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All sourcesNASA NTRSDOE OSTI
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 OSTI2018

Muon-Computed Tomography using POCA Trajectory for Imaging Spent Nuclear Fuel in Dry Storage Casks

Cosmic ray muon-computed tomography (μCT) is a new imaging modality with unique characteristics that can be particularly important for applications in nuclear proliferation detection and international treaty verification. Using cosmic ray muons for nuclear security presents several potential advantages. Among others, muons are generated naturally in the atmosphere, can penetrate high-density materials, and are freely available. No radiological sources are required and consequently there is no associated radiological dose. Recently, the feasibility of using muons for imaging spent nuclear fuel stored in shielded casks has been explored and has been proved beneficial. However, challenges in μCT imaging include low muon flux of ~10,000 muons/m2/min, the effects of multiple Coulomb scattering (MCS) blurring the image, and inefficiency in being able to use all recorded muons for imaging. In this paper, we argue that the use of muon tracing should produce tomographic muon images with improved quality – or more quickly for the same image quality – compared to the case where conventional methods are used. In our paper, we report on the development and assessment of a novel muon tracing method for μCT. The proposed method back projects the muon’s scattering angle into each pixel crossed by its PoCA trajectory then forward projects the variance of the scattering angle in each pixel to detector bins along the muon’s incident horizontal direction. Two scenarios were simulated to assess the expected detection capability of this proposed method. GEANT4 was used to model the main characteristics of 1-60 GeV muons through matter. The simulated images showed an expected improvement in resolution and a reduced the reliance on the muon momentum information compared to a more conventional muon tomography method.

Liu, Zhengzhi↗
DOE OSTI2020

Measurement of azimuthal anisotropy of muons from charm and bottom hadrons in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV with the ATLAS detector

Azimuthal anisotropies of muons from charm and bottom hadron decays are measured in Pb+Pb collisions at s NN = 5.02 TeV . The data were collected with the ATLAS detector at the Large Hadron Collider in 2015 and 2018 with integrated luminosities of 0.5 nb - 1 and 1.4 n b - 1 , respectively. The kinematic selection for heavy-flavor muons requires transverse momentum 4 <lt; p T < 30 GeV and pseudorapidity | η | < 2.0 . The dominant sources of muons in this p T range are semi-leptonic decays of charm and bottom hadrons. These heavy-flavor muons are separated from light-hadron decay muons and punch-through hadrons using the momentum imbalance between the measurements in the tracking detector and in the muon spectrometers. Azimuthal anisotropies, quantified by flow coefficients, are measured via the event-plane method for inclusive heavy-flavor muons as a function of the muon p T and in intervals of Pb+Pb collision centrality. Heavy-flavor muons are separated into contributions from charm and bottom hadron decays using the muon transverse impact parameter with respect to the event primary vertex. Non-zero elliptic ( v 2 ) and triangular ( v 3 ) flow coefficients are extracted for charm and bottom muons, with the charm muon coefficients larger than those for bottom muons for all Pb+Pb collision centralities. The results indicate substantial modification to the charm and bottom quark angular distributions through interactions in the quark-gluon plasma produced in these Pb+Pb collisions, with smaller modifications for the bottom quarks as expected theoretically due to their larger mass.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

An Indirect Search for Weakly Interacting Massive Particles in the Sun Using Upward-going Muons in NOvA

I present the first Dark Matter search results using the full data set collected with the upward-going muon trigger in NOvA. Weakly Interactive Massive Particles (WIMPs) are a theoretical non-baryonic form of Dark Matter. The nature of Dark Matter is one of the most exciting open questions in modern physics. Though its existence can be inferred by astrophysical evidence, its properties are not yet understood. If we assume that Dark Matter particles can produce Standard Model particles through their interactions, an indirect search can help shed light on this mystery.The NOvA collaboration has built a 14 kton, fine-grained, low-Z, total absorption tracking calorimeter at an off-axis angle to the NuMI neutrino beam. Even though the detector is optimized to observe electron neutrino appearance from a muon neutrino beam, it has a unique potential for more exotic searches given its excellent granularity and energy resolution and relatively low-energy neutrino thresholds. In fact, with an efficient upward-going muon trigger and sufficient background suppression offline, NOvA is capable of a competitive indirect Dark Matter search for low-mass WIMPs.The idea of the upward-going muon trigger is first to select high-quality muon tracks, then use the timing information of all of the hits of each track to estimate directionality. In this way, the background flux is suppressed by more than a factor of 10^5 at trigger level to a rate of approximately 1 Hz. To further optimize this search, we use only upward-going muons that point to the Sun, so our search occurs at night when the Sun is on the other side of the Earth. This strategy also allows us to use the time when the Sun is above the horizon as a control region to estimate the background. Ultimately, implementation of a cut based and maximum likelihood analysis provides a powerful tool for rejecting background and selecting a sample of neutrino-induced upward-going muons. The overall background rejection power achieved by the analysis is substantial and impressive. Starting with approximately 150,000 events per second, we reduced it to 40 events per year. Since no statistically significant excess was found, a 90\% C.L. upper limit on the expected muon flux of upward-going muons has been set using the upper limit on the number of events given the number of observed events in the signal region. Lastly, by assuming the theory behind the upward-going muon flux, a limit on the WIMP-nucleon spin-dependent cross-section in the Sun was estimated. Although the limits on the spin-dependent cross-section do not appear to be competitive with previous indirect Dark Matter searches, the upward-going muon flux limits are promising. The upward-going muon flux limits could extend these results to a broader class of models that are not specific to the dark matter theory but produce upward-going muons, leading to competitive results.

Principato, Cristiana↗
DOE OSTI2018

A Novel Non-Parametric Density Estimation Approach to Measuring Muon Ionization Cooling and Reverse Emittance Exchange in the MICE Experiment

The Muon Ionization Cooling Experiment (MICE) located at Rutherford Ap- pleton Laboratory in the U.K. has demonstrated muon ionization beam cooling for the rst time. A beam of muons in MICE is produced from high-energy proton beam collision with a xed target, generating pions which in turn decay into muons. Pion-decay muons, thus, are tertiary particles and, as a result, occupy a large vol- ume in position{momentum phase space. To t the muon beam into smaller and more cost-eective accelerating devices, muon beam phase{space volume needs to be reduced (beam cooling). Ionization beam cooling, which before MICE has never been demonstrated experimentally for muons, is the only technique fast enough to be used for muons within their short lifetime. Ionization cooling occurs when muons traverse an absorbing material and lose momentum through ionization energy loss. The cooling eect in MICE is measured using two scintillating-ber tracking detec- tors. These trackers, one upstream and one downstream of the absorber, reconstruct and measure the position and momentum coordinates of each muon. Given the pre- cision MICE needed to demonstrate beam cooling, it is necessary to develop analysis tools that can account for any eects that may lead to inaccurate measurement of cooling, such as non{linear eects in beam optics. Non{parametric density estima- tion techniques, such as kernel density estimation (KDE), provide a basis for creating analysis tools that are robust against these eects, directly calculating the muon beam phase-space density and volume for demonstrating beam cooling. This thesis focuses on the application of KDE to the measurement of beam cooling in MICE. The KDE technique is validated using known distributions and is applied to sim- ulated and experimental MICE data corresponding to the various magnet, optics, and absorber congurations. Using the KDE technique, muon beam cooling in the four{dimensional transverse phase space, as well as reverse emittance exchange using MICE data have been demonstrated.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Measurement of the nuclear modification factor for muons from charm and bottom hadrons in Pb+Pb collisions at 5.02 TeV with the ATLAS detector

Heavy-flavour hadron production provides information about the transport properties and microscopic structure of the quark–gluon plasma created in ultra-relativistic heavy-ion collisions. A measurement of the muons from semileptonic decays of charm and bottom hadrons produced in Pb+Pb and pp collisions at a nucleon–nucleon centre-of-mass energy of 5.02 TeV with the ATLAS detector at the Large Hadron Collider is presented. The Pb+Pb data were collected in 2015 and 2018 with sampled integrated luminosities of 208 μb –1 and 38 μb –1 , respectively, and pp data with a sampled integrated luminosity of 1.17 pb –1 were collected in 2017. Muons from heavy-flavour semileptonic decays are separated from the light-flavour hadronic background using the momentum imbalance between the inner detector and muon spectrometer measurements, and muons originating from charm and bottom decays are further separated via the muon track's transverse impact parameter. Differential yields in Pb+Pb collisions and differential cross sections in pp collisions for such muons are measured as a function of muon transverse momentum from 4 GeV to 30 GeV in the absolute pseudorapidity interval |n| < 2. Nuclear modification factors for charm and bottom muons are presented as a function of muon transverse momentum in intervals of Pb+Pb collision centrality. The bottom muon results are the most precise measurement of b quark nuclear modification at low transverse momentum where reconstruction of B hadrons is challenging. The measured nuclear modification factors quantify a significant suppression of the yields of muons from decays of charm and bottom hadrons, with stronger effects for muons from charm hadron decays.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

First Muon Neutrino on Argon Cross Section Measurements With an Off-Axis Beam

While over ninety years have passed since neutrinos were first predicted in 1930 by Wolfgang Pauli, much about them is still unknown [20]. How many types of neutrinos there are, how precisely neutrinos change flavor, and how neutrinos interact with various types of matter are largely unanswered questions that have implications for fields beyond particle physics, such as cosmology and astrophysics. The final question can be answered partially by differential cross section measurements, two of which constitute the primary result of this thesis. The NeUtrinos at the Main Injector (NuMI) Beam at Fermilab in Batavia, IL provides a source of muon neutrinos and muon antineutrinos to the MicroBooNE experiment, an 85 ton liquid argon time projection chamber (LArTPC). The technology allows for high precision particle tracking and energy reconstruction that can be used to make cross section measurements. Necessary work for making these measurements for which the author of this thesis made an essential contribution is presented in detail in References [21] [22] [11] [23]. The measurement presented in this thesis is made with 2.187e20 Protons on Target (POT), the standard metric for an amount of beam exposure, of data when the beam was in forward horn current mode. Single-differential cross section measurements in terms of muon candidate kinetic energy and direction are made, and their statistical fits with simulation are 5.8 (12 d.o.f.) and 11.4 (10 d.o.f.), respectively. This indicates that the muon kinematics for muon neutrino and muon antineutrino charged-current (CC) events primarily in the energy range [0-3] GeV can be trusted for oscillation experiments, including DUNE, because of the agreement to within the associated systematic and statistical uncertainties between the measurement and the model in every bin of both single-differential cross sections. This result adds to the corresponding result for the Booster Neutrino Beam (BNB) because it covers a completely different energy region than that measurement, a double-differential cross section in terms of muon momentum and direction [14]. This result contributes to reducing the uncertainty in near-far event rate comparisons in long baseline neutrino experiments and also adds to existing knowledge of the neutrino-nucleus interaction by describing the outgoing muon kinematics in interactions of muon neutrinos and muon antineutrinos. This result is the first-ever measurement of differential cross sections of muon neutrinos and muon antineutrinos in liquid argon made with an off-axis beam.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Modern Muon Physics: Selected Issues

The muon was discovered almost hundred years ago, but still remains largely a mystery. For a long time, the only difference between a muon and an electron was the approximately 200 times greater mass of the muon. However, with the later discovery of the charm quantum number, the muon played a decisive role in the formulation of the Standard Model of elementary particles, determining together with muon neutrino and the strange s and the charm c quarks the second generation of particles of this model. The equality of the reaction constant of muon decay with the constant of the vector interaction of beta-decay played a decisive role in the formulation of the conservation of the vector current (CVC) of the weak interaction of elementary particles. Processes involving muons testified in favor of the partial conservation of the axial current of weak interaction (PCAC), that is, one pion exchange in the interaction of the lepton and hadron currents. It was the muon that gave a rise to hopes of creating an alternative energy source within the framework of Muon Catalyzed Fusion (μCF). The possible realization of this process in the future as the intensity of muon beams increases can revolutionired energy supply. Nuclear fission by muons and the study of heavy-nucleus mesoatoms introduced muon physics into several separate branches of physical research.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗