Measurement of the muon anomalous precession frequency with the Run-2/3 data in the Muon g-2 experiment at Fermilab
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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...
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.
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.
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.
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.
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.
The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider.
The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider.
The Muon Campus at Fermilab provides world class accelerator infrastructure supporting the next generation intensity frontier experiments. The anti-proton source from the Tevatron era was converted to the present day Muon Campus at the end of the collider program in 2011. Currently, the Muon Campus delivers highly polarized muon beams to the Muon g-2 experiment and in a few years, it will provide muon beams to the Mu2e experiment. The Muon g-2 experiment is a high precision test of the standard model; it is precise enough to measure QED, Weak, and QCD Standard Model contributions.The Muon g-2 experiment looks for a significant deviation from the Standard Model whereas the Mu2e experiment looks for rare processes using high intensity muon beams. The Muon g-2 experiment has measured the anomalous magnetic moment of muons to an unprecedented 460 ppb precision with Run 1 data. The experiment has completed 5 runs, accumulating 19$\times$ Brookhaven E821 data set. The Mu2e experiment has completed the construction phase and first beam to the Diagnostic Absorber was run on April 14, 2022. Installation and commissioning of the Mu2e experiment will begin in 2023 and beam commissioning and physics run is currently planned for 2026.
We present the detection of directional muon beams produced using a PW laser facility at the Lawrence Berkeley National Laboratory. The muon source is a multi-GeV electron beam generated in a laser-plasma accelerator interacting with a high- converter target. The GeV photons resulting from the interaction are converted into a high-flux, directional muon beam via pair production. By employing scintillators to capture delayed events, we were able to identify the produced muons and characterize the source. Using theoretical knowledge of the muon production process combined with simulations that are in excellent agreement with the experiments, we demonstrate that laser-plasma accelerators have the capability of generating electron beams with characteristics suitable to produce GeV-scale muons that offer unique advantages with respect to the cosmic background. Laser-plasma-accelerator-based muon sources can therefore enhance muon imaging applications thanks to their compactness, directionality, and high yields, which reduce the exposure time by orders of magnitude compared to cosmic ray muons. Using the eant4-based simulation code we developed to gain insight into the experimental results, we can design future experiments and applications based on LPA-generated muons.
The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab has a goal of measuring the muon anomaly ($a_\mu$) with unprecedented precision using positive muons. This measurement is motivated by the difference between the previous Brookhaven $a_\mu$ measurement and Standard Model prediction exceeding three standard deviations, which hints at the possibility of physics beyond the Standard Model. Muons are circulated in a storage ring, and the measurement requires a precise determination of the muon anomalous precession frequency (spin precession relative to momentum) from the resulting decay positron time and energy measurements collected with calorimeters. The average magnetic field seen by the muons needs to be known with high precision, and so the storage ring magnetic field is shimmed to be very uniform and is continually monitored with nuclear magnetic resonance (NMR) probes. Detailed Muon Campus beamline and muon storage ring simulations are also required for quantifying beam dynamics and spin-related systematic effects in the determination of the muon anomalous precession frequency, e.g. muon losses during the measurement window. At the time of the conference, the experiment has recently commenced Run-3, and the release of Run-1 physics results is planned for 2020.
Current discrepancy between the measurement and the prediction of the muon anomalous magnetic moment can be resolved in the presence of a long-range force created by ordinary atoms acting on the muon spin via axial-vector and/or pseudoscalar coupling, and requiring a tiny O(10 –13 eV) spin energy splitting between muon state polarized in the vertical direction. We suggest that an extension of the muon spin resonance (μSR) experiments can provide a definitive test of this class of models. We also derive indirect constraints on the strength of the muon spin force by considering the muon-loop-induced interactions between nuclear spin and external directions. The limits on the muon spin force extracted from the comparison of 199 Hg/ 201 Hg and 129 Xe/ 131 Xe spin precession are strong for the pseudoscalar coupling but are significantly relaxed for the axial-vector one. These limits suffer from significant model uncertainties, poorly known proton/neutron spin content of these nuclei, and therefore do not exclude the possibility of a muon spin force relevant for the muon g – 2.
Atmospheric muons are typically high energy, highly penetrating charged particles. They interact with matter primarily through multiple Coulomb scatterings. Muon scattering intensities can be used to characterize the density and atomic number of the matter that they pass through. Previously, the Los Alamos National Laboratory (LANL) muon tomography team performed muon imaging of the partially filled MC-10 spent nuclear fuel (SNF) cask at Idaho National Laboratory (INL). This experiment demonstrated the feasibility of muon imaging for the verification of spent fuel container contents. That original effort used the mini muon tracker array, consisting of two arrays of drift tubes on either side of the SNF cask. The reconstructed image quality was limited by statistics, largely due to low muon flux at high zenith angles. A LANL led team will perform new measurements with a larger array, the Giant Muon Tracker (GMT), to improve data collection rates and statistics. In this work, simulations were performed with the GMT near the partially filled INL MC-10 cask. For more general fuel diversion detection, a full MC-10 cask and casks with a singular missing fuel bundle were also simulated. To understand minimum measurement times needed for missing bundle identification, 100 000 to millions of tracked muons (corresponding to 1.4 days to several weeks measurement time) were analyzed. Simulated images were then analyzed visually and numerically to explore techniques designed to minimize the collection time needed to identify the diversion of fuel in each scenario.
A production rate of 0.065 + or - 0.003 Ar-37 atom/kg min of K-39 at 2-mwe depth below sea level was measured by sweeping argon from potassium solutions. This rate is unaffected by surrounding the solution by paraffin and is attributed to negative muon captures and the electromagnetic interaction of fast muons, and not to nucleonic cosmic ray component. The Ar-37 yield from K-39 by the stopping of negative muons in a muon beam of a synchrocyclotron was measured to be 8.5 + or - 1.7%. The stopping rate of negative cosmic ray muons at 2-mwe depth below sea level from these measurements and an estimated 17% electromagnetic production is 0.63 + or - 0.13 muon(-)/kg min. Previous measurements on the muon stopping rate vary by a factor of 5. Our value is slightly higher but is consistent with two previous high values. The sensitivity of the Ar-37 radiochemical method for the detection of muons is considerably higher than that of the previous radiochemical methods and could be used to measure the negative muon capture rates at greater depths.
The proton is the major component of the visible matter of our universe, so being able to determine its fundamental properties, such as its charge radius, is of vital importance. In recent years, several experiments have been performed for the accurate measurement of the proton radius with different experimental techniques. The main and most common are based on two different techniques: ep scattering and Lamb shift spectroscopy of regular hydrogen atoms. The latter can also be performed on muonic hydrogen atoms with a significant improvement in accuracy. Recent measurements that use this method have highlighted a discrepancy between the results obtained with the diffusion of electrons and those obtained with the spectroscopic technique leading to the so-called ?proton radius puzzle?. The explanation of why this difference between the measured values exists is still a matter of discussion. The last attempt to address the puzzle was the PRad Experiment. It was performed with a unique experimental setup that gave the scientists an excellent control on the systematic errors that are usually present in electron-proton scattering experiments. This has significantly increased the precision of the measurement, bringing it in the same area as the spectroscopic ones done on muonic hydrogen atoms, which are considered the most precise. However, to solve the puzzle once and for all, even more precise electron scattering measurements are needed. Alternatively, new methods can be used, such as eg. muon-proton scattering at low transferred momenta in order to lower the systematic errors that comes with the measurement. This thesis tries to address this problem by studying the set up of an intense muon beam at the Jefferson Laboratory (JLab) that can be used to carry out a high-precision m ? p scattering experiment. Using Montecarlo simulations I studied the muon production resulting from the interaction of the primary electron beam with the beam-dump at JLab Hall-A. The simulations were performed using the FLUKA package via the FLAIR graphical interface. In this study, I modified an existing geometry (built for the ?Beam Dump eXperiment?) and performed several studies in order to optimize the muon beam parameters. In order to estimate the beam intensity, I studied the muon generation and transportation through the concrete bunker surrounding the Hall-A beam-dump. Detailed studies on muon attenuation and dispersion at different depth allowed me to track the beam profile in space and momentum as a function of the distance from the beam-dump. Last, but not least, I studied a possible tagging system for the muon beam. The tagging system will allow us to know with good precision (O(1=1000)) the energy of each muon of the beam. Based on the results obtained, I created an event generator that incorporates the detailed description of the muon beam (energy, position, emittance) useful to define and optimize the experimental setup for a future measurement of the proton radius at the JLab.
The muon trigger system of the CMS experiment uses a combination of hardware and software to identify events containing a muon. During Run 2 (covering 2015-2018) the LHC achieved instantaneous luminosities as high as 2 $\times$ 10$^{34}$cm$^{-2}$s$^{-1}$ while delivering proton-proton collisions at $\sqrt{s} =$ 13 TeV. The challenge for the trigger system of the CMS experiment is to reduce the registered event rate from about 40 MHz to about 1 kHz. Significant improvements important for the success of the CMS physics program have been made to the muon trigger system via improved muon reconstruction and identification algorithms since the end of Run 1 and throughout the Run 2 data-taking period. The new algorithms maintain the acceptance of the muon triggers at the same or even lower rate throughout the data-taking period despite the increasing number of additional proton-proton interactions in each LHC bunch crossing. In this paper, the algorithms used in 2015 and 2016 and their improvements throughout 2017 and 2018 are described. Measurements of the CMS muon trigger performance for this data-taking period are presented, including efficiencies, transverse momentum resolution, trigger rates, and the purity of the selected muon sample. This paper focuses on the single- and double-muon triggers with the lowest sustainable transverse momentum thresholds used by CMS. The efficiency is measured in a transverse momentum range from 8 to several hundred GeV.