The spin precession frequency of muons stored in the $(g-2)$ storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for: a nonzero $Δω_{a}$ (=$ω_{a}^{μ^{+}}-ω_{a}^{μ^{-}}$); and a sidereal variation of $ω_{a}^{μ^{\pm}}$. No significant effect is found, and the following limits on the standard-model extension parameters are obtained: $b_{Z} =-(1.0 \pm 1.1)\times 10^{-23}$ GeV; $(m_μd_{Z0}+H_{XY}) = (1.8 \pm 6.0 \times 10^{-23})$ GeV; and the 95% confidence level limits $\check{b}_{\perp}^{μ^{+}}< 1.4 \times 10^{-24}$ GeV and $\check{b}_{\perp}^{μ^{-}} < 2.6 \times 10^{-24}$ GeV.
The status of Lorentz- and CPT-violation searches using measurements of the anomalous magnetic moment of the muon is reviewed. Results from muon g-2 experiments have set the majority of the most stringent limits on Standard- Model Extension Lorentz and CPT violation in the muon sector. These limits are consistent with calculations of the level of Standard-Model Extension effects required to account for the current 3.7σ experiment-theory discrepancy in the muon's g-2. The prospects for the new Muon g-2 Experiment at Fermilab to improve upon these searches is presented.
Following a suggestion of Kostelecky et al. we have evaluated a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. Hamiltonian terms beyond the standard model violating CPT and Lorentz invariance would contribute frequency shifts $δν_{12}$ and $δν_{34}$ to $ν_{12}$ and $ν_{34}$, the two transitions involving muon spin flip, which were precisely measured in ground state muonium in a strong magnetic field of 1.7 T. The shifts would be indicated by anti-correlated oscillations in $ν_{12}$ and $ν_{34}$ at the earth's sidereal frequency. No time dependence was found in $…
This article discusses tests of CPT and Lorentz invariance with data from the muon g-2 experiment at Brookhaven National Laboratory. According to an extension of the Standard Model by Kostelecky et al., CPT/Lorentz violating terms in the Lagrangian induce a shift of the anomaly frequency omega_a of muons in a magnetic field. This shift is predicted to be different for positive and negative muons and to oscillate with the Earth's sidereal frequency. We discuss the sensitivity of the g-2 experiment to different parameters of this Standard Model extension and propose an analysis method to search …
Upon a suggestion of Kostelecky et al., we have performed a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. New terms in their standard model extension violating CPT and Lorentz symmetry would appear as anti-correlated frequency shifts, oscillating at the earth's sidereal frequency, in the two ground state hyperfine transitions involving muon spin flip, $ν_{12}$ and $ν_{34}$, which were measured in a strong magnetic field of 1.7 T. No such time dependence was observed in $ν_{12}$ or $ν_{34}$ at the level of 20 Hz, limiting the size of some CPT and Lorentz violati…
We study the sensitivity of the Iron Calorimeter (ICAL) at the India-Based Neutrino Observatory (INO) to Lorentz and CPT violation in the neutrino sector. Its ability to identify the charge of muons in addition to their direction and energy makes ICAL a useful tool in putting constraints on these fundamental symmetries. Using resolution, efficiencies, errors and uncertainties obtained from ICAL detector simulations, we determine sensitivities to $δ{b}_{31}$, which parametizes the violations in the muon neutrino sector. We carry out calculations for three generic cases representing mixing in th…
Recent results announced as measurements of the muon's anomalous magnetic moment are in fact measurements of the muon's anomalous spin precession frequency. This precession frequency receives contributions from both the muon's anomalous magnetic and electric dipole moments. We note that all existing data cannot resolve this ambiguity, and the current deviation from standard model predictions may equally well be interpreted as evidence for new physics in the muon's anomalous magnetic moment, new physics in the muon's electric dipole moment, or both.
We show that atmospheric neutrinos can provide a sensitive and robust probe of CPT violation (CPTV). We perform realistic event-rate calculations and study the variations of the ratio of total muon to antimuon survival rates with $L/E$ and $L$ ($L$ $\equiv$ baseline length, $E$ $\equiv$ neutrino energy) in a detector capable of identifying the muon charge. We demonstrate that measurements of these ratios when coupled with the significant $L$ and $E$ range which characterizes the atmospheric neutrino spectrum provides a method of both detecting the presence of such violations and putting bounds…
We have studied $CPT$ violation in neutrino oscillation considering three flavor framework with matter effect. We have constructed a new way to find the oscillation probability incorporating $CPT$ violating terms without any approximation. Then $CPT$ violation with atmospheric neutrinos for a magnetized iron calorimeter detector considering the muons (directly measurable with high resolution) of the charge current events has been studied for zero and nonzero $θ_{13}$ values. It is found that a potential bound of $δb_{32} \lapp 6\times 10^{-24}$ GeV at 99% CL can be obtained with 1 Mton.year ex…
The 6-year dataset of high-energy starting events (HESE) at IceCube indicates a spectrum of astrophysical neutrinos much softer than expected from the Fermi shock acceleration mechanism. On the other hand, IceCube's up-going muon neutrino dataset and Fermi-LAT's gamma-ray spectrum point to an $E^{-2}$ neutrino spectrum. If the HESE data above 200 TeV are fit with the latter flux, an excess at lower energies ensues, which then suggests a multicomponent spectrum. We show that the HESE dataset can be explained by a single $E^{-2}$ power-law neutrino flux from a muon-damped $pγ$ source if neutrino…
The Muon g-2 experiment at Fermilab, with the aim to measure the muon anomalous magnetic moment to an unprecedented level of 140~ppb, has started beam and detector commissioning in Summer 2017. To deal with incoming data projected to be around tens of petabytes, a robust data reconstruction and analysis chain based on Fermilab's \textit{art} event-processing framework is developed. Herein, I report the current status of the framework, together with its novel features such as multi-threaded algorithms for online data quality monitor (DQM) and fast-turnaround operation (nearline). Performance of…
If the technology for muon storage rings one day permits sensitivity to precession at the order of $10^{-8}$ Hz, the local gravitational field of Earth can be a dominant contribution to the precession of the muon, which, if ignored, can fake the signal for a nonzero muon electric dipole moment (EDM). Specifically, the effects of Earth's gravity on the motion of a muon's spin is indistinguishable from it having a nonzero EDM of magnitude $d_μ\sim 10^{-29}$ e cm in a storage ring with vertical magnetic field of $\sim$ 1 T, which is significantly larger than the expected upper limit in the Standa…
The ideas and formulas presented in the article will help to bring together the theoretical predictions for the anomalous magnetic moment of muon and the results of the "Muon g-2" experiment. In doing so, we are discussing the new effect exclusively within the Standard Model. In quantum physics a state with spin perpendicular to a magnetic field can be expressed as a superposition of energy eigenstates with spins parallel and antiparallel to the field: the resultant spin precession is due to the energy difference between the two eigenstates. If the state, like the muon, is unstable and can dec…
A recently developed Standard-Model Extension (SME) formalism for neutrino oscillations that includes Lorentz and CPT violation is used to analyze the sidereal time variation of the neutrino event excess measured by the Liquid Scintillator Neutrino Detector (LSND) experiment. The LSND experiment, performed at Los Alamos National Laboratory, observed an excess, consistent with neutrino oscillations, of ${\barν}_e$ in a beam of ${\barν}_μ$. It is determined that the LSND oscillation signal is consistent with no sidereal variation. However, there are several combinations of SME coefficients that …
The neutral Higgs boson is expected to have a mass in the region 90-150 GeV in various schemes within the Minimal Supersymmetric extension to the Standard Model. A first generation Muon Collider is uniquely suited to investigate the mass, width and decay modes of the Higgs boson, since the coupling of the Higgs to muons is expected to be strong enough for it to be produced in the s channel mode in the muon collider. Due to the narrow width of the Higgs, it is necessary to measure and control the energy of the individual muon bunches to a precision of a few parts in a million. We investigate th…
We consider searching for light sterile fermions and new forces by using long baseline oscillations of neutrinos and antineutrinos. A new light sterile state and/or a new force can lead to apparent CPT violation in muon neutrino and antineutrino oscillations. As an example, we present an economical model of neutrino masses containing a sterile neutrino. The potential from the Standard Model neutral current gives rise to a difference between the disappearance probabilities of neutrinos and antineutrinos, when mixing with a light sterile neutrino is considered. The addition of a B-L interaction …
The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab has a goal of measuring the muon anomaly ($a_μ$) with unprecedented precision using positive muons. This measurement is motivated by the difference between the previous Brookhaven $a_μ$ 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 tim…
The Fermi National Accelerator Laboratory (FNAL) Muon $g-2$ Experiment has measured the positive muon magnetic anomaly $a_μ \equiv (g_μ-2)/2$ 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 $4.2σ$, 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 …
We give the geralized expression of spin precession of extended bunch particles having both anomalous magnetic and electric dipole moments in storage ring. The transversal betatron oscillation formula of the bunch is also given. The latter is the generalization of the Farley's pitch correction \cite{Farley}, including radial oscillation as well as vertical one. Some useful formulae for muon storage ring are discussed in appendix.
T2K is a long-baseline neutrino oscillation experiment, in which a muon neutrino beam is produced at J-PARC and detected 295 km away at the Super-Kamiokande detector. The T2K experiment observed electron-neutrino appearance in 2012. This observation enables T2K to explore CP violation in the lepton sector by comparing electron-neutrino appearance and electron-antineutrino appearance. Indeed, the number of observed electron neutrino events up to 2012 is, though within statistical fluctuation, larger than the expectation, which suggests maximal CP violation. Since 2013, T2K has been accumulating…
On 2010 MINOS experiment was showing an hint of possible different mass splitting and mixing angles for neutrinos and anti-neutrinos, suggesting a charge-parity-time (CPT) violation in the lepton sector; last year 2012 a second result from MINOS showed a reduced discrepancy between the two set of parameters, nearly compatible with no CPT violation. We proposed an experiment for more precise estimation of neutrino oscillation parameters being useful not only for a complete discrimination for CPT scenarios, but also for mass hierarchy and theta 13 determination, and mostly for the first oscillat…
The MiniBooNE Collaboration reports a search for \numu and \numubar disappearance in the \dmsq region of a few \evsq. These measurements are important for constraining models with extra types of neutrinos, extra dimensions an d CPT violation. Fits to the shape of the \numu and \numubar energy spectra reveal no evidence for disappearance at 90% confidence level (CL) in either mode. This is the first test of \numubar disappearance between \dmsq=0.1-10\evsq.
The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has measured the muon anomalous precession frequency $ω_a$ to an uncertainty of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data collected in four storage ring configurations during its first physics run in 2018. When combined with a precision measurement of the magnetic field of the experiment's muon storage ring, the precession frequency measurement determines a muon magnetic anomaly of $a_μ({\rm FNAL}) = 116\,592\,040(54) \times 10^{-11}$ (0.46 ppm). This article describes the multiple techniq…
We have searched for sidereal variations in the rate of antineutrino interactions in the MINOS Near Detector. Using antineutrinos produced by the NuMI beam, we find no statistically significant sidereal modulation in the rate. When this result is placed in the context of the Standard Model Extension theory we are able to place upper limits on the coefficients defining the theory. These limits are used in combination with the results from an earlier analysis of MINOS neutrino data to further constrain the coefficients.
The sidereal time dependence of MiniBooNE electron neutrino and anti-electron neutrino appearance data are analyzed to search for evidence of Lorentz and CPT violation. An unbinned Kolmogorov-Smirnov test shows both the electron neutrino and anti-electron neutrino appearance data are compatible with the null sidereal variation hypothesis to more than 5%. Using an unbinned likelihood fit with a Lorentz-violating oscillation model derived from the Standard Model Extension (SME) to describe any excess events over background, we find that the electron neutrino appearance data prefer a sidereal tim…
Data from the muon g-2 experiment at Brookhaven National Lab has been analyzed to search for a muon electric dipole moment(EDM), which would violate parity and time reversal symmetries. An EDM would cause a tilt in the spin precession plane of the muons, resulting in a vertical oscillation in the position of electrons hitting the detectors. No signal has been observed. Based on this analysis, an improved limit of $2.8 \times 10^{-19} e-cm(95% CL) is set on the muon EDM.
A new measurement of the positive muon's anomalous magnetic moment has been made at the Brookhaven Alternating Gradient Synchrotron using the direct injection of polarized muons into the superferric storage ring. The angular frequency difference omega_{a} between the angular spin precession frequency omega_{s} and the angular orbital frequency omega_{c} is measured as well as the free proton NMR frequency omega_{p}. These determine R = omega_{a} / omega_{p} = 3.707~201(19) times 10^{-3}. With mu_{mu} / mu_{p} = 3.183~345~39(10) this gives a_{mu^+} = 11~659~191(59) times 10^{-10} (pm 5 ppm), in…
We review the spin equations for the muon in the 1.45~T muon storage ring at Brookhaven National Laboratory, which has subsequently been relocated to Fermilab. Muons are stored in a uniform 1.45~T magnetic field, and vertical focusing is provided by four sets of electrostatic quadrupoles placed symmetrically around the storage ring. The storage ring is operated at the "magic $γ= 29.3$" so that the effect of the motional magnetic field cancels for muons at the magic momentum. We point out the relative sizes of the various terms in the spin equations, and show that for experiments that use the m…
The J-PARC muon g-2/EDM experiment aims to measure the muon magnetic moment anomaly $a_μ = (g -2 ) / 2 ~ $. The target sensitivity for $a_μ$ is a statistical uncertainty of $450 \times 10^{-9}$, and $a_μ$ can be extracted by measuring the spin precession of muons ($ω_a$). The $ω_a$ can be extracted from the distribution of muon decay time, and the time is measured by reconstructing tracks of positrons which are decayed from the muons. To extract $ω_a$ precisely, the systematic effects on $ω_a$ should be controlled under the aforementioned sensitivity. To study systematic effects, we develop a …
Three independent searches for an electric dipole moment (EDM) of the positive and negative muons have been performed, using spin precession data from the muon g-2 storage ring at Brookhaven National Laboratory. Details on the experimental apparatus and the three analyses are presented. Since the individual results on the positive and negative muon, as well as the combined result, d=-0.1(0.9)E-19 e-cm, are all consistent with zero, we set a new muon EDM limit, |d| < 1.9E-19 e-cm (95% C.L.). This represents a factor of 5 improvement over the previous best limit on the muon EDM.
We derive in full generality the equations that govern the time dependence of the energy ${\mathcal E}$ of the decay electrons in a muon $g-2$ experiment. We include both electromagnetic and gravitational effects and we estimate possible systematics on the measurements of $g-2\equiv 2(1+a)$, whose experimental uncertainty will soon reach $Δa/a\approx 10^{-7}$. In addition to the standard modulation of ${\mathcal E}$ when the motion is orthogonal to a constant magnetic field $B$, with angular frequency $ω_a=e a |B|/m$, we study effects due to: (1) a non constant muon $γ$ factor, in presence of …
The possibility of Lorentz Invariance Violation (LIV) may appear in unified theories, such as string theory, which allow the existence of a new space-time structure at the Planck scale ($M_p \sim 10^{19}$ GeV). This effect can be observed at low energies with a strength of $\sim 1/M_p$ using the perturbative approach. In the minimal Standard Model extension (SME) framework, the neutrino mass-induced flavor oscillation gets modified in the presence of LIV. The Iron Calorimeter (ICAL) detector at the proposed India-based Neutrino Observatory (INO) offers a unique window to probe these LIV parame…
The Fermi National Accelerator Laboratory has measured the anomalous precession frequency $a^{}_μ= (g^{}_μ-2)/2$ of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7$^\circ$C. The measured field is weighted by the muon distribution resulting in $\tildeω'^{}_p$, the d…
Final Report on the Measurement of the Positive Muon Anomalous Magnetic Moment at Fermilab to 127 ppb
University of Michigan（密歇根大学）；University of Liverpool（利物浦大学）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；University of Virginia（弗吉尼亚大学）；Department of Physics and Astronomy, University College London（伦敦大学学院物理与天文系）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Cornell University（康奈尔大学）；INFN, Sezione di Pisa（意大利国家核物理研究所比萨分部）；Michigan State University（密歇根州立大学）；University of Washington（华盛顿大学）；North Central College（北中央学院）
