Muon (g-2) Experiments Matthew Wright Luo Ouyang

Magnetic Moments Dipole moments of the circulating current: Intrinsic magnetic moment  – magnetic moment g – gyromagnetic ratios – spin

Dirac Equation predicts g  2 In nature, radiative corrections make g ≠ 2 ‘ a ’ is the anomaly g - factor

Standard Model (SM) value for g-2

Purpose (g-2) experiment provides a precise check of the development of QED and the standard model of particle physics, and accesses new physics in a way complementary to other probes. The muon anomaly is particularly valuable in restricting models of physics beyond the standard model.

Muon, a lepton, is a point-like elementary particle, with no sub-structures. It is like an electron, only about 200 times heavier than the electron.  Enhanced high sensitivity of a  to all kind of interesting physics effects  It can be measured with high precision as well as predicted unambiguously in the SM  It can easily be polarized and perfectly transport polarization information to the electrons produced in their decay  High energetic muon lives 30 times longer than in its rest frame Muon (μ)

Decay involved Muon source: The dominant muon decay:

g-2 procession - Orbital angular frequency -spin procession angular frequency With an electric quadrupole field for vertical focusing 0 decayed from are detected

The CERN Experiments

BNL AGS E821 A New Precision Measurement of the Muon g-2 Value at the level of 0.5 ppm

Collaboration Institutes The experiment is run by an international collaboration of 68 physicists from 11 institutes in the United States, Germany, The Netherlands, Russia and Japan. Co-Spokesmen: B. Lee Roberts (BU), Vernon Hughes (deceased) (Yale) Resident Spokesman: Bill Morse (BNL) Project Manager: Gerry Bunce (BNL) Collaboration institutes: Boston University, Brookhaven National Laboratory, Cornell University, Faireld University, University of Heidelberg, University of Illinois, Max Planck Institute fur Med. Forschung –Heidelberg, University of Minnesota, Scuola Normale Superiore, University of Tokyo, KEK, Riken, Yale University

Diagram of g-2 Experiment

Muon Ring Overview 24 Electromagnetic Calorimeters symmetrically placed around inside of storage ring. 3 Kicker assemblies. Inflector Direct muon injection. Nuclear Magnetic Resonance Suite. (Bennett, 2006)

Muon Storage Magnet A single C shaped 7.112m magnet. Uniform field of T..08% Carbon Steel to minimize extraneous material 150mm Fiberglass insulation to reduce magnetic field variation A Current in 3 NbTi/Cu superconducting coils. (Bennett, 2006)

Nuclear Magnetic Resonance Probe Suite Magnetic Field measured by free- induction decay of protons in water. Absolute Calibration Probe located inside the storage region. 378 Fixed probes both above and below the ring inside the vacuum chamber. These probes monitor the magnetic field during data taking. 17 probes inside a “trolley” that is pulled through ring. Many probes replaced water samples with petroleum jelly. (Bennett, 2006)

Muon Path (Jegerlehner 2007) Muons directly injected into muon ring. Muon spin aligned in one direction. Magnetic field of storage ring is perpendicular to muon spin.

Precession in Muon Ring (Jegerlehner 2007) For every 29 laps around the storage ring, the spin rotates one more time then the muon. The difference between the Rotation of the muon and the precession is Proportional to the g-2.

Electromagnetic Calorimeter Used to measure electron decay energy In order to directly measure g-2 140mm X 230mm X 150mm 52% Lead, 38% Scintillating fiber, 10% epoxy

Calorimeter Placement (Jegerlehner 2007) 24 Calorimeters symmetrically around storage ring. Intercepts about 65% of electrons Greater than 1.8 GeV.

Results of CERN and E821 Experiments Precision increased to.54 ppm during BNL experiment Magnetic moment for both negative and positive charged muons measured to achieve a mean value of (5.4)(3.3)[6.3] x 10^-10 Deviates Further From Theory. (Jegerlehner 2007)

Systematic uncertainty (ppm) E821 final Magnetic field –  p Anomalous precession –  a Statistical uncertainty (ppm) Systematic uncertainty (ppm) Total Uncertainty (ppm) A Summary of the Errors

Data Analysis sources of errors: statistical  Primary and secondary beam fluxes  The number of stored and lost Muons  Counting rates after injection  Running time estimates -Full AGS beam systematic  Errors in knowing the mean field B for the subset of stored muons  Corrections for the effect of the radial part of the electric field  The pitch correction to spin motion for muons oscillating in the vertical direction  The change of mean radius as a function of time due to dierential decay  The effect of muon particle losses  The effect of a nonzero electric dipole moment on the spin motion  Timing errors due to imperfections in the electronics

Theory vs. Experiment E821 achieved 0.54 ppm; e+e- based theory 0.49 ppm ； Hint is 3.2σ

Interpretations of the discrepancy “Firstly, new physics beyond the Standard Model, such as supersymmetry, is being seen. Secondly, there is a small statistical probability that the experimental and theoretical values are consistent (<1%). Thirdly, although unlikely, the history of science in general has taught us that there is always the possibility of mistakes in experiments and theories."

'Adjusting' the Model Potential modifications of the Standard Model. For example, there is supersymmetry, which predicts a partner for every known particle. Every fermion would have a boson partner, and every boson would have a fermion partner. Under certain scenarios, the existence of such particles would have a slight effect on g-2. The muon is not a point particle after all, but is cons- tructed of unkown smaller particles. The W gauge boson may have a g-value which differs from 2.

Experiment: P989 at Fermilab –move the storage ring to Fermilab, improved shimming, new detectors, electronics, DAQ, –new beam structure that takes advantage of the multiple rings available at Fermilab, more muons per hour, less per fill of the ring Theory Improvement: – better R measurements from: KLOE, BaBar, Belle, SND and CMD2 at Novosibirsk – More work on the strong interaction Further improvement

References Moller J.P., Rafael E, Roberts B.L Muon (g － 2): experiment and theory. Reports on Progress in Physics 70:795. Charpak G., Farley F.J.M., Garwin R.L., Muller T, Sens J.C., Zichichi A The Anomalous Magnetic Moment of the Muon. Nuovo Cimento 37: Bennett G.W., Bousquet B., Brown H.N., Muon (g-2) Collaboration Final report of the E821 muon anomalous magnetic moment measurement at BNL. Physical Review D 73: Jegerlehner F Essentials of Muon g-2. ArXiv:hep-ph/ v3 1 Jul Brookhaven National Laboratory. The Muon g-2 Experiment. Backgrounder: Muon g-2.. Accessed Nov http://

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