Jet Measurements Research Articles

Simultaneous energy and mass calibration of large-radius jets with the ATLAS detector using a deep neural network

Abstract The energy and mass measurements of jets are crucial tasks for the Large Hadron Collider experiments. This paper presents a new calibration method to simultaneously calibrate these quantities for large-radius jets measured with the ATLAS detector using a deep neural network (DNN). To address the specificities of the calibration problem, special loss functions and training procedures are employed, and a complex network architecture, which includes feature annotation and residual connection layers, is used. The DNN-based calibration is compared to the standard numerical approach in an extensive series of tests. The DNN approach is found to perform significantly better in almost all of the tests and over most of the relevant kinematic phase space. In particular, it consistently improves the energy and mass resolutions, with a 30% better energy resolution obtained for transverse momenta p T > 500 GeV.

Measurement of groomed event shape observables in deep-inelastic electron-proton scattering at HERA

The H1 Collaboration at HERA reports the first measurement of groomed event shape observables in deep inelastic electron-proton scattering (DIS) at s=319\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s} =319~$$\\end{document}GeV, using data recorded between the years 2003 and 2007 with an integrated luminosity of 351 pb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{pb}^{-1}$$\\end{document}. Event shapes provide incisive probes of perturbative and non-perturbative QCD. Grooming techniques have been used for jet measurements in hadronic collisions; this paper presents the first application of grooming to DIS data. The analysis is carried out in the Breit frame, utilizing the novel Centauro jet clustering algorithm that is designed for DIS event topologies. Events are required to have squared momentum-transfer Q2>150\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^2 > 150$$\\end{document} GeV2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document} and inelasticity 0.2<y<0.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 0.2< y < 0.7$$\\end{document}. We report measurements of the production cross section of groomed event 1-jettiness and groomed invariant mass for several choices of grooming parameter. Monte Carlo model calculations and analytic calculations based on Soft Collinear Effective Theory are compared to the measurements.

Assimilating Sparse 3D-PTV Data Of A Pulsed Jet Using Physics-Informed Neural Networks

Phase-resolved volumetric velocity measurements of a pulsed jet are conducted by means of three-dimensional particle tracking velocimetry (PTV). The resulting scattered and relatively sparse data are densely reconstructed by adopting physics-informed neural networks (PINNs), here regularized by the Navier-Stokes equations. It is shown that the assimilation yields a higher spatial resolution, and the process remains robust, even at low particle densities ( 𝑝𝑝𝑝 &lt; 0.001). This is achieved by enforcing compliance with the governing equations, thus leveraging the spatiotemporal evolution of the measured flow field. The results indicate that the PINN reconstructs unambiguously velocity, vorticity and pressure fields with a level of detail not attainable with conventional methods (binning) or more advanced data assimilation techniques (vortex-in-cell). The results of this article support the findings of Clark di Leoni (2023) suggesting that the PINN methodology is inherently suited to the assimilation of PTV data, in particular under conditions of severe sparsity or during experiments with limited control of seeding concentration.

Measurement of inclusive charged-particle jet production in pp and p-Pb collisions at sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV

Measurements of inclusive charged-particle jet production in pp and p-Pb collisions at center-of-mass energy per nucleon-nucleon collision sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV and the corresponding nuclear modification factor RpPbchjet\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {R}_{\ extrm{pPb}}^{\ extrm{ch}\\ \ extrm{jet}} $$\\end{document} are presented, using data collected with the ALICE detector at the LHC. Jets are reconstructed in the central rapidity region |ηjet| < 0.5 from charged particles using the anti-kT algorithm with resolution parameters R = 0.2, 0.3, and 0.4. The pT-differential inclusive production cross section of charged-particle jets, as well as the corresponding cross section ratios, are reported for pp and p-Pb collisions in the transverse momentum range 10 <pT,jetch\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {p}_{\ extrm{T},\ extrm{jet}}^{\ extrm{ch}} $$\\end{document}< 140 GeV/c and 10 <pT,jetch\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {p}_{\ extrm{T},\ extrm{jet}}^{\ extrm{ch}} $$\\end{document}< 160 GeV/c, respectively, together with the nuclear modification factor RpPbchjet\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {R}_{\ extrm{pPb}}^{\ extrm{ch}\\ \ extrm{jet}} $$\\end{document} in the range 10 <pT,jetch\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {p}_{\ extrm{T},\ extrm{jet}}^{\ extrm{ch}} $$\\end{document}< 140 GeV/c. The analysis extends the pT range of the previously-reported charged-particle jet measurements by the ALICE Collaboration. The nuclear modification factor is found to be consistent with one and independent of the jet resolution parameter with the improved precision of this study, indicating that the possible influence of cold nuclear matter effects on the production cross section of charged-particle jets in p-Pb collisions at sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV is smaller than the current precision. The obtained results are in agreement with other minimum bias jet measurements available for RHIC and LHC energies, and are well reproduced by the NLO perturbative QCD Powheg calculations with parton shower provided by Pythia8 as well as by Jetscape simulations.

Measurement of the fraction of jet longitudinal momentum carried by Λc+ baryons in pp collisions

Recent measurements of charm-baryon production in hadronic collisions have questioned the universality of charm-quark fragmentation across different collision systems. In this work the fragmentation of charm quarks into charm baryons is probed, by presenting the first measurement of the longitudinal jet momentum fraction carried by Λc+ baryons, z∥ch, in hadronic collisions. The results are obtained in proton-proton (pp) collisions at s=13 TeV at the LHC, with Λc+ baryons and charged (track-based) jets reconstructed in the transverse momentum intervals of 3≤pTΛc+&lt;15 GeV/c and 7≤pTjet ch&lt;15 GeV/c, respectively. The z∥ch distribution is compared to a measurement of D0-tagged charged jets in pp collisions as well as to 8 simulations. The data hints that the fragmentation of charm quarks into charm baryons is softer with respect to charm mesons, in the measured kinematic interval, as predicted by hadronization models which include color correlations beyond leading-color in the string formation. © 2024 CERN, for the ALICE Collaboration 2024 CERN

Precision measurements of jet and photon production at the ATLAS experiment

The production of jets and prompt isolated photons at hadron colliders provides stringent tests of perturbative QCD. We present the latest measurements of photon+jets and diphoton production using proton-proton collision data collected by the ATLAS experiment at the LHC. The measurements are compared to state-of-the-art NLO and NNLO predictions.

A formalism for extracting track functions from jet measurements

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called “track functions”, in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which describe measurements of the track energy fraction in identified jets. These track jet functions can be matched onto the universal track functions, with perturbatively calculable matching coefficients that incorporate the jet algorithm dependence. We perform this matching, and present phenomenological results for the charged energy fraction in jets at the LHC and EIC/HERA at collinear next-to-leading logarithmic accuracy. We show that higher moments of the charged energy fraction directly exhibit non-linear Lorentzian renormalization group flows, allowing the study of these flows with collider data. Our factorization theorem enables the extraction of universal track functions from jet measurements, opening the door to their use for a precision jet substructure program.

Using Artificial Intelligence for Rheumatic Heart Disease Detection by Echocardiography: Focus on Mitral Regurgitation.

Identification of children with latent rheumatic heart disease (RHD) by echocardiography, before onset of symptoms, provides an opportunity to initiate secondary prophylaxis and prevent disease progression. There have been limited artificial intelligence studies published assessing the potential of machine learning to detect and analyze mitral regurgitation or to detect the presence of RHD on standard portable echocardiograms. We used 511 echocardiograms in children, focusing on color Doppler images of the mitral valve. Echocardiograms were independently reviewed by an expert adjudication panel. Among 511 cases, 229 were normal, and 282 had RHD. Our automated method included harmonization of echocardiograms to localize the left atrium during systole using convolutional neural networks and RHD detection using mitral regurgitation jet analysis and deep learning models with an attention mechanism. We identified the correct view with an average accuracy of 0.99 and the correct systolic frame with an average accuracy of 0.94 (apical) and 0.93 (parasternal long axis). It localized the left atrium with an average Dice coefficient of 0.88 (apical) and 0.9 (parasternal long axis). Maximum mitral regurgitation jet measurements were similar to expert manual measurements (P value=0.83) and a 9-feature mitral regurgitation analysis showed an area under the receiver operating characteristics curve of 0.93, precision of 0.83, recall of 0.92, and F1 score of 0.87. Our deep learning model showed an area under the receiver operating characteristics curve of 0.84, precision of 0.78, recall of 0.98, and F1 score of 0.87. Artificial intelligence has the potential to detect RHD as accurately as expert cardiologists and to improve with more data. These innovative approaches hold promise to scale echocardiography screening for RHD.

Heavy flavor machine learning algorithms for fast data processing in sPHENIX

The sPHENIX experiment at RHIC utilizes the first new heavy ion detector since the switch on of the LHC experiments. It’s optimized for precision jet and heavy flavor physics measurements, and recorded its first collisions in spring 2023. sPHENIX uses a tracking system with streaming readout and barrel calorimetry to reconstruct the collision topology. Event plane detectors, minimum bias detectors and zero-degree calorimeters are used to characterize the event. The streaming readout detectors are capable of recording 10% of the minimum bias rate, in addition to triggered events, in p+p collisions which will enable unabated, precision b-hadron and heavy flavor jet measurements at RHIC. An AI-assisted hardware trigger demonstrator is under development to sample the remaining 90% of minimum-bias p+p collisions with an aim for further deployment at the EIC.

Jet energy redistribution and broadening using hadron+jet measurements in pp and Pb–Pb collisions with ALICE

In this contribution we present measurements of the semi-inclusive distributions of charged jets recoiling from a trigger hadron (hadron+jet) in pp and Pb–Pb collisions, which provide unique probes of medium-induced modification of jet production. We observe that the jet yield at low pT and at large azimuthal angle between the trigger hadron and jet is significantly enhanced in Pb–Pb collisions with respect to pp collisions, which we interpret through comparisons to model calculations.

Probing initial state effects in nuclear collisions via jet and top-quark measurements with the ATLAS detector

Proton-lead collisions at the Large Hadron Collider energies offer a unique possibility to investigate initial state effects in nuclear collisions. Thanks to its wide acceptance, ATLAS can measure several probes that can help characterise these effects over a wide kinematic range. By analyzing the centrality dependence of dijet production, it is possible to investigate the suppression of dijet events in central collisions compared to peripheral ones and correlate it to the kinematic of the parton-parton scattering, accessible via the measurement of both jets in the final state. Also, the first measurement of the inclusive crosssection for top-quark pair production in dilepton and lepton+jet decay modes is reported. This process is sensitive to effects at high Bjorken-x values, which are hard to access experimentally using other available probes, and thus provides complementary information on the behavior of nuclear parton densities. In 2016, the ATLAS experiment collected 165 nb−1 of proton-lead collisions at a center-of-mass energy of 8.16 TeV per nucleon pair. In this article, new measurements of the centrality dependence of dijet production and the observation of top-quark pair production using this dataset are presented.

Exploring the spin structure of the nucleon at STAR

Understanding the internal spin structure of the nucleon remains a challenge in strong interaction physics. The unique capability of RHIC opened new avenues in studying the internal structure of the proton with unprecedented depth and precision. Significant progress has been made in the last few years through various measurements at STAR. The longitudinal spin measurements have contributed significantly to our understanding of the quark and gluon helicity distributions inside the proton. The longitudinal double-spin asymmetry, ALL, from STAR inclusive jet and dijet measurements provides the first evidence of a positive gluon polarization with partonic momentum fraction x &gt; 0.05. The reconstruction of W±/Z in longitudinally polarized proton-proton collisions indicates that there is a flavor separation of the light sea quark helicity distributions. In transversely polarized proton collisions, W±/Z-bosons provide the first constraint on the sea-quark Sivers function and contributes to the tests of the predicted sign change. The tilt of the dijet opening angle provides a direct access to the first Mellin momentum of the Sivers function and avoids the spin-correlated fragmentation contributions. The novel measurements of the azimuthal distributions of identified hadrons in jets and spin-dependent dihadron correlations directly probe the collinear quark transversity in the proton, with the former coupled to the transverse momentum dependent (TMD) Collins fragmentation function and the latter to the dihadron interference fragmentation function. These measurements shed lights on Sivers function, quark transversity and spin-dependent fragmentation functions in both collinear and TMD formalism. In this proceeding, recent jet results on both the longitudinal and transverse spin structure of the proton from STAR are presented.

New measurements of inclusive jet suppression and jet ν2 in Pb–Pb collisions at √SNN = 5.02 TeV with ALICE

We report measurements of the inclusive charged-particle jet yield in central Pb–Pb collisions at √SNN = 5.02 TeV. Uncorrelated background is suppressed by a novel mixed-event technique, enabling extension of the jet RAA measurement down to pT = 13.5 GeV/c, with kinematic overlap with RHIC jet measurements. We also present measurements of inclusive charged-particle jet v2 in semi-central Pb–Pb collisions at √SNN = 5.02 TeV, and azimuthal dependence of jet yield suppression for event topologies selected using eventshape engineering.

Resolving medium properties using high-pT jets with jet and in-jet correlations in PbPb collisions at 5.02 TeV with the CMS detector

Even though the quark-gluon plasma produced in high-energy heavy ion collisions has been studied in detail for years, there are still properties that are not known to a good precision. One example of such property is the medium resolution length, which is related to the smallest angle of emission where the medium can still resolve the daughter particles as individual particles. This can be probed for example through the energy-energy correlator. The medium resolution length has implications for parton energy loss, since two particles will emit energy more vigorously compared to one. Also other details of the parton energy loss, like the path-length dependency, could use precision measurements to provide better discriminating power between available theoretical models. Jets are a good observable to experimentally tackle these questions. In this talk, we present recent, high-precision CMS jet measurements in lead-lead collisions at √SNN = 5.02 TeV aimed to explore the properties of the quark-gluon plasma.

Measurement of charged and full jet production and nuclear modification factor in pp and p–Pb collisions with ALICE

The study of jet production in small collision systems is essential for testing our understanding of perturbative and non perturbative QCD and cold nuclear matter (CNM) effects. In addition, studies at high multiplicity in small collision systems exhibit signatures of collectivity, which is still not fully understood within a unified picture across system size. Jet quenching in small systems is not observed within current measurement precision, calling for more precise jet measurements. Results of charged particle and fully reconstructed jet production in pp and p-Pb collisions are presented at √SNN = 5.02 and 8 TeV, along with the corresponding nuclear modification factor RpPb at √SNN = 5.02 TeV. These results are the most precise measurements of the RpPb by ALICE to date. To investigate whether jet energy is redistributed in CNM, the crosssection ratios for different jet resolution parameters (R) are compared between pp and p–Pb collisions, as well as within each collision system. Finally, comparisons between data and model predictions are discussed. This result extends previous LHC measurements to lower jet transverse momentum, constraining hard parton production and fragmentation mechanisms applied in model calculations, and the impact of the nuclear-modified parton distribution function on jet production. This measurement also provides new constraints on jet quenching in small collision systems.

Detailed mixing measurements from single-hole converging ECN injectors using Rayleigh scattering

Time resolved liquid and vapor fields of dodecane and oxymethylene ethers are measured from Spray A-3 and Spray D using high speed Rayleigh scattering and diffuse back illumination at the Engine Combustion Network (ECN) Spray A condition of 900 K and 22.8 kg/m3. Global quantities including mixture fraction, vapor and liquid penetration, as well as spreading angle are measured. The mixture fraction fields and vapor penetration profiles are well predicted by the 1-D Musculus-Kattke model. The mixture fraction field and vapor penetration from Spray A-3 are similar to those measured from Spray A in previous works. Spray D exhibits higher mixture fraction fields and vapor penetration due to its larger nozzle diameter. The quasi-steady mixture fraction fields from these injectors scale well when distance from the injector is normalized by the nozzle diameter. The turbulent dissipation structures were also analyzed based on the orientation, thickness, and magnitude of the mixing layers. The orientation and thickness are similar to other measurements in atmospheric gas jets, while the magnitude is lower. The thickness and magnitude are subject to uncertainties due to limitations in the imaging resolution of the system but still provide an order of magnitude as a useful reference for comparison against computational fluid dynamic simulations.

The Jet Opening Angle and Event Rate Distributions of Short Gamma-Ray Bursts from Late-time X-Ray Afterglows

We present a comprehensive study of 29 short gamma-ray bursts (SGRBs) observed ≈0.8−60 days postburst using Chandra and XMM-Newton. We provide the inferred distributions of the SGRB jet opening angles and true event rates to compare against neutron star merger rates. We perform a uniform analysis and modeling of their afterglows, obtaining 10 opening angle measurements and 19 lower limits. We report on two new opening angle measurements (SGRBs 050724A and 200411A) and eight updated values, obtaining a median value of 〈θ j〉 ≈ 6.°1 [−3.°2, +9.°3] (68% confidence on the full distribution) from jet measurements alone. For the remaining events, we infer θ j ≳ 0.°5–26°. We uncover a population of SGRBs with wider jets of θ j ≳ 10° (including two measurements of θ j ≳ 15°), representing ∼28% of our sample. Coupled with multiwavelength afterglow information, we derive a total true energy of 〈E true,tot〉 ≈ 1049–1050 erg, which is consistent with magnetohydrodynamic jet launching mechanisms. Furthermore, we determine a range for the beaming-corrected event rate of Gpc−3 yr−1, set by the inclusion of a population of wide jets on the low end, and the jet measurements alone on the high end. From a comparison with the latest merger rates, our results are consistent with the majority of SGRBs originating from binary neutron star mergers. However, our inferred rates are well above the latest neutron star–black hole merger rates, consistent with at most a small fraction of SGRBs originating from such mergers.

Performance studies of jet flavor tagging and measurement of Rb(Rc) using ParticleNet at CEPC

Jet flavor tagging plays a crucial role in the measurement of relative partial decay widths of [Formula: see text] boson, denoted as [Formula: see text]([Formula: see text]), which is considered as a fundamental test of the Standard Model and sensitive probe to new physics. In this study, a Deep Learning algorithm, ParticleNet, is employed to enhance the performance of jet flavor tagging. The combined efficiency and purity of [Formula: see text]-tagging is improved by more than 50% compared to the Circular Electron Positron Collider (CEPC) baseline software. In order to measure [Formula: see text]([Formula: see text]) with this new flavor tagging approach, we have adopted the double-tagging method. The precision of [Formula: see text]([Formula: see text]) is improved significantly, in particular to [Formula: see text], which has seen a reduction in statistical uncertainty by 40%.

Mach Number and Heating Effects on Turbulent Supersonic Jets

Modern experimental techniques were used to obtain detailed aerodynamic and thermodynamic data for turbulent supersonic jets. Operating points from the work of Seiner et al. for heated Mach 2 jets were used as a starting point for the matrix of cases examined here using a geometrically similar Mach 2 nozzle. Two additional nozzles were examined having design Mach numbers of 1.36 and 1.63. For each Mach number, multiple jet temperatures were investigated. Jet measurements were first made with stagnation pressure and temperature probes for comparison to the previous experiments. The experiments focused on modern nonintrusive measurement techniques, including particle image velocimetry for mean and root-mean-square (rms) velocities, and rotationally resolved Raman scattering spectroscopy for mean and rms temperatures. Experimental results showed that as jet Mach number increases, the overall jet mixing rate decreases, as indicated by the potential core length, downstream mean velocities, and turbulence levels. Similar behavior was observed in the mean temperatures and rms temperatures. The suppression of turbulence as the jet Mach number increases is due to compressibility. For a fixed jet Mach number, increasing the jet temperature resulted in faster mixing by all measures. Peak turbulent stress levels, located along the lipline of the jet, demonstrated trends in individual stress components that differed depending on whether jet Mach number or temperature was varied, but indicated that the turbulence structure parameter was very similar when varying either jet temperature or Mach number.

Jets in e+A SIDIS and Denominator Regularization

We compute the in-medium jet broadening to leading order in energy in the opacity expansion. At leading order in αs the elastic energy loss gives a jet broadening that grows with ln E. The next-to-leading order in αs result is a jet narrowing, due to destructive LPM interference effects, that grows with ln2 E. We find that in the opacity expansion the jet broadening asymptotics are— unlike for the mean energy loss—extremely sensitive to the correct treatment of the finite kinematics of the problem; integrating over all emitted gluon transverse momenta leads to a prediction of jet broadening rather than narrowing. We compare the asymptotics from the opacity expansion to a recent twist-4 derivation and find a qualitative disagreement: the twist-4 derivation predicts a jet broadening rather than a narrowing. Comparison with current jet measurements cannot distinguish between the broadening or narrowing predictions. We comment on the origin of the difference between the opacity expansion and twist-4 results.We also introduce a novel regularization scheme in quantum field theory, denominator regularization (den reg). Den reg is as simple to apply as the usual dimensional regularization, works simply with a minimal subtraction scheme, and manifestly 1) maintains Lorentz invariance, 2) maintains gauge invariance, 3) maintains supersymmetry, 4) correctly predicts the axial anomaly, and 5) yields Green functions that satisfy the Callan-Symanzik equation. Den reg also naturally enables regularization in asymmetric spacetimes, finite spacetimes, curved spacetimes, and in thermal field theory.