Event Shape Variables Research Articles

Non-universal Milan factors for QCD jets

Using the dispersive method we perform a two-loop analysis of the leading non-perturbative power correction to the change in jet transverse momentum pT, in the small R limit of a Cambridge-Aachen jet clustering algorithm. We frame the calculation in such a way so as to maintain connection with the universal “Milan factor” that corrects for the naive inclusive treatment of the leading hadronization corrections. We derive an enhancement factor that differs from the universal Milan factor computed for event-shape variables as well as the corresponding enhancement factor previously derived for the kt algorithm. Our calculation directly exploits the soft and triple-collinear limit of the QCD matrix element and phase space, which is relevant for capturing the coefficient of the leading 1/R power correction. As an additional check on our approach, we also independently confirm the known result for the kt algorithm.

Subleading power corrections for event shape variables in e+e-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+ e^-$$\\end{document} annihilation

We consider subleading power corrections to event shape variables in e+e-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+e^-$$\\end{document} collisions at the first order in the QCD coupling αS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _{\ extrm{S}}$$\\end{document}. We start from the jettiness variable τ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _2$$\\end{document} and the y23\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y_{23}$$\\end{document} resolution variable for the kT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_T$$\\end{document} jet clustering algorithm and we analytically compute the corresponding cumulative cross section. We investigate the origin of the different power suppressed contributions in the two-jet limit and trace it back to their different coverage of the phase space. We extend our analysis to the case of thrust and of the C-parameter, and we finally discuss a class of observables that depend on a continuous parameter giving different weight to central and forward emissions and we evaluate the corresponding subleading power corrections.

Next-to-leading power corrections to event-shape variables

Next-to-leading power corrections to event-shape variables

Four-jet event shapes in hadronic Higgs decays

We present next-to-leading order perturbative QCD predictions for four-jet-like event-shape observables in hadronic Higgs decays. To this end, we take into account two Higgs-decay categories: involving either the Yukawa-induced decay to a \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{b}}\\overline{{\ ext{b}} }$$\\end{document} pair or the loop-induced decay to two gluons via an effective Higgs-gluon-gluon coupling. We present results for distributions related to the event-shape variables thrust minor, light-hemisphere mass, narrow jet broadening, D-parameter, and Durham four-to-three-jet transition variable. For each of these observables we study the impact of higher-order corrections and compare their size and shape in the two Higgs-decay categories. We find large NLO corrections with a visible shape difference between the two decay modes, leading to a significant shift of the peak in distributions related to the H → gg decay mode.

Event shape selection method in search of the chiral magnetic effect in heavy-ion collisions

The search for the chiral magnetic effect (CME) in heavy-ion collisions has been impeded by the significant background arising from the anisotropic particle emission pattern, particularly elliptic flow. To alleviate this background, the event shape selection (ESS) technique categorizes collision events according to their shapes and projects the CME observables to a class of events with minimal flow. In this study, we explore two event shape variables to classify events and two elliptic flow variables to regulate the background. Each type of variable can be calculated from either single particles or particle pairs, resulting in four combinations of event shape and elliptic flow variables. By employing a toy model and the realistic event generator, event-by-event anomalous-viscous fluid dynamics (EBE-AVFD), we discover that the elliptic flow of resonances exhibits correlations with both the background and the potential CME signal, making the resonance flow unsuitable for background control. Through the EBE-AVFD simulations of Au+Au collisions at sNN=200 GeV with various input scenarios, we ascertain that the optimal ESS strategy for background control entails utilizing the single-particle elliptic flow in conjunction with the event shape variable based on particle pairs.

Measurements of multijet event isotropies using optimal transport with the ATLAS detector

A measurement of novel event shapes quantifying the isotropy of collider events is performed in 140 fb−1 of proton-proton collisions with s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV centre-of-mass energy recorded with the ATLAS detector at CERN’s Large Hadron Collider. These event shapes are defined as the Wasserstein distance between collider events and isotropic reference geometries. This distance is evaluated by solving optimal transport problems, using the ‘Energy-Mover’s Distance’. Isotropic references with cylindrical and circular symmetries are studied, to probe the symmetries of interest at hadron colliders. The novel event-shape observables defined in this way are infrared- and collinear-safe, have improved dynamic range and have greater sensitivity to isotropic radiation patterns than other event shapes. The measured event-shape variables are corrected for detector effects, and presented in inclusive bins of jet multiplicity and the scalar sum of the two leading jets’ transverse momenta. The measured distributions are provided as inputs to future Monte Carlo tuning campaigns and other studies probing fundamental properties of QCD and the production of hadronic final states up to the TeV-scale.

Hadronic decays of Higgs boson at NNLO matched with parton shower

We present predictions for hadronic decays of the Higgs boson at next-to-next-to-leading order (NNLO) in QCD matched with parton shower based on the POWHEG framework. Those include decays into bottom quarks with full bottom-quark mass dependence, light quarks, and gluons in the heavy top quark effective theory. Our calculations describe exclusive decays of the Higgs boson with leading logarithmic accuracy in the Sudakov region and next-to-leading order (NLO) accuracy matched with parton shower in the three-jet region, with normalizations fixed to the partial width at NNLO. We estimated remaining perturbative uncertainties taking typical event shape variables as an example and demonstrated the need of future improvements on both parton shower and matrix element calculations. The calculations can be used immediately in evaluations of the physics performances of detector designs for future Higgs factories.

Soft-drop grooming for hadronic event shapes

Soft-drop grooming of hadron-collision final states has the potential to significantly reduce the impact of non-perturbative corrections, and in particular the underlying-event contribution. This eventually will enable a more direct comparison of accurate perturbative predictions with experimental measurements. In this study we consider soft-drop groomed dijet event shapes. We derive general results needed to perform the resummation of suitable event-shape variables to next-to-leading logarithmic (NLL) accuracy matched to exact next-to-leading order (NLO) QCD matrix elements. We compile predictions for the transverse-thrust shape accurate to NLO + NLL′ using the implementation of the Caesar formalism in the Sherpa event generator framework. We complement this by state-of-the-art parton- and hadron-level predictions based on NLO QCD matrix elements matched with parton showers. We explore the potential to mitigate non-perturbative corrections for particle-level and track-based measurements of transverse thrust by considering a wide range of soft-drop parameters. We find that soft-drop grooming indeed is very efficient in removing the underlying event. This motivates future experimental measurements to be compared to precise QCD predictions and employed to constrain non-perturbative models in Monte-Carlo simulations.

Energy-energy correlation in hadronic Higgs decays: analytic results and phenomenology at NLO

In this work we complete the investigation of the recently introduced energy-energy correlation (EEC) function in hadronic Higgs decays at next-to-leading order (NLO) in fixed-order perturbation theory in the limit of vanishing light quark masses. The full analytic NLO result for the previously unknown EEC in the H → qoverline{q} + X channel is given in terms of classical polylogarithms and cross-checked against a numerical calculation. In addition to that, we discuss further corrections to predictions of the Higgs EEC event shape variable, including quark mass corrections, effects of parton shower and hadronization. We also estimate the statistical error on the measurements of the Higgs EEC at future Higgs factories and compare with the current perturbative uncertainty.

C-parameter hadronisation in the symmetric 3-jet limit and impact on alpha _s fits

Hadronisation corrections are crucial in extractions of the strong coupling constant (alpha _s) from event-shape distributions at lepton colliders. Although their dynamics cannot be understood rigorously using perturbative methods, their dominant effect on physical observables can be estimated in singular configurations sensitive to the emission of soft radiation. The differential distributions of some event-shape variables, notably the C parameter, feature two such singular points. We analytically compute the leading non-perturbative correction in the symmetric three-jet limit for the C parameter, and find that it differs by more than a factor of two from the known result in the two-jet limit. We estimate the impact of this result on strong coupling extractions, considering a range of functions to interpolate the hadronisation correction in the region between the 2 and 3-jet limits. Fitting data from ALEPH and JADE, we find that most interpolation choices increase the extracted alpha _{s}, with effects of up to 4% relative to standard fits. This brings a new perspective on the long-standing discrepancy between certain event-shape alpha _s fits and the world average.

Measurement of hadronic event shapes in high-pT multijet final states at sqrt{s} = 13 TeV with the ATLAS detector

A measurement of event-shape variables in proton-proton collisions at large momentum transfer is presented using data collected at sqrt{s} = 13 TeV with the ATLAS detector at the Large Hadron Collider. Six event-shape variables calculated using hadronic jets are studied in inclusive multijet events using data corresponding to an integrated luminosity of 139 fb−1. Measurements are performed in bins of jet multiplicity and in different ranges of the scalar sum of the transverse momenta of the two leading jets, reaching scales beyond 2 TeV. These measurements are compared with predictions from Monte Carlo event generators containing leading-order or next-to-leading order matrix elements matched to parton showers simulated to leading-logarithm accuracy. At low jet multiplicities, shape discrepancies between the measurements and the Monte Carlo predictions are observed. At high jet multiplicities, the shapes are better described but discrepancies in the normalisation are observed.

Transverse energy\u2013energy correlations of jets in the electron\u2013proton deep inelastic scattering at HERA

We study the event shape variables, transverse energy–energy correlation TEEC (cos phi ) and its asymmetry ATEEC (cos phi ) in deep inelastic scattering (DIS) at the electron–proton collider HERA, where phi is the angle between two jets defined using a transverse-momentum (k_T) jet algorithm. At HERA, jets are defined in the Breit frame, and the leading nontrivial transverse energy–energy correlations arise from the 3-jet configurations. With the help of the NLOJET++, these functions are calculated in the leading order (LO) and the next-to-leading order (NLO) approximations in QCD at the electron–proton center-of-mass energy sqrt{s}=314 GeV. We restrict the angular region to -0.8 le cos phi le 0.8, as the forward- and backward-angular regions require resummed logarithmic corrections, which we have neglected in this work. Following experimental jet-analysis at HERA, we restrict the DIS-variables x, y=Q^2/(x s), where Q^2=-q^2 is the negative of the momentum transfer squared q^2, to 0 le x le 1, 0.2 le y le 0.6, and the pseudo-rapidity variable in the laboratory frame (eta ^mathrm{{lab}}) to the range -1 le eta ^mathrm{{lab}} le 2.5. The TEEC and ATEEC functions are worked out for two ranges in Q^2, defined by 5.5,mathrm{GeV}^2 le Q^2 le 80,mathrm{GeV}^2, called the low-Q^2-range, and 150,mathrm{GeV}^2 le Q^2 le 1000,mathrm{GeV}^2, called the high-Q^2-range. We show the sensitivity of these functions on the parton distribution functions (PDFs), the factorization (mu _F) and renormalization (mu _R) scales, and on alpha _s(M_Z^2). Of these the correlations are stable against varying the scale mu _F and the PDFs, but they do depend on mu _R. For the choice of the scale mu _R= sqrt{langle E_Trangle ^2 +Q^2}, advocated in earlier jet analysis at HERA, the shape variables TEEC and ATEEC are found perturbatively robust. These studies are useful in the analysis of the HERA data, including the determination of alpha _s(M_Z^2) from the shape variables.

J/ψ production dynamics: event shape, multiplicity and rapidity dependence in proton+proton collisions at LHC energies using PYTHIA8

High-multiplicity pp collisions at the Large Hadron Collider (LHC) energies have created special importance in view of the underlying event (UE) observables. The recent results of the LHC, such as long range angular correlation, flow-like patterns, strangeness enhancement etc. in high-multiplicity events are not yet completely understood. In the same direction, the understanding of multiplicity dependence of J/ψ production is highly necessary. Transverse spherocity, which is an event shape variable, helps to investigate the particle production by isolating the hard and the soft components. In the present study, we have investigated the multiplicity dependence of J/ψ production at mid-rapidity and forward rapidity through the transverse spherocity analysis and tried to understand the role of jets by separating the isotropic and jetty events from the minimum bias collisions. We have analyzed the J/ψ production at the mid-rapidity and forward rapidities via dielectron and dimuon channels, respectively, using a 4C tuned PYTHIA8 event generator. The analysis has been performed in two different center-of-mass energies: and 13 TeV, to see the energy dependence of jet contribution to the multiplicity dependence study of J/ψ production. Furthermore, we have studied the production dynamics through the dependence of thermodynamic parameters on event multiplicity and transverse spherocity.

Comparison of coupling constant by using momentum spectra and event shape variables in different interactions

We describe in this paper the quantum chromodynamics prediction to calculate the strong coupling constant by using event shape variables as well as momentum spectra. By fitting the dispersive model and employing our parameters on event shape distribution, we obtain the perturbative value of [Formula: see text] = 0.1305 ± 0.0474 and also the non-perturbative value of α0 = 0.5246 ± 0.0516 GeV for electron–proton interactions. Next, by using momentum spectra for the same interactions, we obtain αs = 0.1572 ± 0.029. Our values in both methods are consistent with those obtained from electron–positron annihilations measured previously. When we find coupling constant for different flavours, we observe that they do not affect our results considerably. This is in accordance with quantum chromodynamics theory. All these features will be explained in the main text.

Optimizing the parton shower model in PYTHIA with pp collision data at √s = 13 TeV

Production of quarks and gluons in hadron collisions tests Quantum Chromodynamics (QCD) over a wide range of energy. Models of QCD are implemented in event generators to simulate hadron collisions and evolution of quarks and gluons into jets of hadrons. pythia8 uses the parton shower model for simulating particle collisions and is optimized using experimental observations. Recent measurements of event shape variables and jet cross-sections in [Formula: see text] collisions at [Formula: see text] TeV at the Large Hadron Collider have been used to optimize the parton shower model as used in PYTHIA8.

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

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.

Soft-drop event shapes in electron–positron annihilation at next-to-next-to-leading order accuracy

We present predictions for soft-drop event shapes of hadronic final states in electron–positron annihilation at next-to-next-to-leading order accuracy in perturbation theory obtained using the CoLoRFulNNLO subtraction method. We study the impact of the soft drop on the convergence of the perturbative expansion for the distributions of three event shape variables, the soft-drop thrust, the hemisphere jet and narrow jet invariant masses. We find that grooming generally improves perturbative convergence for these event shapes. This better perturbative stability, in conjunction with a reduced sensitivity to non-perturbative hadronization corrections makes soft-drop event shapes promising observables for the precise determination of the strong coupling at lepton colliders.

Two-loop anomalous dimensions of generic dijet soft functions

We present compact integral representations for the calculation of two-loop anomalous dimensions for a generic class of soft functions that are defined in terms of two light-like Wilson lines. Our results are relevant for the resummation of Sudakov logarithms for e+e− event-shape variables and inclusive hadron-collider observables at next-to-next-to-leading logarithmic accuracy within Soft-Collinear Effective Theory (SCET). Our formalism applies to both SCET-1 and SCET-2 soft functions and we clarify the relation between the respective soft anomalous dimension and the collinear anomaly exponent. We confirm existing two-loop results for about a dozen dijet soft functions and obtain new predictions for the angularity event shape and the soft-drop jet-grooming algorithm.

The properties of C-parameter and coupling constants

We present the properties of the C-parameter as an event-shape variable. We calculate the coupling constants in the perturbative and also in the non-perturbative parts of the QCD theory, using the dispersive as well as the shape function models. By fitting the corresponding theoretical predictions to our data, we find $\alpha _{\mathrm {s}} (M_{Z^{0}})$ = 0.117 ± 0.014 and α 0(μ I ) = 0.491 ± 0.043 for dispersive model and $\alpha _{\mathrm {s}} (M_{Z^{0}})$ = 0.124 ± 0.015 and λ 1 = 1.234 ± 0.052 for the shape function model. Our results are consistent with the world average value of $\alpha _{\mathrm {s}} (M_{Z^{0}})$ = 0.118 ± 0.002. All these features are explained in the main text.

Event shape variables, a tool for QCD study

The proton-proton collisions at LHC energies reveals important new phenomena observed in heavy ions collisions and not completely understood in small systems. Different approaches and techniques have been implemented to study those processes, but still the details of the underlying event, which correspond at certain level to soft processes remains unknown. Here we present a study of proton-proton collisions using the event shape variable sphericity for identified particles combined with multiplicity bins. The results allow us to get important features of collisions, which could be used to explore in more details and extract phenomena of QCD processes.