Event shape variables measured using multijet final states in proton-proton collisions at $\sqrt{s} =$ 13 TeV

TL;DR

The paper measures four global event shape variables in 13 TeV proton-proton collisions with the CMS detector, using an energy scale defined by $H_{\mathrm{T},2}$ to organize multijet events. Distributions are unfolded to particle level and compared to predictions from PYTHIA8 (CUETP8M1/Monash), MadGraph5_amc@nlo+pythia8, and Herwig++, revealing that agreement improves with higher $H_{\mathrm{T},2}$ and that ME-based approaches generally capture energy flow more accurately than LO PS models. The study quantifies the impact of ISR, FSR, and MPI on ESVs and provides guidance for tuning MC generators to better describe multijet QCD dynamics at the LHC. Overall, the results enhance understanding of hadronization and energy flow in multijet final states, with practical implications for MC tuning and precision QCD tests at high energy.

Abstract

The study of global event shape variables can provide sensitive tests of predictions for multijet production in proton-proton collisions. This paper presents a study of several event shape variables calculated using jet four momenta in proton-proton collisions at a centre-of-mass energy of 13 TeV and uses data recorded with the CMS detector at the LHC corresponding to an integrated luminosity of 2.2 fb$^{-1}$. After correcting for detector effects, the resulting distributions are compared with several theoretical predictions. The agreement generally improves as the energy, represented by the average transverse momentum of the two leading jets, increases.

Figures (11)

• Figure 1: Total uncertainty (black line) for the four event shape variables: the complement of transverse thrust ($\tau_{\perp}$) (upper left), total jet broadening ($B_{\mathrm{Tot}}$) (upper right), total jet mass ($\rho_{\mathrm{Tot}}$) (lower left) and total transverse jet mass ($\rho_{\mathrm{Tot}}^{\mathrm{T}}$) (lower right) evaluated with jets for $225 <H_{\mathrm{T},2}\xspace < 298\xspace\,\text{Ge\spaceV}\xspace$. The contributions from different sources are also shown in each plot: JES (red dashed line), JER (blue dotted line), unfolding (pink dash-dotted line), PDF (light-blue dash-dotted line) and statistics (grey dashed line).
• Figure 2: The effects of MPI, ISR, and FSR in pythia8 CUETP8M1 on $\tau_{\perp}$ (upper left), $B_{\mathrm{Tot}}$ (upper right), $\rho_{\mathrm{Tot}}$ (lower left) and $\rho_{\mathrm{Tot}}^{\mathrm{T}}$ (lower right) for a typical range $225 <H_{\mathrm{T},2}\xspace < 298\xspace\,\text{Ge\spaceV}\xspace$. The ratio plots for simulation (MC) with respect to data are shown in the lower panel of each plot. The inner gray band represents the statistical uncertainty and the yellow band represents the total uncertainty (systematic + statistical) in each plot.
• Figure 3: Normalized differential distributions of unfolded data compared with theoretical (MC) predictions of pythia8 CUETP8M1 (red line), pythia8 Monash (blue dash-dotted line), MadGraph5_amc@nlo (pink dash-dot-dotted line) and herwig++ (brown dash-dot-dotted line) as a function of ESV: complement of transverse thrust ($\tau_{\perp}$) (upper left), total jet broadening ($B_{\mathrm{Tot}}$) (upper right), total jet mass ($\rho_{\mathrm{Tot}}$) (lower left) and total transverse jet mass ($\rho_{\mathrm{Tot}}^{\mathrm{T}}$) (lower right) for $73 <H_{\mathrm{T},2}\xspace < 93\xspace\,\text{Ge\spaceV}\xspace$. In each ratio plot, the inner gray band represents statistical uncertainty and the yellow band represents the total uncertainty (systematic and statistical components added in quadrature) on data and the MC predictions include only statistical uncertainty.
• Figure 4: Normalized differential distributions of unfolded data compared with theoretical (MC) predictions of pythia8 CUETP8M1 (red line), pythia8 Monash (blue dash-dotted line), MadGraph5_amc@nlo (pink dash-dot-dotted line) and herwig++ (brown dash-dot-dotted line) as a function of ESV: complement of transverse thrust ($\tau_{\perp}$) (upper left), total jet broadening ($B_{\mathrm{Tot}}$) (upper right), total jet mass ($\rho_{\mathrm{Tot}}$) (lower left) and total transverse jet mass ($\rho_{\mathrm{Tot}}^{\mathrm{T}}$) (lower right) for $93 <H_{\mathrm{T},2}\xspace < 165\xspace\,\text{Ge\spaceV}\xspace$. In each ratio plot, the inner gray band represents statistical uncertainty and the yellow band represents the total uncertainty (systematic and statistical components added in quadrature) on data and the MC predictions include only statistical uncertainty.
• Figure 5: Normalized differential distributions of unfolded data compared with theoretical (MC) predictions of pythia8 CUETP8M1 (red line), pythia8 Monash (blue dash-dotted line), MadGraph5_amc@nlo (pink dash-dot-dotted line) and herwig++ (brown dash-dot-dotted line) as a function of ESV: complement of transverse thrust ($\tau_{\perp}$) (upper left), total jet broadening ($B_{\mathrm{Tot}}$) (upper right), total jet mass ($\rho_{\mathrm{Tot}}$) (lower left) and total transverse jet mass ($\rho_{\mathrm{Tot}}^{\mathrm{T}}$) (lower right) for $165 <H_{\mathrm{T},2}\xspace < 225\xspace\,\text{Ge\spaceV}\xspace$. In each ratio plot, the inner gray band represents statistical uncertainty and the yellow band represents the total uncertainty (systematic and statistical components added in quadrature) on data and the MC predictions include only statistical uncertainty.