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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Core-Noise

This presentation is a technical progress report and near-term outlook for NASA-internal and NASA-sponsored external work on core (combustor and turbine) noise funded by the Fundamental Aeronautics Program Subsonic Fixed Wing (SFW) Project. Sections of the presentation cover: the SFW system level noise metrics for the 2015, 2020, and 2025 timeframes; the emerging importance of core noise and its relevance to the SFW Reduced-Noise-Aircraft Technical Challenge; the current research activities in the core-noise area, with some additional details given about the development of a high-fidelity combustion-noise prediction capability; the need for a core-noise diagnostic capability to generate benchmark data for validation of both high-fidelity work and improved models, as well as testing of future noise-reduction technologies; relevant existing core-noise tests using real engines and auxiliary power units; and examples of possible scenarios for a future diagnostic facility. The NASA Fundamental Aeronautics Program has the principal objective of overcoming today's national challenges in air transportation. The SFW Reduced-Noise-Aircraft Technical Challenge aims to enable concepts and technologies to dramatically reduce the perceived aircraft noise outside of airport boundaries. This reduction of aircraft noise is critical for enabling the anticipated large increase in future air traffic. Noise generated in the jet engine core, by sources such as the compressor, combustor, and turbine, can be a significant contribution to the overall noise signature at low-power conditions, typical of approach flight. At high engine power during takeoff, jet and fan noise have traditionally dominated over core noise. However, current design trends and expected technological advances in engine-cycle design as well as noise-reduction methods are likely to reduce non-core noise even at engine-power points higher than approach. In addition, future low-emission combustor designs could increase the combustion-noise component. The trend towards high-power-density cores also means that the noise generated in the low-pressure turbine will likely increase. Consequently, the combined result from these emerging changes will be to elevate the overall importance of turbomachinery core noise, which will need to be addressed in order to meet future noise goals.

Hultgren, Lennart S.↗
NASA NTRS2011

Core Noise - Increasing Importance

This presentation is a technical summary of and outlook for NASA-internal and NASA-sponsored external research on core (combustor and turbine) noise funded by the Fundamental Aeronautics Program Subsonic Fixed Wing (SFW) Project. Sections of the presentation cover: the SFW system-level noise metrics for the 2015, 2020, and 2025 timeframes; turbofan design trends and their aeroacoustic implications; the emerging importance of core noise and its relevance to the SFW Reduced-Perceived-Noise Technical Challenge; and the current research activities in the core-noise area, with additional details given about the development of a high-fidelity combustor-noise prediction capability as well as activities supporting the development of improved reduced-order, physics-based models for combustor-noise prediction. The need for benchmark data for validation of high-fidelity and modeling work and the value of a potential future diagnostic facility for testing of core-noise-reduction concepts are indicated. The NASA Fundamental Aeronautics Program has the principal objective of overcoming today's national challenges in air transportation. The SFW Reduced-Perceived-Noise Technical Challenge aims to develop concepts and technologies to dramatically reduce the perceived aircraft noise outside of airport boundaries. This reduction of aircraft noise is critical to enabling the anticipated large increase in future air traffic. Noise generated in the jet engine core, by sources such as the compressor, combustor, and turbine, can be a significant contribution to the overall noise signature at low-power conditions, typical of approach flight. At high engine power during takeoff, jet and fan noise have traditionally dominated over core noise. However, current design trends and expected technological advances in engine-cycle design as well as noise-reduction methods are likely to reduce non-core noise even at engine-power points higher than approach. In addition, future low-emission combustor designs could increase the combustion-noise component. The trend towards high-power-density cores also means that the noise generated in the low-pressure turbine will likely increase. Consequently, the combined result from these emerging changes will be to elevate the overall importance of turbomachinery core noise, which will need to be addressed in order to meet future noise goals.

Hultgren, Lennart S.↗
NASA NTRS2024

Heterogeneous Outgassing Regions Identified on Active Centaur 29P/Schwassmann–Wachmann 1

Centaurs are transitional objects between primitive trans-Neptunian objects and Jupiter-family comets. Their compositions and activities provide fundamental clues regarding the processes affecting the evolution of and interplay between these small bodies. Here we report observations of centaur 29P/Schwassmann–Wachmann 1 (29P) with the James Webb Space Telescope (JWST). We identified localized jets with heterogeneous compositions driving the outgassing activity. We employed the NIRSpec mapping spectrometer to study the fluorescence emissions of CO and obtain a definitive detection of CO 2 for this target. The exquisite sensitivity of the instrument also enabled carbon and oxygen isotopic signatures to be probed. Molecular maps reveal complex outgassing distributions, such as jets and anisotropic morphology, which indicate that 29P’s nucleus is dominated by active regions with heterogeneous compositions. These distributions could reflect that it has a bilobate structure with compositionally distinct components or that strong differential erosion takes place on the nucleus. As there are no missions currently planning to visit a centaur, these observations demonstrate JWST’s unique capabilities in characterizing these objects.

Sara Faggi↗
DOE OSTI2022

Search for a W' boson decaying to a vector-like quark and a top or bottom quark in the all-jets final state at $\sqrt{\mathrm{s}}$ = 13 TeV

A search is presented for a heavy W' boson resonance decaying to a B or T vector-like quark and a t or a b quark, respectively. The analysis is performed using proton-proton collisions collected with the CMS detector at the LHC. The data correspond to an integrated luminosity of 138 fb -1 at a center-of-mass energy of 13 TeV. Both decay channels result in a signature with a t quark, a Higgs or Z boson, and a b quark, each produced with a significant Lorentz boost. The all-hadronic decays of the Higgs or Z boson and of the t quark are selected using jet substructure techniques to reduce standard model backgrounds, resulting in a distinct three-jet W' boson decay signature. No significant deviation in data with respect to the standard model background prediction is observed. Upper limits are set at 95% confidence level on the product of the W' boson cross section and the final state branching fraction. A W' boson with a mass below 3.1 TeV is excluded, given the benchmark model assumption of democratic branching fractions. In addition, limits are set based on generalizations of these assumptions. These are the most sensitive limits to date for this final state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1994

Comptonization of diffuse ambient radiation by a relativistic jet: The source of gamma rays from blazars?

Recent Energy Gamma Ray Experiment Telescope (EGRET) observations of blazars have revealed strong, variable gamma-ray fluxes with no signatures of gamma-ray absorption by pair production. This radiation probably originates from the inner parts of relativistic jets which are aimed nearly toward us. On sub-parsec scales, the jet will be pervaded by radiation from the broad-line region, as well as by photons from the central continuum source (some of which will be scattered by thermal plasma). In a frame moving with the relativistic outflow, the energy of this ambient radiation would be enhanced. This radiation would be Comptonized by both cold and relativistic electrons in the jet, yielding (in the observer's frame) a collimated beam of X-rays and gamma rays. On the assumption that this process dominates self-Comptonization of synchrotron radiation, we develop a self-consistent model for variable gamma-ray emission, involving a single population of relativistic electrons accelerated by a disturbance in the jet. The spectral break between the X-ray and gamma-ray band, observed in 3C 279 and deduced for other blazars, results from inefficient radiative cooling of lower energy electrons. The existence of such a break strongly favors a model involving Comptonization of an external radiation field over a synchrotron self-Compton model. We derive constraints on such model parameters as the location and speed of the source, its dimensions and internal physical parameters, the maximum photon energies produced in the source, and the density and distribution of ambient radiation. Finally, we discuss how observations might discriminate between our model and alternative ones invoking Comptonization of ambient radiation.

Sikora, Marek↗
DOE OSTI2025

Configuration, Performance, and Commissioning of the ATLAS b-jet Triggers for the 2022 and 2023 LHC data-taking periods

In 2022 and 2023, the Large Hadron Collider produced approximately two billion hadronic interactions each second from bunches of protons that collide at a rate of 40 MHz. The ATLAS trigger system is used to reduce this rate to a few kHz for recording. Selections based on hadronic jets, their energy, and event topology reduce the rate to 𝒪(10) kHz while maintaining high efficiencies for important signatures resulting in b-quarks, but to reach the desired recording rate of hundreds of Hz, additional real-time selections based on the identification of jets containing b-hadrons (b-jets) are employed to achieve low thresholds on the jet transverse momentum at the High-Level Trigger. The configuration, commissioning, and performance of the real-time ATLAS b-jet identification algorithms for the early LHC Run 3 collision data are presented. These recent developments provide substantial gains in signal efficiency for critical signatures; for the Standard Model production of Higgs boson pairs, a 50% improvement in selection efficiency is observed in final states with four b-quarks or two b-quarks and two hadronically decaying τ-leptons.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Measurement of the Higgs boson production rate in association with top quarks in final states with electrons, muons, and hadronically decaying tau leptons at $\sqrt{s} =$ 13 TeV

The rate for Higgs (${\mathrm{H}} $) bosons production in association with either one (${\mathrm{t}} {\mathrm{H}} $) or two (${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $) top quarks is measured in final states containing multiple electrons, muons, or tau leptons decaying to hadrons and a neutrino, using proton–proton collisions recorded at a center-of-mass energy of $13\,\text {Te}\text {V} $ by the CMS experiment. The analyzed data correspond to an integrated luminosity of 137$\,\text {fb}^{-1}$. The analysis is aimed at events that contain ${\mathrm{H}} \rightarrow {\mathrm{W}} {\mathrm{W}} $, ${\mathrm{H}} \rightarrow {\tau } {\tau } $, or ${\mathrm{H}} \rightarrow {\mathrm{Z}} {\mathrm{Z}} $ decays and each of the top quark(s) decays either to lepton+jets or all-jet channels. Sensitivity to signal is maximized by including ten signatures in the analysis, depending on the lepton multiplicity. The separation among ${\mathrm{t}} {\mathrm{H}} $, ${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $, and the backgrounds is enhanced through machine-learning techniques and matrix-element methods. The measured production rates for the ${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $ and ${\mathrm{t}} {\mathrm{H}} $ signals correspond to $0.92 \pm 0.19\,\text {(stat)} ^{+0.17}_{-0.13}\,\text {(syst)} $ and $5.7 \pm 2.7\,\text {(stat)} \pm 3.0\,\text {(syst)} $ of their respective standard model (SM) expectations. The corresponding observed (expected) significance amounts to 4.7 (5.2) standard deviations for ${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $, and to 1.4 (0.3) for ${\mathrm{t}} {\mathrm{H}} $ production. Assuming that the Higgs boson coupling to the tau lepton is equal in strength to its expectation in the SM, the coupling $y_{{\mathrm{t}}}$ of the Higgs boson to the top quark divided by its SM expectation, $\kappa _{{\mathrm{t}}}=y_{{\mathrm{t}}}/y_{{\mathrm{t}}}^{\mathrm {SM}}$, is constrained to be within $-0.9< \kappa _{{\mathrm{t}}}< -0.7$ or $0.7< \kappa _{{\mathrm{t}}}< 1.1$, at 95% confidence level. This result is the most sensitive measurement of the ${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $ production rate to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Model-agnostic search for dijet resonances with anomalous jet substructure in proton–proton collisions at $\sqrt{s}$ = 13 TeV

This paper presents a model-agnostic search for narrow resonances in the dijet final state in the mass range 1.8-6 TeV. The signal is assumed to produce jets with substructure atypical of jets initiated by light quarks or gluons, with minimal additional assumptions. Search regions are obtained by utilizing multivariate machine-learning methods to select jets with anomalous substructure. A collection of complementary anomaly detection methods - based on unsupervised, weakly supervised, and semisupervised algorithms - are used in order to maximize the sensitivity to unknown new physics signatures. These algorithms are applied to data corresponding to an integrated luminosity of 138 fb -1 , recorded by the CMS experiment at the LHC, at a center-of-mass energy of 13 TeV. No significant excesses above background expectations are seen. Exclusion limits are derived on the production cross section of benchmark signal models varying in resonance mass, jet mass, and jet substructure. Many of these signatures have not been previously sought, making several of the limits reported on the corresponding benchmark models the first ever. When compared to benchmark inclusive and substructure-based search strategies, the anomaly detection methods are found to significantly enhance the sensitivity to a variety of models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2022

The X-Ray Polarization View of Mrk 421 in an Average Flux State as Observed By the Imaging X-Ray Polarimetry Explorer

Particle acceleration mechanisms in supermassive black hole jets, such as shock acceleration, magnetic reconnection, and turbulence, are expected to have observable signatures in the multiwavelength polarization properties of blazars. The recent launch of the Imaging X-Ray Polarimetry Explorer (IXPE) enables us, for the first time, to use polarization in the X-ray band (2–8 keV) to probe the properties of the jet synchrotron emission in high-synchrotron-peaked BL Lac objects (HSPs). We report the discovery of X-ray linear polarization (degree Π x = 15% ± 2% and electric vector position angle ψ x = 35° ± 4°) from the jet of the HSP Mrk 421 in an average X-ray flux state. At the same time, the degree of polarization at optical, infrared, and millimeter wavelengths was found to be lower by at least a factor of 3. During the IXPE pointing, the X-ray flux of the source increased by a factor of 2.2, while the polarization behavior was consistent with no variability. The higher level of Π x compared to longer wavelengths, and the absence of significant polarization variability, suggest a shock is the most likely X-ray emission site in the jet of Mrk 421 during the observation. The multiwavelength polarization properties are consistent with an energy-stratified electron population, where the particles emitting at longer wavelengths are located farther from the acceleration site, where they experience a more disordered magnetic field.

acceleration of particles↗
NASA NTRS2013

Experimental Measurements of Sonic Boom Signatures Using a Continuous Data Acquisition Technique

A wind tunnel investigation was conducted in the Langley Unitary Plan Wind Tunnel to determine the effectiveness of a technique to measure aircraft sonic boom signatures using a single conical survey probe while continuously moving the model past the probe. Sonic boom signatures were obtained using both move-pause and continuous data acquisition methods for comparison. The test was conducted using a generic business jet model at a constant angle of attack and a single model-to-survey-probe separation distance. The sonic boom signatures were obtained at a Mach number of 2.0 and a unit Reynolds number of 2 million per foot. The test results showed that it is possible to obtain sonic boom signatures while continuously moving the model and that the time required to acquire the signature is at least 10 times faster than the move-pause method. Data plots are presented with a discussion of the results. No tabulated data or flow visualization photographs are included.

Wilcox, Floyd J.↗
DOE OSTI2024

Accretion onto a Supermassive Black Hole Binary before Merger

While supermassive binary black holes (SMBBHs) inspiral toward merger they may also accrete matter from a surrounding disk. To study the dynamics of this system requires simultaneously describing the evolving spacetime and the magnetized plasma. We present the first relativistic calculation simulating two equal-mass, nonspinning black holes as they inspiral from a 20 M (G = c = 1) initial separation almost to merger. Our results imply important observational consequences: for instance, the accretion rate $\dot{M}$ onto the black holes first decreases and then plateaus, dropping by only a factor of ~3 despite the rapid inspiral. An estimated bolometric light curve follows the same profile, suggesting some merging SMBBHs may be significantly luminous past the predicted circumbinary disk decoupling. The minidisks are nonstandard: Reynolds, not Maxwell, stresses dominate, and they oscillate between two states. In one part of the cycle, "sloshing" streams transfer mass between minidisks, carrying kinetic energy at a rate sometimes as high as the peak minidisk bolometric luminosity. We also discover that episodic accretion drives time-varying minidisk tilts. These complex dynamics all contribute to unique cyclical behavior in the light curves of late-time inspiraling SMBBHs. The poloidal magnetic flux on the black holes is roughly constant at a dimensionless level $\phi$ ~ 2–3, but doubles just before merger; for significant black hole spin, this flux predicts powerful jets with variability driven by binary dynamics, another potentially unique electromagnetic signature. This simulation is the first to employ our multipatch infrastructure PATCHWORK MHD, decreasing the computational expense to ~3% of conventional single-grid methods' cost.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2019

Predicting Jet Noise for Full-Scale Low-Boom Aircraft

Supersonic vehicle research addresses the development of tools, technologies, and knowledge to help eliminate technical barriers to practical commercial supersonic flight. While the major focus of this research has been on reducing the ground signature at supersonic cruise, airplanes must also satisfy noise constraints during takeoff and landing at subsonic speeds, and jet noise is the main sound source. We use computational aeroacoustic sim- ulation tools to assess new designs at these lower speeds. We are further scrutinizing both modeling and simulation practices and the use of hybrid Reynolds-averaged Navier Stokes/Large- Eddy Simulations methods and developing new methods to predict jet noise on a full flight configuration.

Stich, Gerrit-Daniel↗
NASA NTRS2018

Simulated Encounters of the Parker Solar Probe with a Coronal-Hole Jet

Solar coronal jets are small, transient, collimated ejections most easily observed in coronal holes (CHs). The upcoming Parker Solar Probe (PSP) mission provides the first opportunity to encounter CH jets in situ near the Sun and examine their internal structure and dynamics. Using projected mission orbital parameters, we have simulated PSP encounters with a fully three-dimensional magnetohydrodynamic (MHD) model of a CH jet. We find that three internal jet regions, featuring different wave modes and levels of compressibility, have distinct identifying signatures detectable by PSP. The leading Alfvén wave front and its immediate wake are characterized by transAlfvénic plasma flows with mild density enhancements. This front exhibits characteristics of a fast switch-on MHD shock, whose arrival is signaled by the sudden onset of large-amplitude transverse velocity and magnetic-field oscillations highly correlated in space and time. The trailing portion is characterized by supersonic but subAlfvénicout flows of dense plasma with uncorrelated velocity and magnetic-field oscillations. This compressible region contains most of the jet's mass. The volume between the immediate wake and dense jet, the remote wake,mixes and transitions the characteristics of the two other regions. In addition to probing each region separately, we also simulate a corotational PSP-jet encounter. In this scenario, the simulated spacecraft hovers over the jet producing CH, as may occur during the mission's corotational phases, sampling each jet region in turn. We estimate that PSP will encounter numerous CH jets over the lifetime of the mission.

Roberts, Merrill A.↗
NASA NTRS2023

Plasmoids, Flows, and Jets During Magnetic Reconnection in a Failed Solar Eruption

We report a detailed analysis of a failed eruption and flare in active region 12018 on 2014 April 3 using multiwavelength observations from the Solar Dynamics Observatory/Atmospheric Imaging Assembly, IRIS, STEREO, and Hinode/Solar Optical Telescope. At least four jets were observed to emanate from the cusp of this small active region (large bright point) with a null-point topology during the 2 hr prior to the slow rise of a filament. During the filament slow rise multiple plasma blobs were seen, most likely formed in a null-point current sheet near the cusp. The subsequent filament eruption, which was outside the IRIS field of view, was accompanied by a flare but remained confined. During the explosive flare reconnection phase, additional blobs appeared repetitively and moved bidirectionally within the flaring region below the erupting filament. The filament kinked, rotated, and underwent leg–leg reconnection as it rose, yet it failed to produce a coronal mass ejection. Tiny jet-like features in the fan loops were detected during the filament slow rise/preflare phase. We interpret them as signatures of reconnection between the ambient magnetic field and the plasmoids leaving the null-point sheet and streaming along the fan loops. We contrast our interpretation of these tiny jets, which occur within the large-scale context of a failed filament eruption, with the local nanoflare-heating scenario proposed by Antolin et al.

Sun: jets↗
NASA NTRS2011

The 2010 Very High Energy Gamma-Ray Flare and 10 Years of Multi-Wavelength Observations of M87

The giant radio galaxy M87 with its proximity (16 Mpc), famous jet, and very massive black hole ((3-6) X 10(exp 9) Solar Mass) provides a unique opportunity to investigate the origin of very high energy (VHE; E>100 GeV) gamma-ray emission generated in relativistic outflows and the surroundings of super-massive black holes. M87 has been established as a VHE gamma -ray emitter since 2006. The VHE gamma -ray emission displays strong variability on timescales as short as a day. In this paper, results from a joint VHE monitoring campaign on M87 by the MAGIC and VERITAS instruments in 2010 are reported. During the campaign, a flare at VHE was detected. triggering further observations at VHE (H.E.S.S.), X-rays (Chandra), and radio (43 GHz VLBA). The excellent sampling of the VHE gamma-ray light curve enables one to derive a precise temporal characterization of the flare: the single, isolated flare is well described by a two-sided exponential function with significantly different flux rise and decay times of rise tau ((sup rise sub d) = (1:69 +/- 0:30) days and tau(sup decay sub d = (0:611 +/- 0:080) days, respectively. While the overall variability pattern of the 2010 flare appears somewhat different from that of previous VHE flares in 2005 and 2008, they share very similar timescales (approx day), peak fluxes (Phi (sub > 0:35 TeV) approx. equals (1 - 3) X 10(exp -11) ph / square cm/s), and VHE spectra. 43 GHz VLBA radio observations of the inner jet regions indicate no enhanced flux in 2010 in contrast to observations in 2008, where an increase of the radio flux of the innermost core regions coincided with a VHE flare. On the other hand, Chandra X-ray observations taken approx 3 days after the peak of the VHE gamma -ray emission reveal an enhanced flux from the core (flux increased by factor approx 2; variability timescale < 2 days). The long-term (2001-2010) multi-wavelength (MWL) light curve of M87, spanning from radio to VHE and including data from HST, LT, VLA and EVN, is used to further investigate the origin of the VHE gamma -ray emission. No unique, common MWL signature of the three VHE flares has been identified. In the outer kpc jet region, in particular in HST-1, no enhanced MWL activity was detected in 2008 and 2010, disfavoring it as the origin of the VHE flares during these years. Shortly after two of the three flares (2008 and 2010), the X-ray core was observed to be at a higher flux level than its characteristic range (determined from more than 60 monitoring observations: 2002-2009). In 2005, the strong flux dominance of HST-1 could have suppressed the detection of such a feature. Published models for VHE gamma -ray emission from M87 are reviewed in the light of the new data.

Abramowski, A.↗
DOE OSTI2020

Collider phenomenology of a gluino continuum

Continuum supersymmetry is a class of models in which the supersymmetric partners together with part of the standard model come from a conformal sector, broken in the IR near the TeV scale. Such models not only open new doors for addressing the problems of the standard model, but also have unique signatures at hadron colliders, which might explain why we have not yet seen any superpartners at the LHC. Here we use gauge-gravity duality to model the conformal sector, generate collider simulations, and finally analyze continuum gluino signatures at the LHC. Due to the increase in the number of jets produced the bounds are weaker than for the minimal supersymmetric standard model with the same gluino mass threshold.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Jet substructure from dark sector showers

We examine the robustness of collider phenomenology predictions for a dark sector scenario with QCD-like properties. Pair production of dark quarks at the LHC can result in a wide variety of signatures, depending on the details of the new physics model. A particularly challenging signal results when prompt production induces a parton shower that yields a high multiplicity of collimated dark hadrons with subsequent decays to Standard Model hadrons. The final states contain jets whose substructure encodes their non-QCD origin. This is a relatively subtle signature of strongly coupled beyond the Standard Model dynamics, and thus it is crucial that analyses incorporate systematic errors to account for the approximations that are being made when modeling the signal. We estimate theoretical uncertainties for a canonical substructure observable designed to be sensitive to the gauge structure of the underlying object, the two-point energy correlator $ {e}_2^{\left(\beta \right)} $ , by computing envelopes between resummed analytic distributions and numerical results from Pythia. We explore the separability against the QCD background as the confinement scale, number of colors, number of flavors, and dark quark masses are varied. Additionally, we investigate the uncertainties inherent to modeling dark sector hadronization. Simple estimates are provided that quantify one’s ability to distinguish these dark sector jets from the overwhelming QCD background. Such a search would benefit from theory advances to improve the predictions, and the increase in statistics using the data to be collected at the high luminosity LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗