nonglobal logarithms. We also present universal results for nonperturbative effects and discuss various jet vetoes.

Figures (5)

• Figure 1: Illustration of the various hierarchical regimes for jet mass measurements in the $R$- and $m_J/p_T^J$-plane.
• Figure 2: Characteristic invariant mass scales of the modes for the regimes 1, 2, and 3. The arrows indicate the relations among them, while the boxes indicate nonglobal correlations. Specifically, as discussed below eq. \ref{['eq:csoft_scaling']}, in regime 2 for the scaling ${\mathcal{T}}_B R^2 \sim {\mathcal{T}}_J$, the soft-collinear and collinear-soft modes merge into a single $n_J$-csoft mode. Similarly, as discussed below eq. \ref{['eq:soft_scaling']}, in regime 1 with the scaling ${\mathcal{T}}_B \sim {\mathcal{T}}_J$, the soft$_{(B)}$ and soft$_{(J)}$ modes merge into a single soft mode. In regime 3, the $n_J$-collinear and soft-collinear modes cannot be merged into a single mode by a scaling choice when employing a jet veto ${\mathcal{T}}_B \ll p_T^J$.
• Figure 3: Coefficients of the soft function $S_\kappa$ for the C-parameter jet veto and for anti-k${}_T$ jets. Shown are the exact results (solid red) together with the corresponding results in the small-$R$ limit (dashed blue) and including the first $\mathcal{O}(R^2)$ corrections (dot-dashed black) for two values $\eta_J=0$ and $\eta_J=1$.
• Figure 4: Jet radius dependence of the spectrum at next-to-leading order, as defined in eq. \ref{['eq:plot']}. Shown are the full anti-$k_T$ result (red solid), the small $R$ result (green dotted), including the $\mathcal{O}(R^2)$ soft ISR (blue dashed) and including the full set of analytic corrections at $\mathcal{O}(R^2)$ (black dot-dashed), always normalized to the full anti-$k_T$ result for $R=1$. We take ${\mathcal{T}}_J/(p_T^J R^2) =1/15 \ll 1$, which allows us to restrict ourselves to the singular terms.
• Figure 5: Jet radius dependence of the fixed-order cumulant at $\mathcal{O}(\alpha_s)$, normalized to the tree-level result, for an anti-$k_T$ jet with $p_T^J = 300$ GeV and ${\mathcal{T}}^{\rm cut}_J/(p_T^J R^2)= 1/15$ for $pp\to H+1$ jet and $pp\to Z+1$ jet.