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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Measurement of the Photon Beam Asymmetry in yP -> K+S0 at Ey=8.5 GeV with GlueX

In this work the photon beam asymmetry Sigma for the reaction yp ? K+S0 (1193) is measured using the GlueX experiment in Hall D at Jefferson Lab. The analysis used data that were collected using a linearly polarized photon beam in the energy range (8.2 - 8.8) GeV incident on a liquid hydrogen target. The beam asymmetries are measured as a function of the Mandelstam variable t and as a single value for the low u region. These are the first exclusive measurements of the photon beam asymmetry Sigma in this reaction at energies above the baryon resonance region. For the t-channel, results are close to unity and show that the reaction is dominated by the natural-parity exchange of the K? (892) Regge trajectory as predicted by theoretical models. A value of Sigma = 0.410±0.090 is obtained for the u-channel and suggests the exchange of both Sigma(J = 1/2) and Y*(J = 3/2) trajectory contributions to the production of K+S0.

Wickramaarachchi, Nilanga↗
DOE OSTI2022

Measurement of the anomalous precession frequency in the Muon $g-2$ experiment at Fermilab

The muon anomalous magnetic moment, $a_\mu=\frac{g-2}{2}$, is a low energy observable that can be both measured and computed with high precision, therefore it can provide an important test of the Standard Model and it is a sensitive probe for new physics. In particular, any discrepancy between the experimental value and the theoretical prediction can be due to Beyond Standard Model physics contribution. The E989 Muon $g-2$ Experiment at Fermilab aims to measure $a_\mu$ with a precision of 140 parts per billion, four time more precisely than the previous experiment at Brookhaven National Laboratory (BNL). E989 seeks to either resolve or confirm the observed discrepancy of $3.7\sigma$ between the Standard Model value and the experimental one. The $a_\mu$ measurement requires a precise determination of both the muon spin anomalous precession frequency and the average magnetic field seen by the muons as they circulate in a storage ring. The anomalous precession frequency measurement is b ased on the time distribution of high-energy decay positrons observed by 24 electromagnetic calorimeters placed around the inner circumference of the ring, while the magnetic field is constantly monitored by NMR probes. Last spring, E989 has published a new measurement of $a_\mu$ from the 2018 data-taking campaign, confirming the previous BNL value with comparable precision, bringing the discrepancy with the theoretical value to $4.2\sigma$. The candidate worked on the measurement of the anomalous precession frequency and on the estimate of the related systematic uncertainties of the 2018 data, giving an important contribution to the data analysis. The result presented in chapters 4 and 5 of this dissertation was included, among three other analyses, to determine the estimate of the anomalous magnetic moment by the Muon g-2 experiment. This work will present the anomalous precession frequency analysis technique and its result, the related systematics and finally the latest $a_\mu$ result.

Sorbara, Matteo↗
NASA NTRS1993

Studies of Greenland using the SEASAT scatterometer

We have used Ku-band (14.6 GHz) Seasat scatterometer (SASS) measurements to study changes in the backscatter of the Greenland ice sheet in response to seasonal changes in the surface and subsurface characteristics of the snow and glacial ice. To overcome the limitations imposed by the 50 km resolution of the SASS measurement, a resolution enhancement algorithm was used to generate 10 km resolution images of the backscatter response. To generate the images, the observed sigma(sup 0) (in dB) was modeled as a linear function of incidence angle theta, i.e., sigma(sup 0)(theta) = A + B(theta - 40 degrees) where theta epsilon (23 degrees, 55 degrees). The variable A can be thought of as the 'incidence angle-normalized sigma(sup 0)', while the gradient B describes the incidence angle dependence of sigma(sup 0). A time-series (one image every two weeks) of vertical and horizontally-polarized A and B was generated spanning a 100 day period between Julian Dates 180 and 280 (i.e. 29 June and 7 October) in 1978. This time series dramatically shows the effects of the summer melt and a clear transition with fall cooling and snowfall towards a typical winter scattering situation. The images also clearly delineate a number of principal snow and ice 'facies' which are identifiable on the surface.

Long, David G.↗
DOE OSTI2024

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

The distribution of earthquakes with depth and stress in subducting slabs

The global variation of Benioff zone seismicity with depth and the orientation of stress axes of deep and intermediate earthquakes is explained using numerical models of subducting slabs. Models that match the seismicity and stress require a barrier to flow at the 670 km seismic discontinuity. The barrier may be a viscosity increase of at least an order of magnitude or a chemical discontinuity. Instantaneous flow is subparallel to the slabs for models with a viscosity increase but contorted for models with a chemical barrier. Log N (number of earthquakes) decreases linearly to 250-300 km depth and increases thereafter. Stress magnitude in the models shows the same pattern, in accord with experiments showing N proportional to e(k-sigma), with k a constant and sigma the stress magnitude. The models predict downdip compression in the slabs at depths below 300-400 km, as observed for earthquake stress axes.

Vassiliou, M. S.↗
DOE OSTI2025

Data-driven high-dimensional statistical inference with generative models

Crucial to many measurements at the LHC is the use of correlated multi-dimensional information to distinguish rare processes from large backgrounds, which is complicated by the poor modeling of many of the crucial backgrounds in Monte Carlo simulations. In this work, we introduce HI-SIGMA, a method to perform unbinned high-dimensional statistical inference with data-driven background distributions. In contradistinction to many applications of Simulation Based Inference in High Energy Physics, HI-SIGMA relies on generative ML models, rather than classifiers, to learn the signal and background distributions in the high-dimensional space. These ML models allow for interpretable inference while also incorporating model errors and other sources of systematic uncertainties. We showcase this methodology on a simplified version of a di-Higgs measurement in the bbγγ final state, where the di-photon resonance allows for background interpolation from sidebands into the signal region. We demonstrate that HI-SIGMA provides improved sensitivity as compared to standard classifier-based methods, and that systematic uncertainties can be straightforwardly incorporated by extending methods which have been used for histogram based analyses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1989

Operating and environmental characteristics of Sigma Tau hydrogen masers used in the Very Long Baseline Array (VLBA)

Presented here are the results obtained from performance evaluation of a pair of Sigma Tau Standards Corporation Model VLBA-112 active hydrogen maser frequency standards. These masers were manufactured for the National Radio Astronomy Observatory (NRAO) for use on the Very Long Baseline Array (VLBA) project and were furnished to the Jet Propulsion Laboratory (JPL) for the purpose of these tests. Tests on the two masers were performed in the JPL Frequency Standards Laboratory (FSL) and included the characterization of output frequency stability versus environmental factors such as temperature, humidity, magnetic field, and barometric pressure. The performance tests also included the determination of phase noise and Allan variance using both FSL and Sigma Tau masers as references. All tests were conducted under controlled laboratory conditions, with only the desired environmental and operational parameters varied to determine sensitivity to external environment.

Tucker, T. K.↗
DOE OSTI2022

X-ray morphology of cluster-mass haloes in self-interacting dark matter

ABSTRACT We perform cosmological zoom-in simulations of 19 relaxed cluster-mass haloes with the inclusion of adiabatic gas in the cold dark matter (CDM) and self-interacting dark matter (SIDM) models. These clusters are selected as dynamically relaxed clusters from a parent simulation with $M_{\rm 200} \simeq (1\!-\!3)\times 10^{15}{\, \rm M_\odot }$. Both the dark matter and the intracluster gas distributions in SIDM appear more spherical than their CDM counterparts. Mock X-ray images are generated based on the simulations and are compared to the real X-ray images of 84 relaxed clusters selected from the Chandra and ROSAT archives. We perform ellipse fitting for the isophotes of mock and real X-ray images and obtain the ellipticities at cluster-centric radii of $r\simeq 0.1\!-\!0.2R_{\rm 200}$. The X-ray isophotes in SIDM models with increasing cross-sections are rounder than their CDM counterparts, which manifests as a systematic shift in the distribution function of ellipticities. Unexpectedly, the X-ray morphology of the observed non-cool-core clusters agrees better with SIDM models with cross-section $(\sigma /m)= 0.5\!-\!1\, {\rm cm}^2\, {\rm g}^{-1}$ than CDM and SIDM with $(\sigma /m)=0.1\, {\rm cm}^2\, {\rm g}^{-1}$. Our statistical analysis indicates that the latter two models are disfavoured at the $68{{\ \rm per\ cent}}$ confidence level (as conservative estimates). This conclusion is not altered by shifting the radial range of measurements or applying a temperature selection criterion. However, the primary uncertainty originates from the lack of baryonic physics in the adiabatic model, such as cooling, star formation and feedback effects, which still have the potential to reconcile CDM simulations with observations.

Shen, Xuejian (ORCID:000000026196823X)↗
DOE OSTI2023

Beam dynamics corrections in the measurement of the anomalous precession frequency at the Muon $g-2$ experiment at Fermilab

The Muon $g-2$ experiment at Fermilab (E989) aims to measure the anomalous magnetic moment of the muon with an accuracy of 140 ppb (parts per billions). This accuracy, obtained by adding in quadrature a statistical and a systematic contribution of comparable value (100 ppb), will allow to reduce the experimental uncertainty (from the previous E821 experiment at BNL \cite{bnl}) of a factor of 4, and represents one of the most precise tests of the Standard Model (SM) theory of elementary particles. The first result on the Run-1 dataset \cite{prl} was released on April 7, 2021, showing a very good agreement with the previous result from BNL experiment, with a slightly better uncertainty. The corresponding experimental average increases the significance of the discrepancy between the measured and Standard Model prediction of 4.2$\sigma$ \cite{white_paper}.\\ \noindent The measured quantity is the muon magnetic anomaly a$_\mu$=$\frac{g_\mu-2}{2}$ where g$_\mu$ is the gyromagnetic factor of the muon. Dirac's equation predicts g$_\mu$ = 2, while radiative corrections, dominated by the QED contribution due to an exchange of a virtual photon, causes a per-mille correction on this quantity. By including all the SM contributions, a$_\mu$ is known at 370 ppb. The E989 experiment measures $a_\mu$ injecting positive muons with momentum of 3.1 GeV/$c$ polarized longitudinally in bunches (called $fills$) with an average rate of 12 Hz, in a storage ring of 14 meters diameter. Due to the parity violation in the weak muon decay, high energy positrons produced are emitted preferably in the muon's spin direction. By counting the number of positrons with energy greater then 1.7 GeV in function of the time, the frequency precession of the muon spin is measured, that together with the measurement of the magnetic field, allows to extract $a_\mu$. The positrons are detected with 24 electromagnetic calorimeters, that measure the energy and the arrival time of the positrons, each made of 54 crystals of lead fluoride (PbF$_2$) read by silicon photomultipliers (SiPM). Together with calorimeters, two tracking detectors are used to make non-destructive measurements of the muon beam characteristic by reconstructing the muon decay position extrapolating backward the decay positrons. The knowledge of the beam motion inside the ring plays a fundamental role in the analysis of $a_{\mu}$, where the measured anomalous precession frequency $\omega_a$ must be corrected for four main beam dynamics effects. A first correction is associated with the presence of an electric field responsible of the vertical focusing on the storage ring, where vertical direction is orthogonal to the orbit and horizontal direction is along the storage ring radius. Due to the oscillations in the vertical direction, the so called vertical betatron oscillations, a second correction is necessary to account for an average angle associated with the muon motion off the ideal orbit. A third correction is caused by lost muons in the ring which have a different spin phase at the injection respect to the decay ones. Finally, due to the correlation between the vertical and horizontal beam motion of the muons and the acceptance of the calorimeter, a correction (called ``phase-acceptance") arises. In Run1, due to the presence of two damaged resistors in one electrostatic quadrupole, this correction had a prominent role. The replacement of the damaged resistors before Run2 decreased this effect by one order of magnitude, and a further reduction in Run-3 was provided by an improved orbit.\\ \noindent The work of this Thesis focuses on the beam dynamics corrections on $\omega_a$. Due to the prominent role in Run-1 a special attention has been put to the phase-acceptance correction\footnote{The effect of this correction on the E821 BNL measurement of the $g-2$ has been evaluated to be within the quoted systematic error.}. Chapter \ref{ch:anomalous_magnetic_moment} introduces the anomalous magnetic moment of the muon. Chapter \ref{ch:early_experiment} describes the history of the Muon $g-2$ experiments. Chapter \ref{ch:theory} discusses the Standard Model prediction and possible new physics scenario. Chapter \ref{ch:muon_g2_experiment} describes the E989 experiment, whose experimental technique and the apparatus are discussed focusing on the improvements needed to reach the final goal on $a_\mu$ measurement. The original work of the Thesis is discussed in the last 5 chapters. Chapter \ref{ch:experiment_technique} presents the analysis technique to extract $\omega_a$, Chapter \ref{ch:beam_dynamics} describes the beam dynamics in the E989 experiment, Chapter \ref{ch:beam_dynamics_correction} discusses the beam dynamics correction to $\omega_a$, and Chapter \ref{sec:pa_corr} focuses on the phase acceptance correction. Finally Chapter \ref{ch:run23_analysis_improvements} contains the Run-2/3 improvements which are expected to allow for an increased precision ons the beam dynamics co...

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Beam dynamics corrections to the Run-1 measurement of the muon anomaly $a_{\mu}$ at Fermilab

The Fermi National Accelerator Laboratory (FNAL) Muon $g\!-\!2$ Experiment has measured the positive muon magnetic anomaly $a_{\mu} \equiv (g_{\mu}-2)/2$ with a precision of 0.46 parts per million, with data collected during its first physics run in 2018. The experimental result combined with the measurement from the former experiment at Brookhaven National Laboratory increases the tension with the Standard Model expectation to $4.2\sigma$, thus strengthening evidence for new physics.The magnetic anomaly is determined from the precision measurements of the muon spin precession frequency, relative to the muon momentum, and the average magnetic field seen by the beam. In an ideal case with muons orbiting in a horizontal plane with a uniform vertical magnetic field, the anomalous precession frequency $\omega_a$ is given by the difference between the spin ($s$) and cyclotron ($c$) frequencies, $\omega_a = \omega_s - \omega_c$. The observable $\omega_a$ is proportional to $a_{\mu}$.This proceeding presents the beam dynamics systematic corrections that are required to adjust the measured muon precession frequency $\omega^{m}_{a}$ to its true physical value $\omega_{a}$.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Small experiment, Big Data: the data production of the Muon $g-2$ Experiment

The Muon $g-2$ Experiment at Fermilab aims to measure the muon anomalous magnetic moment with the unprecedented precision of 140 parts per billion (ppb). In April 2021 the collaboration published the first measurement, based on the first year of data taking. The result confirmed the previous experiment at Brookhaven National Laboratory (BNL), and increased the long-standing tension with the Standard Model prediction to 4.2 $\sigma$. The experiment is now running the sixth year of data acquisition of positive muon data, having accumulated a total of $\sim$19 times the statistics of the BNL experiment. A collaboration-wide effort is now in place to help produce the multi-petabyte-sized data sets, a challenge typically faced by much bigger experiments. Having a quick production turnaround time is of critical importance in order to achieve a timely analysis and publication schedule. In this paper I will describe the production workflow, the former and current challenges, the resources, tools, and the future prospects of the Muon $g-2$ Experiment.

Girotti, Paolo↗
NASA NTRS1973

On a basic model of circulatory, fluid, and electrolyte regulation in the human system based upon the model of Guyton

A detailed description of Guyton's model and modifications are provided. Also included are descriptions of several typical experiments which the model can simulate to illustrate the model's general utility. A discussion of the problems associated with the interfacing of the model to other models such as respiratory and thermal regulation models which is prime importance since these stimuli are not present in the current model is also included. A user's guide for the operation of the model on the Xerox Sigma 3 computer is provided and two programs are described. A verification plan and procedure for performing experiments is also presented.

White, R. J.↗
NASA NTRS1992

Impulsive phase Fe K-alpha emission in a flare of 1989 March

Evidence for enhanced Fe K-alpha line emission that is coincident (to within 15 s) of an intense hard X-ray (greater than 50 keV) burst is presented on the basis of observations of the Fe K-alpha soft X-ray line made with the SMM. Three different models for explaining the K-alpha enhancement are investigated, namely, photoexcitation by soft X-ray thermal bremsstrahlung radiation from an isothermal source, collisional excitation by nonthermal thick-target electrons, and photoexcitation by a nonthermal hard X-ray flux distribution which extends with a power-law spectrum down to the Fe K-alpha ionization threshold at 7.1 keV. It is found that, to within the limits of isothermal temperature and emission measure set by soft X-ray observations, the thermal photoexcitation model cannot reproduce satisfactorily the intensity of enhanced K-alpha emission during the hard X-ray impulsive phase. The impulsive phase K-alpha flux exceeds that predicted by the thermal photoexcitation model by about 3 sigma. The implications of these results for the nonthermal interpretation of impulsive hard X-ray bursts in solar flares are discussed.

Zarro, D. M.↗
NASA NTRS1994

Cold dark matter. 1: The formation of dark halos

We use numerical simulations of critically closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to 256(exp 3) particles using the particle-mesh (PM) method and with up to 144(exp 3) particles using the adaptive particle-particle-mesh (P3M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations, and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all omega = 1 CDM models for linear amplitude sigma(sub 8) greater than or approximately = 0.5 because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low-mass halos. The distribution of halos characterized by their circular velocities for the P3M simulations is in reasonable agreement with the observations for 150 km/s less than or = V(sub circ) less than or = 350 km/s.

Gelb, James M.↗
NASA NTRS2011

Correlations in the (Sub)Mil1imeter Background from ACT x BLAST

We present measurements of the auto- and cross-frequency correlation power spectra of the cosmic (sub)millimeter background at: 250, 350, and 500 microns (1200, 860, and 600 GHz) from observations made with the Balloon-borne Large Aperture Submillimeter Telescope, BLAST; and at 1380 and 2030 microns (218 and 148 GHz) from observations made with the Atacama Cosmology Telescope, ACT. The overlapping observations cover 8.6 deg(sup 2) in an area relatively free of Galactic dust near the south ecliptic pole (SEP). The ACT bands are sensitive to radiation from the CMB, the Sunyaev-Zel'dovich (SZ) effect from galaxy clusters, and to emission by radio and dusty star-forming galaxies (DSFGs), while the dominant contribution to the BLAST bands is from DSFGs. We confirm and extend the BLAST analysis of clustering with an independent pipeline, and also detect correlations between the ACT and BLAST maps at over 25(sigma) significance, which we interpret as a detection of the DSFGs in the ACT maps. In addition to a Poisson component in the cross-frequency power spectra, we detect a clustered signal at 4(sigma), and using a model for the DSFG evolution and number counts, we successfully fit all our spectra with a linear clustering model and a bias that depends only on red shift and not on scale. Finally, the data are compared to, and generally agree with, phenomenological models for the DSFG population. This study represents a first of its kind, and demonstrates the constraining power of the cross-frequency correlation technique to constrain models for the DSFGs. Similar analyses with more data will impose tight constraints 011 future models.

Hajian, Amir↗
NASA NTRS2017

ALMA Detection and Astrobiological Potential of Vinyl Cyanide on Titan

Recent simulations have indicated that vinyl cyanide is the best candidate molecule for the formation of cell membranes/vesicle structures in Titan's hydrocarbon-rich lakes and seas. Although the existence of vinyl cyanide (C2H3CN) on Titan was previously inferred using Cassini mass spectrometry, a definitive detection has been lacking until now. We report the first spectroscopic detection of vinyl cyanide in Titan's atmosphere, obtained using archival data from the Atacama Large Millimeter/submillimeter Array (ALMA), collected from February to May 2014. We detect the three strongest rotational lines of C2H3CN in the frequency range of 230 to 232 GHz, each with greater than 4 sigma confidence. Radiative transfer modeling suggests that most of the C2H3CN emission originates at altitudes of approx. greater than 200 km, in agreement with recent photochemical models. The vertical column densities implied by our best-fitting models lie in the range of 3.7 x 10(exp 13) to 1.4 x 10(exp 14) cm(exp −2). The corresponding production rate of vinyl cyanide and its saturation mole fraction imply the availability of sufficient dissolved material to form approx. 10(exp 7) cell membranes/cu cm in Titan's sea Ligeia Mare.

Palmer, Maureen Y.↗
DOE OSTI2023

Measurement of the muon anomalous precession frequency in runs 2 \& 3 of the Muon $g-2$ Experiment at Fermilab

This dissertation presents a measurement of the muon anomalous precession frequency for the Runs 2 \& 3 data of the E989 Muon $g-2$ Experiment at Fermilab. The muon anomalous precession frequency is one of two key inputs, the other being the magnetic field, used to precisely determine the muon magnetic anomaly, $a_{\mu}$. In April 2021, the E989 collaboration reported its first measurement of $a_{\mu}$ to an unprecedented precision of 460 parts-per-billion (ppb). This result is in agreement with the previous measurement performed by the E821 collaboration at Brookhaven National Laboratory, and the combined experimental value is in tension with the Standard Model prediction at 4.2$\sigma$, a possible hint of new physics. The first result from E989 was based on the Run-1 data, which was collected in 2018 and comprises 6\% of the experiment’s target statistics; the Run-1 result was statistics-limited. The Runs 2 \& 3 data were collected in 2019-2020 and constitute a four-fold increase i n statistics compared to Run-1 and consequently, a factor of two reduction in the measurement’s statistical uncertainty. This reduced statistical uncertainty, as well as continued understanding of systematic effects, will result in an even more precise measurement of $a_{\mu}$ and will help clarify the observed tension between theory and experiment. The precession frequency analysis presented in this dissertation includes a number of improvements compared to Boston University's Run-1 analysis: the implementation of a more robust pileup-subtraction procedure, the implementation of a kernel ratio method, the adoption of the statistically optimal asymmetry-weighted method, and investigations that led to an improved understanding of an outstanding residual slow effect. This dissertation motivates a measurement of the muon magnetic anomaly, describes the experimental principle, gives an overview of the E989 experiment, and presents a precession frequency analysis with full systematic unc ertainty evaluation for the Runs 2 \& 3 data. The combined precession frequency measurement, using the ratio asymmetry-weighted method, has a statistical uncertainty of 201 ppb and a systematic uncertainty of 25 ppb, constituting the most precise determination of the muon anomalous precision frequency to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1985

Sigma Filter

The GLA Fourth-Order model is needed to smooth the topography. This is to remove the Gibbs phenomenon. The Gibbs phenomenon occurs whenever we truncate a Fourier Series. The Sigma factors were introduced to reduce the Gibbs phenomenon. It is found that the smooth Fourier series is nothing but the original Fourier series with its coefficients multiplied by corresponding sigma factors. This operator can be applied many times to obtain high order sigma filtered field and is easily applicable using FFT. It is found that this filter is beneficial in deriving the topography.

Balgovind, R. C.↗