PyEmittance: A General Python Package for Particle Beam Emittance Measurements with Adaptive Quadrupole Scans
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Miskovich, S. A.↗
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Quadrupolar interactions between acceptor pairs in $\mathcal{p}$-doped semiconductors
Here, we consider the interaction between acceptor pairs in doped semiconductors in the limit of large interacceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, the dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-$\mathcal{j}$ symbol, $^\{\frac{^2_3}{\small2} \frac{^2_3}{\small2} \frac{^2_3}{\small2}$$^\}$ = 0. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating $\mathcal{p}$-type semiconductors.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Reconstruction of the 4D beam matrix
The widely used transverse parameters characterizing particle beams are the Twiss parameters. These parameters can be measured experimentally but they do not fully characterize the beam since they do not account for possible correlations in particle distribution between two transverse coordinates. These correlations may occur due to uncompensated magnetic field at the cathode or misalignment of focusing quadrupoles in the transport beamline. We test a novel diagnostic for diagnosing full 4D beam matrix which may be used to identify such imperfections. The diagnostic is based on transporting the beam through the beamline which includes a quadrupole and a skew quadrupole magnets and measuring the resulting 2D beam distribution at the screen downstream. Such a measurement can be viewed as measuring a 2D projection of the 4D distribution. Different settings of the quads provide measurements of different slices of the phase space. The reconstruction of the original beam matrix from a number of measurements is done using machine learning algorithm, which provides a fast and reliable way of reconstruction for an arbitrary configuration of the scanning beamline. In August 2024, we set up the diagnostic beamline to perform a quadrupole scan of the beam. The setup includes a skew quadrupole, a regular quadrupole, and a screen. The images on the screen were post-processed to remove experimental artifacts and enhance contrast by eliminating background noise outside the core of the distribution=. The rms parameters of the distribution were then calculated and used as inputs for the reconstruction algorithm. This algorithm attempts to determine the initial beam matrix that produces expected images on the screen closely matching the observed images across all quadrupole settings. The algorithm found a solution in which the expected rms parameters closely align with the observations. Validation of the results is planned for FY25.
43 PARTICLE ACCELERATORS↗
Nature of Hyperfine Interactions in TbPc 2 Single-Molecule Magnets: Multiconfigurational Ab Initio Study
Lanthanide-based single-ion magnetic molecules can have large magnetic hyperfine interactions as well as large magnetic anisotropy. Recent experimental studies reported tunability of these properties by changes of chemical environments or by application of external stimuli for device applications. In order to provide insight onto the origin and mechanism of such tunability, here we investigate the magnetic hyperfine and nuclear quadrupole interactions for a 159 Tb nucleus in TbPc 2 (Pc = phthalocyanine) single-molecule magnets using multiconfigurational ab initio methods including spin–orbit interaction. Since the electronic ground and first-excited (quasi)doublets are well separated in energy, the microscopic Hamiltonian can be mapped onto an effective Hamiltonian with an electronic pseudospin S = 1/2. From the ab initio calculated parameters, we find that the magnetic hyperfine coupling is dominated by the interaction of the Tb nuclear spin with electronic orbital angular momentum. The asymmetric 4f-like electronic charge distribution leads to a strong nuclear quadrupole interaction with significant transverse terms for the molecule with low symmetry. The ab initio calculated electronic–nuclear spectrum including the magnetic hyperfine and quadrupole interactions is in excellent agreement with the experiment. We further find that the transverse quadrupole interactions significantly influence the avoided level crossings in magnetization dynamics and that the molecular distortions affect mostly the Fermi contact terms as well as the transverse quadrupole interactions. Synopsis Hyperfine interactions for 159 Tb nucleus in TbPc 2 single-molecule magnets are investigated from first-principles using multiconfigurational calculations. Strong nuclear quadrupole and magnetic hyperfine coupling are found, with the latter being dominated by the paramagnetic spin-orbital mechanism. Furthermore, we construct an ab initio pseudospin Hamiltonian and obtain the electronic-nuclear spectrum that is in excellent agreement with experiment. The Zeeman diagram is calculated, and the magnetization dynamics is discussed. The effects of molecular distortions are researched.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Cosmic temperature fluctuations from two years of COBE differential microwave radiometers observations
The first two years of Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) observations of the cosmic microwave background (CMB) anisotropy are analyzed and compared with our previously published first year results. The results are consistent, but the addition of the second year of data increases the precision and accuracy detected CMB temperature fluctuations. The 2 yr 53 GHz data are characterized by rms temperature fluctuations of (delta-T)(sub rms) (7 deg) = 44 +/- 7 micro-K and (delta-T)(sub rms) (10 deg) = 30.5 +/- 2.7 micro-K at 7 deg and 10 deg angular resolution, respectively. The 53 x 90 GHz cross-correlation amplitude at zero lag is C(0)(sup 1/2) = 36 +/- 5 micro-K (68% CL) for the unsmoothed (7 deg resolution) DMR data. We perform a likelihood analysis of the cross-correlation function, with Monte Carlo simulations to infer biases of the method, for a power-law model of initial density fluctuations, P(k) proportional to R(exp n). The Monte Carlo simulations indicate that derived estimates of n are biased by +0.11 +/- 0.01, while the subset of simulations with a low quadrupole (as observed) indicate a bias of +0.31+/- 0.04. Derived values for 68% confidence intervals are given corrected (and not corrected) for our estimated biases. Including the quadrupole anisotropy, the most likely quadrupole-normalized amplitude is Q(sub rms-PS) = 14.3(sup + 5.2 sub -3.3) micro-K (12.8(sup + 5.2 sub -3.3) micro-K0 with a spectral index n = 1.42(sup + 0.49 sub -0.55)(n = 1.53(sup + 0.49 sub -0.55). With n fixed to 1.0 the most likely amplitude is 18.2 +/- 11.5 micro-K (17.4 +/- 1.5 micro-K). The marginal likelihood of n is 1.42 +/- 0.37 (1.53 +/- 0.37). Excluding the quadrupole anisotropy, the most likely quadrupole-normalized amplitude is Q(sub rms-PS) = 17.4(sup + 7.5 sub -5.2) micro-K (15.8(sup + 7.5 sub -5.2) micro-K) with a spectral index n = 1.11(sup + 0.60 sub -0.55) (n = 1.22(sup + 0.60 sub -0.55). With n fixed to 1.0 the most likely amplitude is 18.6 +/- 1.6 micro-K (18.2 +/- 1.6 micro-K). The marginal likelihood of n is 1.11 +/- 0.40 (1.22 +/- 0.40). Our best estimate of the dipole from the 2 yr DMR data is 3.363 +/- 0.024 mK toward Galactic coordinates (l, b) = (264.4 deg +/- 0.2 deg, 48.1 deg +/- 0.4 deg), and our best estimate of the rms quadrupole amplitude in our sky is 6 +/- 3 micro-K (68% CL).
Bennett, C. L.↗
Non-Linear Cosmological Power Spectra in Real and Redshift Space
We present an expression for the non-linear evolution of the cosmological power spectrum based on Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self-gravitating fields. Some exact solutions are found for power-law initial spectra. We have extended this analysis into red-shift space and found a solution for the non-linear, anisotropic redshift-space power spectrum in the limit of plane-parallel redshift distortions. The quadrupole-to-monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, beta. The point of zero-crossing of the quadrupole, kappa(sub o), is found to obey a simple scaling relation and we calculate this scale in the Zel'dovich approximation. This model is found to be in good agreement with a series of N-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole-to-monopole ratio found in the merged QDOT plus 1.2-Jy-IRAS redshift survey. Using a likelihood technique we have estimated that the distortion parameter is constrained to be beta greater than 0.5 at the 95 percent level. Our results are fairly insensitive to the local primordial spectral slope, but the likelihood analysis suggests n = -2 un the translinear regime. The zero-crossing scale of the quadrupole is k(sub 0) = 0.5 +/- 0.1 h Mpc(exp -1) and from this we infer that the amplitude of clustering is sigma(sub 8) = 0.7 +/- 0.05. We suggest that the success of this model is due to non-linear redshift-space effects arising from infall on to caustic and is not dominated by virialized cluster cores. The latter should start to dominate on scales below the zero-crossing of the quadrupole, where our model breaks down.
Taylor, A. N.↗
Deformation and Collectivity in Doubly Magic 208 Pb
Lead-208 is the heaviest known doubly magic nucleus and its structure is therefore of special interest. Despite this magicity, which acts to provide a strong restorative force toward sphericity, it is known to exhibit both strong octupole correlations and some of the strongest quadrupole collectivity observed in doubly magic systems. In this Letter, we employ state-of-the-art experimental equipment to conclusively demonstrate, through four Coulomb-excitation measurements, the presence of a large, negative, spectroscopic quadrupole moment for both the vibrational octupole 3$^{−}_{1}$ and quadrupole 2$^{+}_{1}$ state, indicative of a preference for prolate deformation of the states. The observed quadrupole moment is discussed in the context of the expected splitting of the 3 − ⊗3 − two-phonon states, due to the coupling of the quadrupole and octupole motion. These results are compared with theoretical values from three different methods, which are unable to reproduce both the sign and magnitude of this deformation. Thus, in spite of its well-studied nature, 208 Pb remains a puzzle for our understanding of nuclear structure.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Thermal conductivity and resonant multipole interactions
The influence of multipole interactions on exchanges of rotational energy in molecular collisions was investigated by means of a simple two-state impact parameter approximation. The calculations are restricted to linear molecules and to dipole and quadrupole fields. The effects of such exchanges on the thermal conductivity of gases and of gaseous mixtures was investigated, after correcting the kinetic theory of mixtures to include exchanges between unlike molecules. It was found that dipole-quadrupole and quadrupole-quadrupole interactions may have a significant effect for molecules with low moments of inertia. In particular, quadrupole interactions are important in the hydrogen isotopes, and the calculated corrections for H2 are consistent with recent experimental work by Harris. The theory seems capable of accounting for the anomalies observed in HF + DF and HCl + DCl mixtures in terms of multipolar accidental resonances.
Nyeland, C.↗
An efficient and robust method for predicting helicopter rotor high-speed impulsive noise
A new formulation for the Ffowcs Williams-Hawkings quadrupole source, which is valid for a far-field in-plane observer, is presented. The far-field approximation is new and unique in that no further approximation of the quadrupole source strength is made and integrands with r(exp -2) and r(exp -3) dependence are retained. This paper focuses on the development of a retarded-time formulation in which time derivatives are analytically taken inside the integrals to avoid unnecessary computational work when the observer moves with the rotor. The new quadrupole formulation is similar to Farassat's thickness and loading formulation 1A. Quadrupole noise prediction is carried out in two parts: a preprocessing stage in which the previously computed flow field is integrated in the direction normal to the rotor disk, and a noise computation stage in which quadrupole surface integrals are evaluated for a particular observer position. Preliminary predictions for hover and forward flight agree well with experimental data. The method is robust and requires computer resources comparable to thickness and loading noise prediction.
Brentner, Kenneth S.↗
BATSE Observations of the Large-Scale Isotropy of Gamma-Ray Bursts
We use dipole and quadrupole statistics to test the large-scale isotropy of the first 1005 gamma-ray bursts observed by the Burst and Transient Source Experiment (BATSE). In addition to the entire sample of 1005 gamma-ray bursts, many subsets are examined. We use a variety of dipole and quadrupole statistics to search for Galactic and other predicted anisotropies and for anisotropies in a coordinate-system independent manner. We find the gamma-ray burst locations to be consistent with isotropy, e.g., for the total sample the observed Galactic dipole moment (cos theta) differs from the value predicted for isotropy by 0.9 sigma and the observed Galactic quadrupole moment (sin(exp 2) b - 1/3) by 0.3 sigma. We estimate for various models the anisotropies that could have been detected. If one-half of the locations were within 86 deg of the Galactic center, or within 28 deg of the Galactic plane, the ensuing dipole or quadrupole moment would have typically been detected at the 99% confidence level. We compare the observations with the dipole and quadrupole moments of various Galactic models. Several Galactic gamma-ray bursts models have moments within 2 sigma of the observations; most of the Galactic models proposed to date are no longer in acceptable agreement with the data. Although a spherical dark matter halo distribution could be consistent with the data, the required core radius is larger than the core radius of the dark matter halo used to explain the Galaxy's rotation curve. Gamma-ray bursts are much more isotropic than any observed Galactic population, strongly favoring but not requiring an origin at cosmological distances.
Briggs, Michael S.↗
Evaluating Mass Analyzers as Candidates for Small, Portable, Rugged Single Point Mass Spectrometers for Analysis of Permanent Gases
For Space Shuttle launch safety, there is a need to monitor the concentration Of H2, He, O2, and Ar around the launch vehicle. Currently a large mass spectrometry system performs this task, using long transport lines to draw in samples. There is great interest in replacing this stationary system with several miniature, portable, rugged mass spectrometers which act as point sensors which can be placed at the sampling point. Five commercial and two non-commercial analyzers are evaluated. The five commercial systems include the Leybold Inficon XPR-2 linear quadrupole, the Stanford Research (SRS-100) linear quadrupole, the Ferran linear quadrupole array, the ThermoQuest Polaris-Q quadrupole ion trap, and the IonWerks Time-of-Flight (TOF). The non-commercial systems include a compact double focusing sector (CDFMS) developed at the University of Minnesota, and a quadrupole ion trap (UF-IT) developed at the University of Florida.
Arkin, C. Richard↗
Evaluating Mass Analyzers as Candidates for Small, Portable, Rugged Single Point Mass Spectrometers for Analysis of Permanent Gases
For Space Shuttle launch safety, there is a need to monitor the concentration of H2, He, O2 and Ar around the launch vehicle. Currently a large mass spectrometry system performs this task, using long transport lines to draw in samples. There is great interest in replacing this stationary system with several miniature, portable, rugged mass spectrometers which act as point sensors which can be placed at the sampling point. Five commercial and two non-commercial analyzers are evaluated. The five commercial systems include the Leybold Inficon XPR-2 linear quadrupole, the Stanford Research (SRS-100) linear quadrupole, the Ferran linear quadrupole array, the ThermoQuest Polaris-Q quadrupole ion trap, and the IonWerks Time-of-Flight (TOF). The non-commercial systems include a compact double focusing sector (CDFMS) developed at the University of Minnesota, and a quadrupole ion trap (UF-IT) developed at the University of Florida. The System Volume is determined by measuring the entire system volume including the mass analyzer, its associated electronics, the associated vacuum system, the high vacuum pump and rough pump. Also measured are any ion gauge controllers or other required equipment. Computers are not included. Scan Time is the time required for one scan to be acquired and the data to be transferred. It is determined by measuring the time required acquiring a known number of scans and dividing by said number of scans. Limit of Detection is determined first by performing a zero-span calibration (using a 10-point data set). Then the limit of detection (LOD) is defined as 3 times the standard deviation of the zero data set. (An LOD of 10 ppm or less is considered acceptable.)
Arkin, C. Richard↗
Suppressing Loss of Ions in an Atomic Clock
An improvement has been made in the design of a compact, highly stable mercury- ion clock to suppress a loss of ions as they are transferred between the quadrupole and higher multipole ion traps. Such clocks are being developed for use aboard spacecraft for navigation and planetary radio science. The modification is also applicable to ion clocks operating on Earth: indeed, the success of the modification has been demonstrated in construction and operation of a terrestrial breadboard prototype of the compact, highly stable mercury-ion clock. Selected aspects of the breadboard prototype at different stages of development were described in previous NASA Tech Briefs articles. The following background information is reviewed from previous articles: In this clock as in some prior ion clocks, mercury ions are shuttled between two ion traps, one a 16- pole linear radio-frequency trap, while the other is a quadrupole radio-frequency trap. In the quadrupole trap, ions are tightly confined and optical state selection from a 202Hg lamp is carried out. In the 16-pole trap, the ions are more loosely confined and atomic transitions are interrogated by use of a microwave beam at approximately 40.507 GHz. The trapping of ions effectively eliminates the frequency pulling that would otherwise be caused by collisions between clock atoms and the wall of a gas cell. The shuttling of the ions between the two traps enables separation of the state-selection process from the clock microwave-resonance process, so that each of these processes can be optimized independently of the other. This is similar to the operation of an atomic beam clock, except that with ions the beam can be halted and reversed as ions are shuttled back and forth between the two traps. When the two traps are driven at the same radio frequency, the strength of confinement can be reduced near the junction between the two traps, depending upon the relative phase of the RF voltage used to operate each of the two traps, and can cause loss of ions during each transit between the traps and thereby cause loss of the 40.507-GHz ion-clock resonance signal. The essence of the modification is to drive the two traps at different frequencies typically between 1.5 and 2 MHz for the quadrupole trap and a frequency a few hundred kHz higher for the 16- pole trap. A frequency difference of a few hundred kHz ensures that the ion motion caused by the trapping electric fields is small relative to the diameter of the traps. Unlike in the case in which both traps are driven at the same frequency, the trapping electric fields near the junction are not zero at all times; instead, the regions of low electric field near the junction open and close at the difference frequency. An additional benefit of making the 16-pole trap operate at higher frequency is that the strength or depth of the multipole trap can be increased independent of the quadrupole ion trap.
Prestage, John↗
Electron beam echoes in the IOTA ring
This study is a continuation of previous efforts to demonstrate the possibility of electron beam echo generation in the IOTA ring. Transverse beam echoes are conventionally produced by a dipole kick followed by a single quadrupole kick. We seek to use multiple quadrupole kicks over successive turns to generate an echo larger than that from a single kick. We use beam echo theory and simulations to model and predict the expected echo generated by multiple quadrupole kicks. We also run simulated scans over various parameters relevant to the echo to optimize the echo amplitude, including delay time, quadrupole strength, tune split, and pulse number. Effects due to quantum excitation and synchrotron damping (which are particularly relevant with electrons) were also considered in simulation. Results indicate that given sufficient quadrupole kick strength, we should expect to be able to measure electron beam echoes in the IOTA ring.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Bulk and Nanocrystalline Cesium Lead-Halide Perovskites as Seen by Halide Magnetic Resonance
Lead-halide perovskites increasingly mesmerize researchers because they exhibit a high degree of structural defects and dynamics yet nonetheless offer an outstanding (opto)electronic performance on par with the best examples of structurally stable and defect-free semiconductors. This highly unusual feature necessitates the adoption of an experimental and theoretical mindset and the reexamination of techniques that may be uniquely suited to understand these materials. Surprisingly, the suite of methods for the structural characterization of these materials does not commonly include nuclear magnetic resonance (NMR) spectroscopy. The present study showcases both the utility and versatility of halide NMR and NQR (nuclear quadrupole resonance) for probing the structure and structural dynamics of CsPbX 3 (X = Cl, Br, I), in both bulk and nanocrystalline forms. The strong quadrupole couplings, which originate from the interaction between the large quadrupole moments of, e.g., the 35 Cl, 79 Br, and 127 I nuclei, and the local electric-field gradients, are highly sensitive to subtle structural variations, both static and dynamic. The quadrupole interaction can resolve structural changes with accuracies commensurate with synchrotron X-ray diffraction and scattering. It is shown that space-averaged site-disorder is greatly enhanced in the nanocrystals compared to the bulk, while the dynamics of nuclear spin relaxation indicates enhanced structural dynamics in the nanocrystals. The findings from NMR and NQR were corroborated by ab initio molecular dynamics, which point to the role of the surface in causing the radial strain distribution and disorder. These findings showcase a great synergy between solid-state NMR or NQR and molecular dynamics simulations in shedding light on the structure of soft lead-halide semiconductors.
36 MATERIALS SCIENCE↗
A classical model for three-body interactions in aqueous ionic systems
We present a classical induction model to evaluate the three-body ion–water–water (I–W–W) and water–water–water (W–W–W) interactions in aqueous ionic systems. The classical description of the induction energy is based on electrostatic distributed multipoles up to hexadecapole and distributed polarizabilities up to quadrupole–quadrupole on the O and H atoms of water. The monatomic ions were described by a point charge and a dipole–dipole polarizability, while for the polyatomic ions, distributed multipoles up to hexadecapole and distributed polarizabilities up to quadrupole–quadrupole were used. The accuracy of the classical model is benchmarked against an accurate dataset of 936 (I–W–W) and 2184 (W–W–W) three-body terms for 13 different monatomic and polyatomic cation and anion systems. The classical model shows excellent agreement with the reference second order Moller–Plesset and coupled-cluster single double and perturbative triple [CCSD(T)] three-body energies. The Root-Mean-Square-Errors (RMSEs) for monatomic cations, monatomic anions, and polyatomic ions were 0.29, 0.25, and 0.12 kcal/mol, respectively. The corresponding RMSE for 1744 CCSD(T)/aVTZ three-body (W–W–W) energies, used to train MB-pol, was 0.12 kcal/mol. The accuracy of the proposed classical model demonstrates that the three-body term for aqueous ionic systems can be accurately modeled classically. This approach provides a fast, efficient, and as-accurate path toward modeling the three-body term in aqueous ionic systems that is fully transferable across systems with different ions without the need to fit to tens of thousands of ab initio calculations for each ion to extend existing many-body force fields to interactions between water and ions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
4D beam matrix reconstruction in particle accelerators
Transverse beam parameters in particle accelerators are commonly described using the Twiss parameters, which are experimentally accessible yet inherently limited because they neglect correlations between different transverse coordinates. Such correlations frequently arise from uncompensated cathode magnetic fields or misaligned focusing quadrupoles, affecting beam quality and accelerator performance. To address this limitation, we propose and validate a novel diagnostic method for the complete four-dimensional (4D) transverse beam matrix. Our method involves passing the beam through a beamline comprising both conventional and skew quadrupole magnets, followed by downstream measurements of the resulting two-dimensional (2D) beam profiles. These measurements represent distinct 2D projections of the underlying 4D transverse phase–space distribution. By systematically varying quadrupole strengths, multiple independent projections of the beam phase space are obtained. We reconstruct the original 4D beam matrix from these measured projections using an optimization-based least-square fit, providing fast and robust reconstruction regardless of the specific beamline configuration. Through extensive numerical simulations and realistic particle-tracking studies, we demonstrate the diagnostic’s accuracy, robustness, and capability to achieve reconstruction uncertainties smaller than measurement errors, particularly when employing sufficient numbers of quadrupole scans. This method presents a powerful and flexible approach for comprehensive beam characterization and accelerator tuning.
43 PARTICLE ACCELERATORS↗
The BOSS bispectrum analysis at one loop from the Effective Field Theory of Large-Scale Structure
Abstract We analyze the BOSS power spectrum monopole and quadrupole, and the bispectrum monopole and quadrupole data, using the predictions from the Effective Field Theory of Large-Scale Structure (EFTofLSS). Specifically, we use the one loop prediction for the power spectrum and the bispectrum monopole, and the tree level for the bispectrum quadrupole. After validating our pipeline against numerical simulations as well as checking for several internal consistencies, we apply it to the observational data. We find that analyzing the bispectrum monopole to higher wavenumbers thanks to the one-loop prediction, as well as the addition of the tree-level quadrupole, significantly reduces the error bars with respect to our original analysis of the power spectrum at one loop and bispectrum monopole at tree level. After fixing the spectral tilt to Planck preferred value and using a Big Bang Nucleosynthesis prior, we measureσ 8 = 0.794 ± 0.037,h = 0.692 ± 0.011, and Ω m = 0.311 ± 0.010 to about 4.7%, 1.6%, and 3.2%, at 68% CL, respectively.This represents an error bar reduction with respect to the power spectrum-only analysis of about 30%, 18%, and 13% respectively. Remarkably, the results are compatible with the ones obtained with a power-spectrum-only analysis, showing the power of the EFTofLSS in simultaneously predicting several observables. We find no tension with Planck.
Astronomy & Astrophysics↗