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DOE OSTI2020

Influence of hydrogenation on the vibrational density of states of magnetocaloric LaFe 11.4 Si 1.6 H 1.6

We report on the impact of magnetoelastic coupling on the magnetocaloric properties of LaFe 11.4 Si 1.6 H 1.6 in terms of the vibrational (phonon) density of states (VDOS), which we determined with 57 Fe nuclear resonant inelastic x-ray scattering (NRIXS) measurements and with density functional theory (DFT) based first-principles calculations in the ferromagnetic (FM) low-temperature and paramagnetic (PM) high-temperature phase. In experiments and calculations, we observe pronounced differences in the shape of the Fe-partial VDOS between nonhydrogenated and hydrogenated samples. Furthermore, this shows that hydrogen not only shifts the temperature of the first-order phase transition, but also affects the elastic response of the Fe subsystem significantly. In turn, the anomalous redshift of the Fe VDOS, observed by going to the low-volume PM phase, survives hydrogenation. As a consequence, the change in the Fe-specific vibrational entropy ΔS lat across the phase transition has the same sign as the magnetic and electronic contribution. DFT calculations show that the same mechanism, which is a consequence of the itinerant electron metamagnetism associated with the Fe subsystem, is effective in both the hydrogenated and the hydrogen-free compounds. Although reduced by 50% as compared to the hydrogen-free system, the measured change ΔS lat of 3.2 ± 1.9)J/ kg K across the FM-to-PM transition contributes with ~35 % significantly and cooperatively to the total isothermal entropy change ΔS iso . Hydrogenation is observed to induce an overall blueshift of the Fe VDOS with respect to the H-free compound; this effect, together with the enhanced Debye temperature observed, is a fingerprint of the hardening of the Fe sublattice by hydrogen incorporation. In addition, the mean Debye velocity of sound of LaFe 11.4 Si 1.6 H 1.6 was determined from the NRIXS and the DFT data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Deviations from the Porter-Thomas Distribution due to Nonstatistical 𝛾 Decay below the 150 Nd Neutron Separation Threshold

We introduce a new method for the study of fluctuations of partial transition widths based on nuclear resonance fluorescence experiments with quasimonochromatic linearly polarized photon beams below particle separation thresholds. It is based on the average branching of decays of 𝐽=1 states of an even-even nucleus to the 2$^{+}_{1}$ state in comparison to the ground state. Between 5 and 7 MeV, a constant average branching ratio for 𝛾 decays from 1 − states of 0.490(16) is observed for the nuclide 150 Nd. Assuming 𝜒 2 -distributed partial transition widths, this average branching ratio is related to a degree of freedom of 𝜈 = 1.93⁢(12), rejecting the validity of the Porter-Thomas distribution, requiring 𝜈 = 1. The observed deviation can be explained by nonstatistical effects in the 𝛾-decay behavior with contributions in the range of 9.4(10)% up to 94(10)%.

150 ≤ A ≤ 189↗

DOE OSTI2024

Impact of mechanical tolerances on partial turn skipping in helical flux compression generator

Maintaining tight mechanical tolerances of the components used in helical flux compression generators is crucial for optimizing device performance. Moving beyond current literature, which provides various approximations for acceptable tolerances, a 3D simulation of the armature stator interaction during generator operation was developed, revealing that existing equations frequently misestimate the tolerance limits. Without restricting the generality of the presented approach, the focus was primarily on the armature’s concentricity and roundness, comparing the acceptable tolerance limits between generators of different sizes. An analytical approach for select geometries was developed, confirming the 3D results. Quantitative results reveal that a steeper Gurney angle and increased winding pitch allow for less restrictive tolerances for eccentricity and ellipticity. Even small deviations from the ideal armature positioning and shape will result in fluctuations of the output current time-derivative, observed experimentally and in simulation. Larger deviations then cause partial turn skipping, associated with loss of magnetic flux. The simulation elucidates the impact of tolerance deviations on generator performance by offering precise tolerance ranges for various generator sizes, thereby facilitating informed design decisions.

42 ENGINEERING↗

DOE OSTI2019

Coupling Mechanistically the Convective Motions and Cloud Macrophysics in a Climate Model (Final Technical Report for CM4 Project)

Global climate models fail to adequately represent shallow cumulus conditions. The activities at the University of Texas at Austin focus on deploying advanced statistical approaches to identify linkages between numerical models and observations using the E3SM-Single Column Model (SCM) and different ARM campaigns focused on shallow cumulus conditions at SGP. The current version of the SCM uses CLUBB to represent shallow cumulus. The parameterization represents a significant evolution from older generation parameterizations insofar as it contains a number of prognostic equations that keep track of the turbulent nature of the environment that are carried forward in time. The parameters associated with this scheme address the rate at which different prognostic quantities that determine vertical turbulent fluxes of heat and moisture decay with time. The large number of parameters gives the CLUBB scheme a lot of flexibility. The expectation of its developers is that it should represent any shallowly convective environment. The concern among developers and other theorists was not whether it could represent any one environment, but whether a single judicious choice of parameters would allow it to predict the turbulent characteristics of a range of environments. Through several exhaustive studies that made use of Bayesian statistical calibration, tens of thousands of SCM experiments, and ensembles of observations of shallow cumulus at SGP that were also modeled using Large Eddy Simulations (LES), we have only achieved partial success in using CLUBB within SCM to capture important aspects of what has been observed and modeled with LES at SGP. Even as we worked to improve observational tests and make a more scientifically focused attempt at modifying subsets of CLUBB parameters, model performance continues to be lacking in some important respects. In one calibration, we were able to achieve a near perfect match to observed properties of liquid water path, cloud radiative effects, and cloud fraction but with clouds that were trapped within a shallow layer and without the highly turbulent fluxes and vertical extent observed with ARM data and modeled with LES (Figure 1). The conclusion we are reaching is that shallow cumulus conditions are much more challenging to represent than was previously thought. This result is also prompting us to consider some aspects of the experiment design that may be limiting the performance of SCM in this case. The work has garnered the attention of Vincent Larson (CLUBB developer at Univ. Wisconsin – Milwaukee) and model developers Steven Klein and Yunyan Zhang (LLNL) with whom this work and will continue.

58 GEOSCIENCES↗

DOE OSTI2025

An attention-based neural ordinary differential equation framework for modeling inelastic processes

To preserve strictly conservative behavior as well as model the variety of dissipative behavior displayed by solid materials, we propose a significant enhancement to the internal state variable-neural ordinary differential equation (ISV-NODE) framework. In this data-driven, physics-constrained modeling framework internal states are inferred rather than prescribed. The ISV-NODE consists of: (a) a stress model dependent on observable deformation and inferred internal state, and (b) a model of the evolution of the internal states. The enhancements to ISV-NODE proposed in this work are multifold: (a) a partially input convex neural network stress potential provides polyconvexity in terms of observed strain while leaving the inferred state unconstrained, and (b) an internal state flow model uses common latent features to inform novel attention-based gating and drives the flow of internal state only in dissipative regimes. We demonstrated that this architecture can accurately model dissipative and conservative behavior across an isotropic, isothermal elastic-viscoelastic-elastoplastic spectrum with three exemplars, while maintaining fundamental principles by design.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

The photosynthetic response of C 3 and C 4 bioenergy grass species to fluctuating light

Abstract Bioenergy grass species are a renewable energy source, but their productivity has not been fully realized. Improving photosynthetic efficiency has been proposed as a mechanism to increase the productivity of bioenergy grass species. Fluctuating light, experienced by all field grown crops, is known to reduce photosynthetic efficiency. This experiment aimed to evaluate the photosynthetic performance of both C 3 and C 4 bioenergy grass species under steady state and fluctuating light conditions by examining leaf gas exchange. The fluctuating light regime used here decreased carbon assimilation across all species when compared to expected steady state values. Overall, C 4 species assimilated more carbon than C 3 species during the fluctuating light regime, with both photosynthetic types assimilating about 16% less carbon than expected based on steady state measurements. Little diversity was observed in response to fluctuating light among C 3 species, and photorespiration partially contributed to the rapid decreases in net photosynthetic rates during high to low light transitions. In C 4 species, differences among the four NADP‐ME species were apparent. Diversity observed among C 4 species in this experiment provides evidence that photosynthetic efficiency in response to fluctuating light may be targeted to increase C 4 bioenergy grass productivity.

09 BIOMASS FUELS↗

DOE OSTI2023

Comparison of the Chemical Composition of Liquids from the Pyrolysis and Hydrothermal Liquefaction of Lignocellulosic Materials

Major differences in thermal stability and hydrotreatment behavior of HTL and pyrolysis oils have been reported in the literature. However, little is known about the variations in the chemical composition of these oils that could explain such differences. Two commercial wood pyrolysis oils (Pyrovac and BTG), and their water-soluble (WS) and water-insoluble fractions (WIS) were analyzed and compared with the aqueous (WS WD-57 ) and oily (WIS WS-57 ) fractions obtained from hydrothermal liquefaction (HTL) of Douglas-fir. The samples were characterized by GC/MS, Karl Fischer titration, carbonyl content, total acid number, elemental composition, calorific value, proximate analysis, Fourier Transform Infrared Spectroscopy (FTIR), Folin-Ciocalteu (FC), and UV fluorescence. All the fractions were also analyzed by Fourier Transform Ion Cyclotron Resonance Mass Spectroscopy (FT-ICR-MS) and by Electrospray Ionization (EI). The most prevalent class of compounds in the water insoluble phases were phenols derived from lignin. Water-soluble phases contain mostly the oxygenated compounds derived from cellulose and hemicellulose and were richer in carbonyl functional groups. The water content of the resulting aqueous phases were between: 65 (WS BTG ) and 96 (WS Pyrovac ) wt. %. The bio-oil from BTG has higher water content and lower HHV, compared to Pyrovac oil. The GC/MS results of BTG oil show the presence of a more prominent acetic acid peak and higher TAN number than the Pyrovac oil. The GC/MS of Pyrovac oil showed more obvious mono-phenol peaks. The quantification of this family by Folin-Ciocalteu method confirmed higher content of monophenolic compounds compared with the BTG oil. The lower thermal stability of pyrolysis oils compared with HTL biocrudes can be partially explained by the fact that pyrolysis oils (BTG and Pyrovac) contain carbohydrates while HTL biocrude (WIS WD-57 ) doesn’t. Thus, we decided to further investigate the chemical differences between the phenolic rich fractions insoluble in water and the holocellulose derived compounds soluble in water. Even after water extraction, the acid content of the water insoluble fraction from BTG (WISBTG) was higher than the acid content of the water insoluble fraction obtained by HTL (WISWSD-57). Likewise, the acid content of the aqueous phases derived from pyrolysis oils (WS Pyrovac , WS BTG ) was also higher than for the aqueous phase obtained by HTL (WSWSD-57). This result is in part due to the use of bases in the HTL process that neutralizes the acid formed in that process. Moreover, the starting feedstock may also influence the differences between the oils. Although, the UV-Fluorescence spectra, ICR-MS and the EI analyses showed some minor differences in the molecular weight and chemical make-up of the oligomers soluble and insoluble in water from pyrolysis and HTL; the differences observed were not large enough to justify the differences in behavior between these oils reported in the literature. Our results suggest that the differences observed between HTL biocrudes and pyrolysis oils are likely partially due to the presence of holocellulose derived products in the pyrolysis oils and higher acid contents.

09 BIOMASS FUELS↗

DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Measurement of the properties of the dust acoustic wave in a magnetic field

We present the first experimental observations of the dust acoustic wave where the wave was observed to propagate in the directions of gravity and magnetic field when these directions were not aligned. The experiments were conducted in the Magnetized Dusty Plasma eXperiment facility using a novel electrode system that allows for the angle between gravity and the magnetic field to be varied in a controlled way. This letter reports on measurements in an rf glow discharge argon plasma environment where the angle between direction of gravity and the magnetic field is 45 $^{\circ }$ . When there was no applied magnetic field, the wave was observed to propagate in the direction of gravity. However, as the magnetic field increased and the ions transitioned from flowing in the direction of gravity to the direction of the magnetic field, a second wave emerged and two distinct waves were observed to simultaneously propagate, one in the direction of gravity and one in the direction of the magnetic field. As the magnetic field was further increased, the wave that propagated in the direction of gravity was suppressed and the wave was only observed to propagate in the direction of the applied magnetic field. We also observe that the speed and the kinetic temperature of the dust for the mode that propagated in the direction of gravity decreased with increasing magnetic field while the speed and the kinetic temperature of the dust for the mode that propagated in the direction of the magnetic field increased with increasing magnetic field. These measurements suggest that an ion-dust streaming instability is at least partially responsible for the high temperatures that have previously been observed in dusty plasmas when the dust acoustic wave is present.

Williams, J. D. (ORCID:000000025199707X)↗

DOE OSTI2020

Steam oxidation of ytterbium disilicate environmental barrier coatings with and without a silicon bond coat

The current generation of multilayer Si/Yb 2 Si 2 O 7 environmental barrier coatings (EBCs) are temperature limited by the melting point of Si, 1414°C. To investigate higher temperature EBCs, the cyclic steam oxidation of EBCs comprised of a single layer of ytterbium disilicate (YbDS) was compared to multilayered Si/YbDS EBCs, both deposited on SiC substrates using atmospheric plasma spray. In this work, after 500 1-h cycles at 1300°C in 90 vol%H2O-10 vol%air with a gas velocity of 1.5 cm/s, both multilayer Si/YbDS and single layer YbDS grew thinner silica scales than bare SiC, with the single layer YbDS forming the thinnest scale. Both coatings remained fully adherent and showed no signs of delamination. Silica scales formed on the single layer coating were significantly more homogeneous and possessed a markedly lower degree of cracking compared to the multilayered EBC. The single layer EBC also was exposed at 1425°C in steam with a gas velocity of 14 cm/s in an alumina reaction tube. The EBC reduced specimen mass loss compared to bare SiC but formed an extensive 2nd phase aluminosilicate reaction product. A similar reaction product was observed to form on some regions of the bare SiC specimen and appeared to partially inhibit silica volatilization. The 1425°C steam exposures were repeated with a SiC reaction tube and no 2nd phase reaction product was observed to form on the single layer EBC or bare SiC.

36 MATERIALS SCIENCE↗

DOE OSTI2019

How Tropical Pacific Surface Cooling Contributed to Accelerated Sea Ice Melt from 2007 to 2012 as Ice is Thinned by Anthropogenic Forcing

Over the past 40 years the Arctic sea ice minimum in September has declined. The period between 2007 and 2012 showed accelerated melt contributed to the record minima of 2007 and 2012. Here, observational and model evidence shows that the changes in summer sea ice since the 2000s reflects a continuous anthropogenically forced melting masked by interdecadal variability of Arctic atmospheric circulation. This variation is partially driven by teleconnections originating from sea surface temperature (SST) changes in the east-central tropical Pacific via a Rossby wave train propagating into the Arctic (hereafter referred to as the “Pacific-Arctic teleconnection (PARC)”), which represents the leading internal mode connecting the pole to lower latitudes. This mode has contributed to accelerated warming and Arctic sea ice loss from 2007 to 2012, followed by slower declines in recent years, resulting in the appearance of a slowdown over the past 11 years. A pacemaker model simulation, in which we specify observed SST in the tropical eastern Pacific, demonstrates a physically plausible mechanism for the PARC mode. However, the model-based PARC mechanism is considerably weaker and only partially accounts for the observed acceleration of sea ice loss from 2007 to 2012. Further research is needed to identify the reasons for model limitations in reproducing the PARC mode.

Baxter, Ian↗

DOE OSTI2021

CO2 partial pressure and fluxes in the Amazon River Plume using in situ and remote sensing data

Estimations of the global carbon budget include a quantitative understanding of the evolving processes that occur along river-to-ocean gradients. However, high spatiotemporal resolution observations of these processes are limited. Here we present in situ measurements of the partial pressure of CO2 (pCO2) made through the Amazon River plume (ARP) during different discharge seasons, from 2010-2012. We evaluated the spatiotemporal distribution of pCO2 using Soil Moisture and Ocean Salinity (SMOS) satellite observations for each hydrologic period in the ARP. Regression models were used to estimate pCO2 at the ARP for the period of 2010-2014. From these distributions we calculated sea-air gas exchange of CO2 between the plume waters and the atmosphere (F_co2^sea). Intra-annual variability of F_co2^sea was related to discharge at the river mouth and ocean currents as well as trade winds in the plume. Climatic events during the study period had a significant impact on the F_co2^sea. Including the plume area closer to the river mouth makes the ARP a net source of CO2 with an annual net sea-air flux of 8.6 ±7.1 Tg C y-1 from 2011-2014.

Amazon↗

DOE OSTI2021

Partial deconfinement at strong coupling on the lattice

We provide evidence for partial deconfinement — the deconfinement of a SU(M) subgroup of the SU(N) gauge group — by using lattice Monte Carlo simulations. We take matrix models as concrete examples. By appropriately fixing the gauge, we observe that the M × M submatrices deconfine. This gives direct evidence for partial deconfinement at strong coupling. We discuss the applications to QCD and holography.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Kinetics and Reactor Modeling of VFA Ketonization for Sustainable Aviation Fuel Production

Ketonization of volatile fatty acids (VFAs) produced via arrested methanogenesis of wet waste represents the only unit operation of wet waste upgrading to sustainable (net-zero or negative life cycle CO2 emissions) aviation fuel not currently in industrial practice. Ketone product yields of close to 100% have been obtained during gas-phase reactions of VFAs over oxide catalysts at the laboratory scale, but design of an industrial ketonization reactor requires understanding of the impacts of reactant and product partial pressures, deactivation, and heat and mass transport phenomena on observed ketonization rates. Our work leverages rigorous kinetic analysis of ketonization processes to inform reactor scale-up efforts through packed-bed reactor modeling. We first present results of a kinetic study of ketonization of a model VFA, hexanoic acid, over an industrial ZrO2 catalyst performed in a packed-bed microreactor in conditions free of significant heat or mass transfer gradients. Major findings of the analysis include: (i) hexanoic acid saturates all catalyst active sites at relatively low partial pressure (~10 kPa) and (ii) ketonization products 6-undecanone, water, and CO2 inhibit reaction rates. Kinetic data are used to fit a rate expression quantifying the functional dependence of ketonization rate on partial pressures of VFA reactants and ketone, water, and CO2 products. A packed-bed reactor model describing vapor-phase hexanoic acid ketonization over ZrO2 extrudate catalysts is developed based on the kinetic model. The effects of (i) bed- and pellet-scale mass- and heat-transfer limitations and (ii) axial pressure drop guide our development of recommendations for optimal sizing, temperature, and influent flow composition of an industrial-scale ketonization reactor. The quantitative understanding of VFA ketonization developed in this study represents an advance toward derisking the VFA ketonization step of wet waste upgrading to sustainable aviation fuel.

biojet↗

DOE OSTI2020

Wildfire Smoke Particle Properties and Evolution, from Space-Based Multi-Angle Imaging

Emitted smoke composition is determined by properties of the biomass burning source and ambient ecosystem. However, conditions that mediate the partitioning of black carbon (BC) and brown carbon (BrC) formation, as well as the spatial and temporal factors that drive particle evolution, are not understood adequately for many climate and air-quality related modeling applications. In situ observations provide considerable detail about aerosol microphysical and chemical properties, although sampling is extremely limited. Satellites offer the frequent global coverage that would allow for statistical characterization of emitted and evolved smoke, but generally lack microphysical detail. However, once properly validated, data from the National Aeronautics and Space Administration (NASA) Earth Observing System’s Multi-Angle Imaging Spectroradiometer (MISR) instrument can create at least a partial picture of smoke particle properties and plume evolution. We use in situ data from the Department of Energy’s Biomass Burning Observation Project (BBOP) field campaign to assess the strengths and limitations of smoke particle retrieval results from the MISR Research Aerosol (RA) retrieval algorithm. We then use MISR to characterize wildfire smoke particle properties and to identify the relevant aging factors in several cases, to the extent possible. The RA successfully maps qualitative changes in effective particle size, light absorption, and its spectral dependence, when compared to in situ observations. By observing the entire plume uniformly, the satellite data can be interpreted in terms of smoke plume evolution, including size-selective deposition, new-particle formation, and locations within the plume where BC or BrC dominates.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

3D-Printable Fluoropolymer Gas Diffusion Layers for CO 2 Electroreduction

The electrosynthesis of value-added multicarbon products from CO 2 is a promising strategy to shift chemical production away from fossil fuels. Particularly important is the rational design of gas diffusion electrode (GDE) assemblies to react selectively, at scale, and at high rates. However, the understanding of the gas diffusion layer (GDL) in these assemblies is limited for the CO 2 reduction reaction (CO 2 RR): particularly important, but incompletely understood, is how the GDL modulates product distributions of catalysts operating in high current density regimes > 300 mA cm -2 . Here, 3D-printable fluoropolymer GDLs with tunable microporosity and structure are reported and probe the effects of permeance, microstructural porosity, macrostructure, and surface morphology. Under a given choice of applied electrochemical potential and electrolyte, a 100× increase in the C 2 H 4 :CO ratio due to GDL surface morphology design over a homogeneously porous equivalent and a 1.8× increase in the C 2 H 4 partial current density due to a pyramidal macrostructure are observed. Overall, these findings offer routes to improve CO 2 RR GDEs as a platform for 3D catalyst design.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Experimental Demonstration of Dark‐State Metasurface Laser with Controllable Radiative Coupling

Abstract Lasing at the nanoscale using plasmonic nanoparticles offers the prospect of strong field concentration, hence strong light−matter interactions, low lasing thresholds, and ultrafast operation. However plasmonic nanoparticles suffer from high dissipative and radiative losses, the latter being rigidly tied to the shape of the nanoparticles and symmetry of their localized plasmon resonant modes. To overcome this limitation, recent theoretical work proposes using direct lasing into dark surface states to construct lasers that conceptually allow for independent implementation of the lasing state and its coherent radiation output. Here, lasing in dark resonant states of a metasurface laser and controllable coherent outcoupling of radiation with the aid of a tightly coupled, weakly radiative metasurface are demonstrated experimentally. The laser is implemented using a thin, low‐loss dielectric film supporting surface mode‐like dark dielectric bound states and the coupling metasurface is composed of small non‐resonant scatterers that controllably but weakly perturb the dark mode and turn it partially bright. Distinct far‐field signatures that can be observed experimentally for both dark and bright lasing are identified and demonstrated. The scalability of this design, here implemented for lasing in the near‐infrared, enables large‐aperture ultra‐thin coherent light sources with controllable emission from the infrared to the visible.

36 MATERIALS SCIENCE↗

DOE OSTI2024

On gauge amplitudes first appearing at two loops

We study scattering amplitudes in massless non-abelian gauge theory where all outgoing gluons have positive helicity. It has been argued recently by Costello that for a particular fermion representation (8 fundamentals plus one antisymmetric-tensor representation in SU(N)) the one-loop amplitudes vanish identically. We show that this vanishing leads to previously-observed identities among one-loop color-ordered partial amplitudes. We then turn to two loops, where Costello has computed the all-plus amplitudes for this theory, as rational functions of the kinematics for any number of gluons using the celestial chiral algebra (CCA) bootstrap. We show that in dimensional regularization, these two-loop amplitudes are not rational, and they are not even finite as ϵ → 0. However, the finite remainder for four gluons agrees with the formula by Costello. In addition, we provide a mass regulator for the infrared-divergent loop integrals; with this regulator, the CCA bootstrap formula is recovered exactly. Finally, we use the CCA bootstrap to compute the double-trace terms in the theory at two loops for an arbitrary number of gluons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗