CMS-PAS-JME-23-001

CMS-PAS-JME-23-001
A new method for correcting the substructure of multi-prong jets using Lund jet plane reweighting in the CMS experiment
CMS Collaboration
14 February 2025

Abstract: Many analyses at the CERN LHC employ techniques exploiting the substructure of large-radius jets. These techniques aim to identify large-radius jets originating from heavy resonances produced with high momenta that decay into multiple quarks or gluons. The large momentum of the resonance results in all $N$ quarks or gluons from the decay being reconstructed into a single jet with an $N$ -prong substructure. Because of shortcomings in the simulation of these jets, substructure observables are typically calibrated using data samples of large-radius jets originating from decays of boosted W bosons or top quarks. However, this approach cannot be readily applied to jets with four or more prongs because no similar proxies exist in the data. This note presents a new technique for correcting the substructure of simulated large-radius jets from multi-prong decays. The data correspond to an integrated luminosity of 138 fb $^{-1}$ collected by the CMS experiment between 2016-2018 at a center-of-mass energy of 13 TeV. The technique is based on reclustering the jet constituents into several subjets such that each subjet represents a single prong, and separately correcting the radiation pattern in the Lund jet plane of each subjet using a correction derived from data. The correction procedure improves the agreement between data and simulation in several different substructure observables of multi-prong jets. This technique establishes, for the first time, a robust calibration for the substructure of jets with four or more prongs, enabling their usage in future measurements and searches for new phenomena.
Links: CDS record (PDF) ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: The distribution of soft-drop masses for AK8 jets in the semileptonic ${\mathrm{t}\overline{\mathrm{t}}}$ region. The number of simulated events has been scaled to match the observed number of data events. The bottom panel shows the ratio between the observed data and the simulated estimates. Only statistical uncertainties are shown. Good agreement between data and simulation is seen in the central part of the distribution. Only events in the W and t regions, composed of events in the mass ranges of 70-110 GeV and 150-225 GeV, respectively, are used in the analysis.
png pdf	Figure 2: Ratios of the LJP densities between data and simulation in the six subjet $p_{\mathrm{T}}$ bins. Bins with no data or simulation events are shown as white; in the application of the correction, they are assigned a ratio value of unity and an uncertainty of 100%. The combined statistical and systematic uncertainty in the ratio is represented by the area of the hatched region in each bin. The ratios are used to build the corrections to the substructure of a subjet.
png pdf	Figure 2-a: Ratios of the LJP densities between data and simulation in the six subjet $p_{\mathrm{T}}$ bins. Bins with no data or simulation events are shown as white; in the application of the correction, they are assigned a ratio value of unity and an uncertainty of 100%. The combined statistical and systematic uncertainty in the ratio is represented by the area of the hatched region in each bin. The ratios are used to build the corrections to the substructure of a subjet.
png pdf	Figure 2-b: Ratios of the LJP densities between data and simulation in the six subjet $p_{\mathrm{T}}$ bins. Bins with no data or simulation events are shown as white; in the application of the correction, they are assigned a ratio value of unity and an uncertainty of 100%. The combined statistical and systematic uncertainty in the ratio is represented by the area of the hatched region in each bin. The ratios are used to build the corrections to the substructure of a subjet.
png pdf	Figure 2-c: Ratios of the LJP densities between data and simulation in the six subjet $p_{\mathrm{T}}$ bins. Bins with no data or simulation events are shown as white; in the application of the correction, they are assigned a ratio value of unity and an uncertainty of 100%. The combined statistical and systematic uncertainty in the ratio is represented by the area of the hatched region in each bin. The ratios are used to build the corrections to the substructure of a subjet.
png pdf	Figure 2-d: Ratios of the LJP densities between data and simulation in the six subjet $p_{\mathrm{T}}$ bins. Bins with no data or simulation events are shown as white; in the application of the correction, they are assigned a ratio value of unity and an uncertainty of 100%. The combined statistical and systematic uncertainty in the ratio is represented by the area of the hatched region in each bin. The ratios are used to build the corrections to the substructure of a subjet.
png pdf	Figure 2-e: Ratios of the LJP densities between data and simulation in the six subjet $p_{\mathrm{T}}$ bins. Bins with no data or simulation events are shown as white; in the application of the correction, they are assigned a ratio value of unity and an uncertainty of 100%. The combined statistical and systematic uncertainty in the ratio is represented by the area of the hatched region in each bin. The ratios are used to build the corrections to the substructure of a subjet.
png pdf	Figure 2-f: Ratios of the LJP densities between data and simulation in the six subjet $p_{\mathrm{T}}$ bins. Bins with no data or simulation events are shown as white; in the application of the correction, they are assigned a ratio value of unity and an uncertainty of 100%. The combined statistical and systematic uncertainty in the ratio is represented by the area of the hatched region in each bin. The ratios are used to build the corrections to the substructure of a subjet.
png pdf	Figure 3: Ratios of the LJP densities between data and simulation projected into one dimension. The ratio is shown as a function of $\ln(0.8/\Delta)$ for several $k_{\mathrm{T}}$ bins for the subjet $p_{\mathrm{T}}$ bin 110-175 GeV. Statistical uncertainties are shown as the black error bars, and the combined statistical and systematic uncertainties are shown as the blue error bars. The ratio values are seen to change in a relatively smooth manner, and the statistical uncertainties are seen to dominate the uncertainty in each bin.
png pdf	Figure 3-a: Ratios of the LJP densities between data and simulation projected into one dimension. The ratio is shown as a function of $\ln(0.8/\Delta)$ for several $k_{\mathrm{T}}$ bins for the subjet $p_{\mathrm{T}}$ bin 110-175 GeV. Statistical uncertainties are shown as the black error bars, and the combined statistical and systematic uncertainties are shown as the blue error bars. The ratio values are seen to change in a relatively smooth manner, and the statistical uncertainties are seen to dominate the uncertainty in each bin.
png pdf	Figure 3-b: Ratios of the LJP densities between data and simulation projected into one dimension. The ratio is shown as a function of $\ln(0.8/\Delta)$ for several $k_{\mathrm{T}}$ bins for the subjet $p_{\mathrm{T}}$ bin 110-175 GeV. Statistical uncertainties are shown as the black error bars, and the combined statistical and systematic uncertainties are shown as the blue error bars. The ratio values are seen to change in a relatively smooth manner, and the statistical uncertainties are seen to dominate the uncertainty in each bin.
png pdf	Figure 3-c: Ratios of the LJP densities between data and simulation projected into one dimension. The ratio is shown as a function of $\ln(0.8/\Delta)$ for several $k_{\mathrm{T}}$ bins for the subjet $p_{\mathrm{T}}$ bin 110-175 GeV. Statistical uncertainties are shown as the black error bars, and the combined statistical and systematic uncertainties are shown as the blue error bars. The ratio values are seen to change in a relatively smooth manner, and the statistical uncertainties are seen to dominate the uncertainty in each bin.
png pdf	Figure 3-d: Ratios of the LJP densities between data and simulation projected into one dimension. The ratio is shown as a function of $\ln(0.8/\Delta)$ for several $k_{\mathrm{T}}$ bins for the subjet $p_{\mathrm{T}}$ bin 110-175 GeV. Statistical uncertainties are shown as the black error bars, and the combined statistical and systematic uncertainties are shown as the blue error bars. The ratio values are seen to change in a relatively smooth manner, and the statistical uncertainties are seen to dominate the uncertainty in each bin.
png pdf	Figure 4: A comparison of the data/simulation agreement of various substructure observables in the W region. The distribution of various simulated processes are shown in the colored histograms and observed data points are shown in black. The brown line shows the total simulated distribution after the LJP correction has been applied to the W-matched $\mathrm{t} \overline{\mathrm{t}}$ and $\mathrm{t}\mathrm{W}$ simulations. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to W-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 4-a: A comparison of the data/simulation agreement of various substructure observables in the W region. The distribution of various simulated processes are shown in the colored histograms and observed data points are shown in black. The brown line shows the total simulated distribution after the LJP correction has been applied to the W-matched $\mathrm{t} \overline{\mathrm{t}}$ and $\mathrm{t}\mathrm{W}$ simulations. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to W-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 4-b: A comparison of the data/simulation agreement of various substructure observables in the W region. The distribution of various simulated processes are shown in the colored histograms and observed data points are shown in black. The brown line shows the total simulated distribution after the LJP correction has been applied to the W-matched $\mathrm{t} \overline{\mathrm{t}}$ and $\mathrm{t}\mathrm{W}$ simulations. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to W-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 4-c: A comparison of the data/simulation agreement of various substructure observables in the W region. The distribution of various simulated processes are shown in the colored histograms and observed data points are shown in black. The brown line shows the total simulated distribution after the LJP correction has been applied to the W-matched $\mathrm{t} \overline{\mathrm{t}}$ and $\mathrm{t}\mathrm{W}$ simulations. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to W-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 4-d: A comparison of the data/simulation agreement of various substructure observables in the W region. The distribution of various simulated processes are shown in the colored histograms and observed data points are shown in black. The brown line shows the total simulated distribution after the LJP correction has been applied to the W-matched $\mathrm{t} \overline{\mathrm{t}}$ and $\mathrm{t}\mathrm{W}$ simulations. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to W-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 4-e: A comparison of the data/simulation agreement of various substructure observables in the W region. The distribution of various simulated processes are shown in the colored histograms and observed data points are shown in black. The brown line shows the total simulated distribution after the LJP correction has been applied to the W-matched $\mathrm{t} \overline{\mathrm{t}}$ and $\mathrm{t}\mathrm{W}$ simulations. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to W-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 4-f: A comparison of the data/simulation agreement of various substructure observables in the W region. The distribution of various simulated processes are shown in the colored histograms and observed data points are shown in black. The brown line shows the total simulated distribution after the LJP correction has been applied to the W-matched $\mathrm{t} \overline{\mathrm{t}}$ and $\mathrm{t}\mathrm{W}$ simulations. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to W-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 5: A comparison of the data-simulation agreement of various substructure observables in the t region. The brown line shows the total simulated distribution after the LJP correction has been applied to the top-matched $\mathrm{t} \overline{\mathrm{t}}$ simulation. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to top-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 5-a: A comparison of the data-simulation agreement of various substructure observables in the t region. The brown line shows the total simulated distribution after the LJP correction has been applied to the top-matched $\mathrm{t} \overline{\mathrm{t}}$ simulation. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to top-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 5-b: A comparison of the data-simulation agreement of various substructure observables in the t region. The brown line shows the total simulated distribution after the LJP correction has been applied to the top-matched $\mathrm{t} \overline{\mathrm{t}}$ simulation. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to top-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 5-c: A comparison of the data-simulation agreement of various substructure observables in the t region. The brown line shows the total simulated distribution after the LJP correction has been applied to the top-matched $\mathrm{t} \overline{\mathrm{t}}$ simulation. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to top-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 5-d: A comparison of the data-simulation agreement of various substructure observables in the t region. The brown line shows the total simulated distribution after the LJP correction has been applied to the top-matched $\mathrm{t} \overline{\mathrm{t}}$ simulation. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to top-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 5-e: A comparison of the data-simulation agreement of various substructure observables in the t region. The brown line shows the total simulated distribution after the LJP correction has been applied to the top-matched $\mathrm{t} \overline{\mathrm{t}}$ simulation. Only statistical uncertainties are shown, and the computed $\chi^2$ is based only on statistical uncertainties. The correction is only applied to top-matched jets; the other background processes are not corrected. The data-simulation agreement of the various substructure distributions generally improves after applying the correction.
png pdf	Figure 6: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for boosted W jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 6-a: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for boosted W jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 6-b: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for boosted W jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 6-c: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for boosted W jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 7: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for $\mathrm{ R \to WW \to 4q }$ jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 7-a: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for $\mathrm{ R \to WW \to 4q }$ jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 7-b: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for $\mathrm{ R \to WW \to 4q }$ jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 7-c: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for $\mathrm{ R \to WW \to 4q }$ jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 8: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for $\mathrm{ H \to t\bar{t} \to 6q }$ jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 8-a: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for $\mathrm{ H \to t\bar{t} \to 6q }$ jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 8-b: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for $\mathrm{ H \to t\bar{t} \to 6q }$ jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 8-c: A comparison of the HERWIG (red), PYTHIA (blue) and reweighted PYTHIA (purple) samples for $\mathrm{ H \to t\bar{t} \to 6q }$ jets. The systematic uncertainty in the reweighted PYTHIA samples is shown in the light purple shading. The $\chi^2$ values are computed using only the statistical uncertainties.
png pdf	Figure 9: Distributions of the $\Delta R$ between subjets found by the reclustering procedure and closest generator-level quarks of the heavy resonance decay for various jet types. The $\Delta R$ distributions for all signals are found to peak towards zero, indicating that the reclustering procedure is performing well.
png pdf	Figure 10: A comparison of correction factors for jet tagging efficiencies of various types, using standard calibration techniques based on SM proxy objects (blue), an extension of SM-proxy-based techniques using hard gluon radiation [23] (red), and the LJP reweighting technique (purple).

Tables
png pdf	Table 1: A comparison of the tagging efficiency in PYTHIA vs HERWIG for jets of various kinds. See text for details.
png pdf	Table 2: Uncertainties on the LJP reweighting scale factor for tagging jets from various processes. Uncertainties that not applicable to a given process are denoted with a dash.
png pdf	Table 3: A comparison of scale factors derived using the LJP correction procedure and other methods. The scale factors derived with the LJP ratio have larger uncertainties, but agree well with those from traditional methods. The comparison for the $\mathrm{R} \rightarrow \mathrm{W}\mathrm{W}$ was taken from a recent search by the CMS Collaboration [23].

Summary

A new method to improve the modeling in simulation of large-radius multi-prong jets originating from the decay of heavy resonances into multiple quarks has been presented. The method is based on a reclustering of the multi-prong jet into separate subjets for each prong. The emissions of each subjet are corrected using the ratio of the Lund jet plane (LJP) densities between data and simulation, derived from a sample of boosted W jets. The correction for the full jet is computed based on the corrections of each of the subjets. The method successfully improves the agreement between data and simulation of substructure observables of two-pronged W jets and three-pronged top quark jets. The LJP reweighting is also used to correct simulations using PYTHIA for the parton shower to match HERWIG, validating that the correction performs well for jets with more than three prongs. The method can be used to correct the efficiency of substructure-based event selection criteria. Efficiencies for W and top tagging corrected with the LJP method agree well the efficiencies measured directly in data. The LJP method allows for the calibration of jet tagger efficiencies for multi-prong jets for which there are no comparable standard candles available in data. The proper calibration of large-radius jets with high prong multiplicities enables a new class of searches targeting such signatures to be performed and interpreted.

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