Jet Veto Clustering Logarithms Beyond Leading Order

TL;DR

This paper tackles the challenge of jet-radius dependent clustering logarithms in exclusive jet-binned cross sections, focusing on the 0-jet case. By blending SCET soft-function factorization with NLO subtraction techniques, the authors compute the leading O(αs^3) clustering terms proportional to ln^2 R, encapsulated in the coefficient C3^(2). They derive analytic structure from soft, collinear, and collinear-soft subtractions and perform a detailed numerical evaluation of the regulated real emissions, complemented by analytic virtual contributions, obtaining C3^(2) = 0.438 ± 0.011 with a breakdown into color channels. The findings show that these NLO clustering terms have a modest impact on the Higgs H+0-jet cross section, implying improved reliability in uncertainty estimates for jet-veto predictions and paving the way for higher-order resummation efforts.

Abstract

Many experimental analyses separate events into exclusive jet bins, using a jet algorithm to cluster the final state and then veto on jets. Jet clustering induces logarithmic dependence on the jet radius R in the cross section for exclusive jet bins, a dependence that is poorly controlled due to the non-global nature of the clustering. At jet radii of experimental interest, the leading order (LO) clustering effects are numerically significant, but the higher order effects are currently unknown. We rectify this situation by calculating the most important part of the next-to-leading order (NLO) clustering logarithms of R for any 0-jet process, which enter as $O(α_s^3)$ corrections to the cross section. The calculation blends subtraction methods for NLO calculations with factorization properties of QCD and soft-collinear effective theory (SCET). We compare the size of the known LO and new NLO clustering logarithms and find that the impact of the NLO terms on the 0-jet cross section in Higgs production is small. This brings clustering effects under better control and may be used to improve uncertainty estimates on cross sections with a jet veto.

Figures (5)

• Figure 1: Schematic form of the leading order, real emission, and virtual matrix elements. In each case the parent gluon is emitted from the soft Wilson line (the double lines) and undergoes a collinear splitting. The collinear factorization is represented by '$\otimes$', with the splitting functions giving the matrix element in terms of the final state particles (those crossing the dashed line). In the virtual matrix elements, the loop contribution is shown in blue.
• Figure 2: Example fits to the regulated real emission contribution and fit residuals, for $R_c = 1.0$ and $x_c = 0.1$. For each of the 5 distinct contributions, the black data points whose values and uncertainties come from the numerical calculation are plotted against the fit in red using the form in eq. \ref{['eq:fitform']}. The residual difference is shown by the blue band, where the uncertainties on the data set the width of the band. The blue numbers on the right of each plot set the vertical scale for the residuals.
• Figure 3: Jet algorithm dependence in the calculation, shown for the $ggg$ channel as an example. The fractional uncertainty for the anti-$\mathrm{k}_\mathrm{T}$ algorithm is shown in black, along with the percent difference in $R_{ggg}$ to the anti-$\mathrm{k}_\mathrm{T}$ result for the C/A (red, dashed) and $\mathrm{k}_\mathrm{T}$ (blue, dotted) algorithms. The fact that the difference between algorithms lies within the uncertainty of the anti-$\mathrm{k}_\mathrm{T}$ result suggests that the value of $C_3^{(2)}$ is the same for the $\mathrm{k}_\mathrm{T}$-type algorithms.
• Figure 4: Final results for the $C_3^{(2)}$ values in the 3 different channels. The points are a combination of the fits to the regulated real emission, described in sec. \ref{['subsec:regreal']}, and the virtual contributions given in eq. \ref{['eq:C32virtterms']}. The results are shown for various $R_c$ and $x_c$ values, and the coefficients are independent of these cut parameters. The uncertainties are set entirely by the fits to the real emission terms, and the gray band shows the average value (with uncertainty).
• Figure 5: The integral $A_x (R_c)$ defined in eq. \ref{['eq:AxRc']}.