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DOE OSTI2014

Event-by-event weighting at next-to-leading order

We present a general method of associating next-to-leading order weights to leading order phase space configurations at hadron colliders. The method relies on a re-organization of phase space for the real radiation contributions, defining a one-to-many map such that each point in the real phase space is associated with a distinct Born topology. As a result virtual and real singularities cancel at each Born phase space point. The new phase space maps can be used in a traditional approach for NLO calculations. However, interesting applications arise when one instead integrates out the real radiation up to a specified scale. This allows one to define NLO weights for individual phase space points that are present at LO. This method allows for the extension of matrix element methods to next-to-leading order, even in the presence of jets. We discuss some recent applications of the matrix element method to Higgs physics at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

TU-AB-BRC-08: Egs-brachy, a Fast and Versatile Monte Carlo Code for Brachytherapy Applications

Purpose: To introduce egs-brachy, a new, fast, and versatile Monte Carlo code for brachytherapy applications. Methods: egs-brachy is an EGSnrc user-code based on the EGSnrc C++ class library (egs++). Complex phantom, applicator, and source model geometries are built using the egs++ geometry module. egs-brachy uses a tracklength estimator to score collision kerma in voxels. Interaction, spectrum, energy fluence, and phase space scoring are also implemented. Phase space sources and particle recycling may be used to improve simulation efficiency. HDR treatments (e.g. stepping source through dwell positions) can be simulated. Standard brachytherapy seeds, as well as electron and miniature x-ray tube sources are fully modelled. Variance reduction techniques for electron source simulations are implemented (Bremsstrahlung cross section enhancement, uniform Bremsstrahlung splitting, and Russian Roulette). TG-43 parameters of seeds are computed and compared to published values. Example simulations of various treatments are carried out on a single 2.5 GHz Intel Xeon E5-2680 v3 processor core. Results: TG-43 parameters calculated with egs-brachy show excellent agreement with published values. Using a phase space source, 2% average statistical uncertainty in the PTV ((2mm){sup 3} voxels) can be achieved in 10 s for 100 {sup 125}I or {sup 103}Pd seeds in a 36.2 cm{sup 3} prostate PTV, 31 s for 64 {sup 103}Pd seeds in a 64 cm{sup 3} breast PTV, and 56 s for a miniature x-ray tube in a 27 cm{sup 3} breast PTV. Comparable uncertainty is reached in 12 s in a (1 mm){sup 3} water voxel 5 mm away from a COMS 16mm eye plaque with 13 {sup 103}Pd seeds. Conclusion: The accuracy of egs-brachy has been demonstrated through benchmarking calculations. Calculation times are sufficiently fast to allow full MC simulations for routine treatment planning for diverse brachytherapy treatments (LDR, HDR, miniature x-ray tube). egs-brachy will be available as free and open-source software to the medical physics research community. This work is partially funded by the Canada Research Chairs program, the Natural Sciences and Engineering Research Council of Canada, and the Ontario Ministry of Research and Innovation (Ontario Early Researcher Award).

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation

Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory

Not Available

Qin, Hong↗

DOE OSTI2022

Characterization of nonlinear ultrasonic waves behavior while interacting with poor interlayer bonds in large-scale additive manufactured materials

Over the past decades, researchers have developed several nonlinear ultrasonic techniques for quality control of materials commonly used in different applications. Owing to the superior sensitivity of nonlinear ultrasound waves to small defects such as micro-cracks, their applicability in different nondestructive testing (NDT) problems has been investigated in numerous studies. These studies utilize frequency domain analysis to detect the generation of higher harmonics because of the formation of defects in the inspected medium. Frequency domain analysis based on the Fourier transform is a significant approach used in linear systems; however, it may not perform adequately on nonlinear systems. Hence, studies on nonlinear dynamics and physics consider analyzing systems' behavior in the phase-space domain. In contrast to the frequency domain analysis, which can result in information loss, analysis in the phase-space domain retains all the information regarding a system's states. Here, we investigate the nonlinearities induced by poor interlayer bonding in polymer-based additive manufactured parts in the phase-space domain. It is convenient to characterize the nonlinearity in the phase-space domain because it provides a geometrical representation of a system's states. Two types of low quality interlayer bond are considered. The first type is simulated artificially while the second type is manufactured by reducing the bond quality during the printing process. The analysis verified that the received ultrasonic signals exhibit classical nonlinear behavior in the phase-space domain while interacting with simulated poor interlayer bonds. In addition, the results showed that the behavior of ultrasonic waves is amplitude-dependent and evolves into models that have not been previously reported. Furthermore, Largest Lyapunov Exponent (LLE) is used to quantify the behavior of nonlinear ultrasonic waves while interacting with poor interlayer bonds. Using LLE, it was observed that the divergence rate of the phase-space trajectories depends on the amplitude of the excitation. This observation quantitatively proves that nonlinear behavior of ultrasound while interacting with poor interlayer bonds can be amplitude-dependent. The results of both simulated and inherent poor interlayer bond cases showed that LLE can be used as a reliable quantitative damage-sensitive feature to detect and potentially characterize weak bonds, which are difficult to detect using conventional approaches. Additionally, the reported results in the phase-space domain provide a basis for proposing a new mathematical model for ultrasonic waves interacting with poor interlayer bonds.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices

The study of nonlinear oscillator chains in classical many-body dynamics has a storied history going back to the seminal work of Fermi et al. [Los Alamos Scientific Laboratory Report No. LA-1940, 1955 (unpublished)]. Here, we introduce a family of such systems which consist of chains of N harmonically coupled particles with the nonlinearity introduced by confining the motion of each individual particle to a box or stadium with hard walls. The stadia are arranged on a one-dimensional lattice but they individually do not have to be one dimensional, thus permitting the introduction of chaos already at the lattice scale. For the most part we study the case where the motion is entirely one dimensional. We find that the system exhibits a mixed phase space for any finite value of N . Computations of Lyapunov spectra at randomly picked phase space locations and a direct comparison between Hamiltonian evolution and phase space averages indicate that the regular regions of phase space are not significant at large system sizes. While the continuum limit of our model is itself a singular limit of the integrable sinh Gordon theory, we do not see any evidence for the kind of nonergodicity famously seen in the work of Fermi et al. Finally, we examine the chain with particles confined to two-dimensional stadia where the individual stadium is already chaotic and find a much more chaotic phase space at small system sizes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

A Monte Carlo approach to validation of FFF VMAT treatment plans for the TrueBeam linac

Purpose: To commission and benchmark a vendor-supplied (Varian Medical Systems) Monte Carlo phase-space data for the 6 MV flattening filter free (FFF) energy mode on a TrueBeam linear accelerator for the purpose of quality assurance of clinical volumetric modulated arc therapy (VMAT) treatment plans. A method for rendering the phase-space data compatible with BEAMnrc/DOSXYZnrc simulation software package is presented. Methods: Monte Carlo (MC) simulations were performed to benchmark the TrueBeam 6 MV FFF phase space data that have been released by the Varian MC Research team. The simulations to benchmark the phase space data were done in three steps. First, the original phase space which was created on a cylindrical surface was converted into a format that was compatible with BEAMnrc. Second, BEAMnrc was used to create field size specific phase spaces located underneath the jaws. Third, doses were calculated with DOSXYZnrc in a water phantom for fields ranging from 1 Multiplication-Sign 1 to 40 Multiplication-Sign 40 cm{sup 2}. Calculated percent depth doses (PDD), transverse profiles, and output factors were compared with measurements for all the fields simulated. After completing the benchmarking study, three stereotactic body radiotherapy (SBRT) VMAT plans created with the Eclipse treatment planning system (TPS) were calculated with Monte Carlo. Ion chamber and film measurements were also performed on these plans. 3D gamma analysis was used to compare Monte Carlo calculation with TPS calculations and with film measurement. Results: For the benchmarking study, MC calculated and measured values agreed within 1% and 1.5% for PDDs and in-field transverse profiles, respectively, for field sizes >1 Multiplication-Sign 1 cm{sup 2}. Agreements in the 80%-20% penumbra widths were better than 2 mm for all the fields that were compared. With the exception of the 1 Multiplication-Sign 1 cm{sup 2} field, the agreement between measured and calculated output factors was within 1%. It is of note that excellent agreement in output factors for all field sizes including highly asymmetric fields was achieved without accounting for backscatter into the beam monitor chamber. For the SBRT VMAT plans, the agreement between Monte Carlo and ion chamber point dose measurements was within 1%. Excellent agreement between Monte Carlo, treatment planning system and Gafchromic film dose distribution was observed with over 99% of the points in the high dose volume passing the 3%, 3 mm gamma test. Conclusions: The authors have presented a method for making the Varian IAEA compliant 6 MV FFF phase space file of the TrueBeam linac compatible with BEAMnrc/DOSXYZnrc. After benchmarking the modified phase space against measurement, they have demonstrated its potential for use in MC based quality assurance of complex delivery techniques.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2026

Velocity-space Origins of the Pressure–Strain Interaction in Multipopulation Distributions and Its Application to Magnetic Reconnection

A forefront research question is how energy evolves in weakly collisional plasmas for which departures from local thermodynamic equilibrium (LTE) are significant. The standard approach is studying the terms in the non-LTE energy evolution equation derived by taking the second moment of the Boltzmann equation, but the resultant fluid metrics do not retain information about which particles at which velocities drive energy evolution. A widely studied channel for internal energy density evolution is the pressure–strain interaction. Here, we employ the kinetic pressure–strain, a phase-space diagnostic whose velocity-space integral recovers the pressure–strain interaction to disambiguate the contributions to the pressure–strain interaction from disparate particle populations in composite phase-space densities. We develop phase-space analogs of the pressure–strain interaction decompositions to provide the phase-space origins of normal versus sheared flow. We introduce the “kinetic strain-rate” tensor, the phase-space analog of the strain-rate tensor, which we argue is needed to interpret the phase-space origins of the pressure–strain interaction. To demonstrate the utility of these quantities, we investigate them for composite electron distributions near the electron diffusion region in two-dimensional particle-in-cell simulations of antiparallel symmetric magnetic reconnection. We find that the phase-space-based diagnostics isolate the roles of distinct populations. These results contribute to a growing body of work providing new methods for quantifying phase-space energy evolution for a broad array of processes, from magnetic reconnection to collisionless shocks and turbulence, opening new pathways for answering longstanding problems of particle energization in weakly collisional plasmas.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

SU-E-T-386: A Monte Carlo Dose Calculation Framework for Electron Beams On Varian TrueBeam

Purpose: The design of the linac head is different for TrueBeam than Clinac, and there are differences in measured dose distributions in water phantoms between TrueBeam and Clinac for electron beams. Therefore, MC models for Clinac may not be applied directly to the Truebeam linac. The purpose of this study is to validate a Monte Carlo (MC) dose calculation framework for electron beams on Varian TrueBeam with phase space files provided by Varian. Methods: The particle histories from the phase space file were used as input for the down-stream simulation including jaws, applicators, and water phantom. MC packages BEAMnrc/DOSYXZnrc were used. The down-stream beam components were modeled according to manufacturer specifications and the dose distributions were compared with the measured data of standard cones. The measurements were performed in a water phantom with a p-type electron field diode (diameter 0.2cm) and ion chamber (CC13). Depth dose and orthogonal profiles at depths defined by R{sub 1} {sub 0} {sub 0}, R{sub 5} {sub 0}, Rp were compared. Results: Preliminary results for a 16 MeV phase space and 10x10, 15x15, and 20x20 cm{sup 2} applicator are presented. Simulations were run for a statistical uncertainty of <2% at depth of maximum dose for a voxel resolution of 0.5x0.5x0.2cm{sup 2}. Dose and range differences for the PDD profiles were within 2% and 1 mm, respectively. Dose differences within the central 80% of the beam width for the orthogonal profiles at depth of maximum dose were less than 2% for the 10x10, 15x15, and 20x20 cm{sup 2} applicator, respectively. Conclusion: Varian electron phase space files simulations are in agreement with measured commissioning data. These phase space files can be used in the simulation of TrueBeam linacs, and will provide reproducibility across publications. Analyses for all electron energies and standard applicators are under way and results will be included in the presentation.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2019

Linear Light Amplifier and Amplification of N-Photon States

We consider a linear quantum amplifier consisting of NA two-level atoms and study the problem of amplification of N-photon states. The N-photon states are associated with N-quantum states of the harmonic oscillator. We show that the process of interaction of the electromagnetic field with atoms can be associated with some transformation of the phase space and functions defined on this phase space. We consider the Husimi functions QN(q, p) of N-quantum states of the harmonic oscillator, which are defined on the phase space, investigate transformation of these functions, and find an explicit form of the density matrix of the amplified N-photon state. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Measurements of the charge asymmetry in top-quark pair production in the dilepton final state at s = 8 TeV with the ATLAS detector

We presented measurements of the top-antitop quark pair production charge asymmetry in the dilepton channel, characterized by two high- pT leptons (electrons or muons), using data corresponding to an integrated luminosity of 20.3 fb $-$1 from pp collisions at a center-of-mass energy $\sqrt{s}$ = 8 TeV collected with the ATLAS detector at the Large Hadron Collider at CERN. Inclusive and differential measurements as a function of the invariant mass, transverse momentum, and longitudinal boost of the $t\bar{t}$ system are performed both in the full phase space and in a fiducial phase space closely matching the detector acceptance. Two observables are studied: A $ℓℓ\atop{C}$ based on the selected leptons and A$t\bar{t}\atop{C}$ based on the reconstructed $t\bar{t}$ final state. The inclusive asymmetries are measured in the full phase space to be A $ℓℓ\atop{C}$ = 0.008 ± 0.006 and A$t\bar{t}\atop{C}$= 0.021 ± 0.016 , which are in agreement with the Standard Model predictions of A $ℓℓ\atop{C}$ = 0.0064 ± 0.0003 and A$t\bar{t}\atop{C}$ = 0.0111 ± 0.0004 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

A single-atom library for guided monometallic and concentration-complex multimetallic designs

Atomically dispersed single-atom catalysts have the potential to bridge heterogeneous and homogeneous catalysis. Dozens of single-atom catalysts have been developed, and they exhibit notable catalytic activity and selectivity that are not achievable on metal surfaces. Although promising, there is limited knowledge about the boundaries for the monometallic single-atom phase space, not to mention multimetallic phase spaces. Here, single-atom catalysts based on 37 monometallic elements are synthesized using a dissolution-and-carbonization method, characterized and analyzed to build the largest reported library of single-atom catalysts. In conjunction with in situ studies, we uncover unified principles on the oxidation state, coordination number, bond length, coordination element and metal loading of single atoms to guide the design of single-atom catalysts with atomically dispersed atoms anchored on N-doped carbon. We utilize the library to open up complex multimetallic phase spaces for single-atom catalysts and demonstrate that there is no fundamental limit on using single-atom anchor sites as structural units to assemble concentration-complex single-atom catalyst materials with up to 12 different elements. Furthermore, our work offers a single-atom library spanning from monometallic to concentration-complex multimetallic materials for the rational design of single-atom catalysts.

36 MATERIALS SCIENCE↗

DOE OSTI2014

SU-E-T-459: Dosimetric Consequences of Rotated Elliptical Proton Spots in Modeling In-Air Proton Fluence for Calculating Doses in Water of Proton Pencil Beams

Purpose: We present a study of dosimetric consequences on doses in water in modeling in-air proton fluence independently along principle axes for rotated elliptical spots. Methods: Phase-space parameters for modeling in-air fluence are the position sigma for the spatial distribution, the angle sigma for the angular distribution, and the correlation between position and angle distributions. Proton spots of the McLaren proton therapy system were measured at five locations near the isocenter for the energies of 180 MeV and 250 MeV. An elongated elliptical spot rotated with respect to the principle axes was observed for the 180 MeV, while a circular-like spot was observed for the 250 MeV. In the first approach, the phase-space parameters were derived in the principle axes without rotation. In the second approach, the phase space parameters were derived in the reference frame with axes rotated to coincide with the major axes of the elliptical spot. Monte-Carlo simulations with derived phase-space parameters using both approaches to tally doses in water were performed and analyzed. Results: For the rotated elliptical 180 MeV spots, the position sigmas were 3.6 mm and 3.2 mm in principle axes, but were 4.3 mm and 2.0 mm when the reference frame was rotated. Measured spots fitted poorly the uncorrelated 2D Gaussian, but the quality of fit was significantly improved after the reference frame was rotated. As a Result, phase space parameters in the rotated frame were more appropriate for modeling in-air proton fluence of 180 MeV protons. Considerable differences were observed in Monte Carlo simulated dose distributions in water with phase-space parameters obtained with the two approaches. Conclusion: For rotated elliptical proton spots, phase-space parameters obtained in the rotated reference frame are better for modeling in-air proton fluence, and can be introduced into treatment planning systems.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

Simulation of convective transport during frequency chirping of a TAE using the MEGA code

Here, we present a procedure to examine energetic particle phase-space during long range frequency chirping phenomena in tokamak plasmas. To apply the proposed method, we have performed self-consistent simulations using the MEGA code and analyzed the simulation data. We demonstrate a traveling wave in phase-space and that there exist specific slices of phase-space on which the resonant particles lie throughout the wave evolution. For non-linear evolution of an n = 6 toroidicity-induced Alfvén eigenmode (TAE), our results reveal the formation of coherent phase-space structures (holes/clumps) after coarse-graining of the distribution function. These structures cause a convective transport in phase-space which implies a radial drift of the resonant particles. We also demonstrate that the rate of frequency chirping increases with the TAE damping rate. Our observations of the TAE behavior and the corresponding phase-space dynamics are consistent with the Berk–Breizman theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Geometrical splitting technique to improve the computational efficiency in Monte Carlo calculations for proton therapy

Purpose: To present the implementation and validation of a geometrical based variance reduction technique for the calculation of phase space data for proton therapy dose calculation. Methods: The treatment heads at the Francis H Burr Proton Therapy Center were modeled with a new Monte Carlo tool (TOPAS based on Geant4). For variance reduction purposes, two particle-splitting planes were implemented. First, the particles were split upstream of the second scatterer or at the second ionization chamber. Then, particles reaching another plane immediately upstream of the field specific aperture were split again. In each case, particles were split by a factor of 8. At the second ionization chamber and at the latter plane, the cylindrical symmetry of the proton beam was exploited to position the split particles at randomly spaced locations rotated around the beam axis. Phase space data in IAEA format were recorded at the treatment head exit and the computational efficiency was calculated. Depth-dose curves and beam profiles were analyzed. Dose distributions were compared for a voxelized water phantom for different treatment fields for both the reference and optimized simulations. In addition, dose in two patients was simulated with and without particle splitting to compare the efficiency and accuracy of the technique. Results: A normalized computational efficiency gain of a factor of 10-20.3 was reached for phase space calculations for the different treatment head options simulated. Depth-dose curves and beam profiles were in reasonable agreement with the simulation done without splitting: within 1% for depth-dose with an average difference of (0.2 {+-} 0.4)%, 1 standard deviation, and a 0.3% statistical uncertainty of the simulations in the high dose region; 1.6% for planar fluence with an average difference of (0.4 {+-} 0.5)% and a statistical uncertainty of 0.3% in the high fluence region. The percentage differences between dose distributions in water for simulations done with and without particle splitting were within the accepted clinical tolerance of 2%, with a 0.4% statistical uncertainty. For the two patient geometries considered, head and prostate, the efficiency gain was 20.9 and 14.7, respectively, with the percentages of voxels with gamma indices lower than unity 98.9% and 99.7%, respectively, using 2% and 2 mm criteria. Conclusions: The authors have implemented an efficient variance reduction technique with significant speed improvements for proton Monte Carlo simulations. The method can be transferred to other codes and other treatment heads.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

Longitudinal Beam Parameter Tolerances of NSLS-II

Similar to the transverse phase space, the beam parameters in the longitudinal phase space must also be monitored and controlled. In the longitudinal phase space the fundamental parameters are: bunch arrival time(or the corresponding RF phase), average momentum, bunch length, and momentum spread. These parameters are usually perturbed by the various noises in a real machine. The noises could excite longitudinal bunch motion, seen by the users as timing jitter, intensity and wavelength variation, and transverse position shift et al. The longitudinal oscillations also cause longitudinal emittance growth, therefore lengthen the bunch and increase the momentum spread, and eventually decrease the brightness. As a rule of thumb for the tolerances, either transverse or longitudinal, the perturbation caused by the noises should not result in a decrease of brightness by more than 10%. The users are concerned about the longitudinal beam parameters in several ways. First the timing jitter affects the timing-dependent experiments. Even though a photo-diode detection system is usually used to to determine the arrival time, the bandwidth is only about 1 kHz. The users from this category ask for a timing jitter tolerance to be 5% of the RMS bunch length over the frequency range from 500 Hz to 50 kHz. This corresponds to a phase error of Δφ = 1.6 mr or 0.1° for a 10 ps bunch with a 500 MHz rf system.

47 OTHER INSTRUMENTATION↗

DOE OSTI2018

Longitudinal Beam Parameter Tolerance of NSLS-II

36 MATERIALS SCIENCE↗

DOE OSTI2020

Measurement of the cross section for $\text{t}\bar{\text{t}}$ production with additional jets and b jets in pp collisions at $\sqrt{s}=$ 13 TeV

Measurements of the cross section for the production of top quark pairs in association with a pair of jets from bottom quarks $ \left({\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{b}\overline{\mathrm{b}}}\right) $ and in association with a pair of jets from quarks of any flavor or gluons $ \left({\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}}\right) $ and their ratio are presented. The data were collected in proton-proton collisions at a center-of-mass energy of 13 TeV by the CMS experiment at the LHC in 2016 and correspond to an integrated luminosity of 35.9 fb$^{−1}$. The measurements are performed in a fiducial phase space and extrapolated to the full phase space, separately for the dilepton and lepton+jets channels, where lepton corresponds to either an electron or a muon. The results of the measurements in the fiducial phase space for the dilepton and lepton+jets channels, respectively, are $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}} $ = 2.36±0.02 (stat)±0.20 (syst) pb and 31.0±0.2 (stat)±2.9 (syst) pb, and for the cross section ratio 0.017 ± 0.001 (stat) ± 0.001 (syst) and 0.020 ± 0.001 (stat) ± 0.001 (syst). The values of $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{b}\overline{\mathrm{b}}} $ are determined from the product of the $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}} $ and the cross section ratio, obtaining, respectively, 0.040±0.002 (stat)±0.005 (syst) pb and 0.62±0.03 (stat)±0.07 (syst) pb. These measurements are the most precise to date and are consistent, within the uncertainties, with the standard model expectations obtained using a matrix element calculation at next-to-leading order in quantum chromodynamics matched to a parton shower.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗