The anomalous magnetic moment of the muon
Vladimir TishchenkoBrookhaven National Laboratory
ISU Colloquium 18 April, 2016
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Outline
● Magnetic moment● History of the magnetic moments● Future muon g-2 experiment at
Fermilab
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Magnetic Moment
● … is a vector quantity characterizing magnetic interaction of an object with a magnetic fieldthe torque
current loop
orbiting charged particle
spinning ball of charge
L – orbital angular momentum
S – spin angular momentum (depends on mass distribution) γ - gyromagnetic ratio
if charge distribution is not the same as the mass distribution, introduce g factor,
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Some History
● 1896 Zeeman effect – splitting of spectral lines into several components in presence of a magnetic field
● 1922 Stern-Gerlach experiment● 1924 Pauli postulated a fourth quantum number to explain the
anomalous Zeeman effect● 1925 R. Kronig (20): concept of spinning electron. Unpublished.● 1925 G. E. Uhlenbeck (25) and S. A. Goudsmit (23): hypothesis
of electron spin, with possible quantum numbers of either + ½ or -½. Sent for publication by Ehrenfest: "Well, that is a nice idea, though it may be wrong. But you don't yet have a reputation, so you have nothing to lose".
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Solution of the electron g problem
● 1928 P. Dirac (25)
● 1933 O. Stern and I. Estermann: g-factor of the proton Pauli: “Don't you know the Dirac theory? It is obvious that gp=2.”measured value: gp≈5.6
proton substructure!BNL
μp turned out to be a harbinger of new physics!
Was finally explained, along with the g value of the neutron, g
n=-3.8 om the 1960 by the quark model.
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Nature abhors a vacuum
● At least for the electron, things finally in good shape with Dirac's new theory until...
● 1930s Oppenheimer and others tried to calculate correction to ge=2. Result: infinity.
● 1947 P. Kusch and H.M. Foley: ● 1948 J. Schwinger ● QED● Feynman diagrams...
● 1970s weak interactions unified with QED
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anomalous magnetic moment
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Present status: electron
● 2008 G. Gabrielse, Harvard
● Take α from external measurements to test QED
● Or, assume ge and calculate α
PRL 100 (2008) 120801
PRA 73 (2006) 032504
PRL 106 (2011) 080801
PRL 100 (2008) 120801
μe gives the most precise determination of the fine structure constant!
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Theory● QED now calculated ae to 5th order in (12672 diagrams).
Kinoshita & collaborator., 2008, 2012
Fujikawa, Lee, Sanda 1972; Czarnecki, Krause, Marciano 1996;Knecht, Peris, Perrottet, Rafael, 2002; Czarnecki, Marciano, Vainshtein, 2003;
Nomura & Teubner, 2012;
Prades, Rafael, Vainshtein, 2009
Sensitivity of ae to “new physics” at a mass scale Λ
Berestetskii, 1956
Schwinger 1948
Karplus & Kroll 1950; Petermann, Sommerfield 1957
Lautrup, Peterman, de Rafael 1974;Laporta, Remiddi 1996; Kinoshita 1995
Kinoshita & collaborator., 1983, 2002, 2005, 2007, 2012
Elend 1966
Samuel & Li, 1991
Samuel & Li, 1991
Samuel & Li, 1991
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choice of heavy particles to probe NP
Only exist as complicated multi-body objects
Too fleeting or no electric charge
Neutral (and too light)
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tauon
● mτ = 1777 MeV● (mτ/me)2 ≈ 1.2x107 ● τ meson has heightened
sensitivity to higher-mass exchanges
● ττ ~ 0.29 ps● Limits current precision to
0.052 < aτ <0.013
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muon
● mμ = 106 MeV
● (mμ/me)2 ≈ 4x104 ● ττ ~ 2.2 μs
convenient for exp. study→
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muon● 1933 First observed in cosmic rays. “Particle of uncertain nature”, Paul
Kunze, Z. Phys. 83 (1933) 1.● 1935 Hideki Yukawa: meson theory,
Proc. Phys.-Math. Soc. Jap. 17 (1985), 48● 1936 Seth Neddermeyer and Carl Anderson: particle in cosmic rays
with a mass “greater than an electron but smaller than a proton”. I. I. Rabi: "Who ordered that?"
● … -1957 V.B. Berestetskii, R.P. Feynman, J.S Schwinger: The muon (g − 2) experiment was recognized as a very sensitive test of the existence new fields, and potentially a crucial signpost to the μ–e problem.
● 1956-1957 T.D. Lee, C.N. Yang, C.S. Wu: parity violation ● 1957 R.L. Garwin, L. Lederman, M. Weinrich - antecedent of the (g-2)
measurements
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muon – “self analyzing polarimeter”
e+
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R.L. Garwin, L. Lederman, M. Weinrich, 1957
The magnetizing coil was close wound directly on the graphite to provide a uniform vertical field of 79 gauss per ampere. The various counters defined the event by use of a coincidence-anticoincidence analyzer
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Muon g-2 experiment in a nutshell
1) Take polarized muons (come naturally from pion decay)
2) Inject muons into a uniform magnetic field
– Momentum precession (cyclotron frequency)
– Spin precession
momentum spin
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1st CERN muon g-2 experiment 1958-1962
6-m-long 52-cm-wide 14-cm-gap bending magnet, B=1.5 T. 440 turns during τ=2.2 μs. Muon step size from 0.4cm to 11 cm.Time t spent inside the magnet was determined by by coincidence in counters 123 at input, and counters 466'57 at the output. t=2-8 μs depending on the location of the orbit center on the varying gradient field.
150 MeV/c muons
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1st CERN muon g-2 experiment 1958-1962
→ muon behaved so precisely as a structureless point-like QED particle; a heavy twin for the electron
The first CERN g-2 team: Sens, Charpak, Muller, Farley, Zichichi (CERN/1959)
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1st muon storage ring at CERN, 1962-1968
features:● weak focusing ring, n=0.13● B=1,.711 T● orbit diameter: 5m● aperture: 4cm x 8 cm● beam: 10.5 GeV protons● injection time: 10 ns● rotation time: 50 ns● stored muons:
p=1.28 GeV/c● γ = 12, t=27 μs
problems:● high background● low muon polarization
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1st muon storage ring at CERN, 1962-1968
… after an error in QED LBL calculations was correctedJ. Aldins et al., PRD 1 (1970) 2378
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2nd muon storage ring at CERN, 1969-1976
Motivation● to look for departures from standard QED● to detect contributions of strong interactions to aμ
through hadron loops in the vacuum polarization ● to search for new interactions of the muon
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2nd muon storage ring at CERN, 1969-1976
features:● 40 C-shaped bending
magnets ● pole: 38-cm x 14 cm
(width x gap) ● field in each magnet
stabilized with NMR probes
● electric quadrupoles for vertical focusing
● pion injection!
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2nd muon storage ring at CERN, 1969-1976
● Excellent agreement with theory● QED calculations verified up to
the sixth order● Confirmation of the existence of
hadronic vacuum polarization at the level of 5σ.
● No evidence of special coupling to the muon
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Final stop on the history tour...Brookhaven
Motivation● to measure electroweak
contributions to aμ which arise from single loop diagrams with vitural W and Z bosons
● to search for new interactions of the muon
A picture from 1984 showing the attendees of the first collaboration meeting to develop the BNL g-2 experiment. Standing from left: Gordon Danby, John Field, Francis Farley, Emilio Picasso, and Frank Krienen. Kneeling from left: John Bailey, Vernon Hughes and Fred Combley
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SM prediction for aμ
QED Weak Hadronic
QED: photonic and leptonic (e,τ,μ) loops, Weak: loops involving W±, Z or Higgs suppressed by at least a factor of ,Hadronic: quark and gluon loops. at present not calculable from first principles relies on a dispersion relation approach Total: -- PDG-2013
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Brookhaven storage ring
● Long list of innovations beyond CERN III– Flux in 12 bunches from the AGS
– Long enough beamline to operate with pion or muon injection
– Inflector to get muons through the back yoke...allowed muon injection
– High voltage, fast, non-ferric kickers to shift muon onto orbit in first cycle
– Thin quadrupoles and scalloped vacuum vessels minimize preshower
– In situ, field measurements with NMR trolley
– Continuous NMR monitoring and <0.1 ppm absolute calibration
– Pb/Scifi calorimeters, hodoscopes, and a traceback wire chambers
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BNL g-2 experiment in a nutshell
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BNL g-2 experiment in a nutshell
Determining the anomalous magnetic moment requires measuring
● The spin precession frequency
muon decay is self-analyzing: higher energy positrons are emitted preferen-tially in direction of muon spin
● The magnetic field B ( )
2001 data from E821
wrapped around modulo 100 μs
375 fixed NMR probes 17 NMR trolley probes
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Electric quads to contain the beam vertically
E-field contribution vanishes
+HV
+HV
-HV -HV
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Equation of motion (relative to the ideal orbit)
`
+
+
--
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Some numbers for the g-2 storage ring
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Harmonic motion in the g-2 storage ring
E989 conditions
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Small perturbation
E989 case
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Resonances
bad case
http://www.regentsprep.org
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Resonances for BNL ring
F.J.M. Farley, W.M. Morse, Y.K. SemertzidisE821 notes # 106, 116, 149
Y.K. Semertzidis et al., NIM A503 (2003) 458
http://www.scientificgamer.com
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Muons off-ideal momentum
+
+
--
maximum momentum of stored muons for 4.5-cm-radius aperture:
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... as a function of s
Liouville's theorem: if the motion of a particle is determined by a Hamiltonian, then the phase space density will be constant in time.
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BNL quadrupoles
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Refined equations for discrete quads
W.M. Morse
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CBO
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How to avoid CBO
fill uniformly the phase space!
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positrons from muon decay
center of mass frame laboratory frame
y~0.58 (E=1.8 GeV)
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Electric field correction
E821 CE = 470 ± 50 ppbE989 goal for CE and Cp combo: 30 ppb
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Pitch correction
F.J.N. Farley, Phys. Lett. 42 (1972) 66
E821 CP = 270 ± 40 ppbE989 goal for CE and Cp combo: 30 ppb
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Comparison of Experiment and Theory● Theory uncertainty: 0.42 ppm● Experimental uncertainty: 0.54 ppm
● “interesting but not yet conclusive discrepancy”● new physics signal?
PDG 2013
E821 @ BNL
arX
iv:1
311.2
198
[hep
-ph]
A. Czarnecki and W.J. Marciano, PRD 64 (2001)
Fermilab E989 goal: 0.14 ppm
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Muon g-2 Collaboration (E989)• Domestic Universities
– Boston– Cornell– Illinois – James Madison– Massachusetts– Mississippi– Kentucky – Michigan– Michigan State– Mississippi– Northern Illinois
University – Northwestern – Regis– Virginia– Washington– York College
• National Labs– Argonne– Brookhaven– Fermilab
• Consultants– Muons, Inc.
• Italy – Frascati – Roma – Udine– Naples– Trieste
• China: – Shanghai
• The Netherlands: – Groningen
• Germany: – Dresden
• Japan: – Osaka
• Russia: – Dubna– PNPI– Novosibirsk
EnglandUniversity College LondonLiverpoolOxfordRutherford Lab
KoreaKAIST
Co-spokespersons: David Hertzog, Lee RobertsProject Manager: Chris Polly
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uncertainties in E821 and E989 goals
statistical goal: x20 more muons
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uncertainties in E821 and E989 goalsD. Kawall, UMass
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New calorimeters
• Compact based on fixed space• Non-magnetic to avoid field perturbations
• Resolution not too critical for dwa – Useful for pileup, gain monitoring, shower
partitioning and low thresholds– Goal <5% DE/E at 2 GeV (a soft requirement)
• Gain stability depends on electronics and calibration system
– Goal: Short term < 0.1% DG/G in 600 ms– Goal: Longer term < 1% DG/G in 24 h
• Pileup depends on signal speed and shower separation– Subdivide calorimeter– Use Cherenkov– Goal: 2-pulse separation by space: 2 out of 3– Goal: 2-pulse separation by time: Dt > 5 ns
1 Moliere R2 Moliere R
Head on (high E) High angle (low E)
Crystal Calorimeter
No lightguides!
Platform for Electronics
PbFPbF22 crystals crystals
X0=0.93cm, RM=1.8cm
D. Hertzog, UWpileup
396 CALORIMETER
Figure18.2: Front pictureof the7-crystal test array used in theFTBF. In thisconfiguration,a SiPM is visible on the center channel, while PMTs are used on the remaining elements.These crystals were wrapped in white milliporepaper.
Figure 18.3: Sample 3⇥3⇥14 cm3 PbF2 crystals together with a 16-channel HamamatsuSiPM mounted to our Mark VII, resistive summing, voltage amplifier board. (Note, thesecrystals are larger than in theconceptual design.)
• The absorber must be dense to minimize the Moliere radius and radiation length. Ashort radiation length is critical to minimizethenumber of positrons entering thesideof the calorimeter while maintaining longitudinal shower containment.
• The intrinsic signal speed must be very fast with no residual long-term tail, thusminimizing pileup.
SiPM readout
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New electronics L. Gibbons, Cornell
● 800 MSPS sampling rate● continuous digitization over each 700-μs-long muon spill ● μTCA crate● 10 Gb network for data readout based on AMC13
(designed by CMS)
pileup
μTCA crate
MCH controller
AMC13
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New DAQ T. Gorringe, UKY
fragmentbuffer
fragmentbuffer
eventbuffer
fragmentbuffer
local diskarray
mCPU+GPUcalo FE
mCPUtracker FE
mCPUauxiliary FE
mCPUAnalyzer
rundatabase
x24 caloFrontends
8 GB/s sampleson 10 GbE
histograms,trees
FNALstorage
localrolling copy
aux detectorFrontends
few MB/s hitson VME→PCI
x3 trackerFrontends
~1MB/s hitson 1 GbE
data storage
analysis layer
backend layer
frontend layer
mTCAmTCA
VME
using CUDA, MIDAS, ROOT packages
pileup +statistics
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Laser Calibration SystemG. Venanzoni, Frascati
gain
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New Tracker B. Casey, FNAL
9 independent tracking modules
Purpose: measure the muon beam profile at multiple locations around the ring as a function of time throughout the muon fill. Is needed for understanding systematic uncertainties associated with with ωa measurements (calorimeter pileup, calorimeter gain, muon loss, differential decay syst. uncertainty, etc). Will also be used to search for a tilt in the muon precession plane away from the vertical orientation (which would be indicative of an EDM of the muon).
Design: 5-mm-diameter 10-cm-long straw UV doublets at 7.5º. straw walls: 6 μm Mylar sense wires: 25 μm gold-plated tungsten at 1500 V gas: 80:20 Argon:CO2 readout: ASDQ chips
beam,EDM
Tracker
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New Kicker D. Rubin, CornellCBO
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New Kicker D. Rubin, Cornell
width of pulse is proportional to length of blumlein
CBO
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Upgrade of Quadrupoles to higher HV
E989 goal
E989: 32kV
E821
E989: n=0.18
E821
• Higher admittance of the (g-2) storage ring• Lower CBO systematic error• Lower muon loss systematic error
E821
CBOLost Muons
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New beam collimators
Baseline plan:• Manufacture new collimators• Elliptical profiles to match beta-functions of the g-2 storage ring• Re-evaluate the thickness of collimators• Replace ½-collimators (see picture above) with full-collimators• The number of collimators will be reduced due to conflicts with new tracking chambers• Install sensors for in-beam/out-of-beam status monitoring
Lost Muons
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Muon Campus at Fermilab
pion production target
8 GeV protons from Booster
Recycler
Li lensprotonbeam
120 ns
10 ms 12 Hz
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Muon Campus at Fermilab
`
delivery ring
g-2
Mu2e
protons sent to Recycler
8 GeV protons from Booster
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MC1 (g-2) building
beneficial occupancy May 2014
● Hall temperature stability +/- 1ºC● Stable floor (reinforced concrete, 84-cm-thick)
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Storage ring at BNL in 2011 (E821)
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September 2012: first yoke piece removed
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30 September 2012
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14 June 2013
The transport fixture and coils are outside Bldg. 919 at BNL. The superconducting coils are attached to the transport fixture.
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22 June 2013
Moving from Bldg. 919 to BNL Lab. gate
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24 June 2013
Leaving Smith Point Marina on Long Island
Craning onto the barge
unloading...
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journey from NY to IL
more photos and info: http://muon-g-2.fnal.gov/bigmove
St. Louis
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20 July 2013
Arriving Lemont, IL
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At Fermilab
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Ring reassembly at Fermilab
June 23, 2014. Bottom yoke. Reassembly progresses well. Superconducting coils will be moved into the experimental hall end of July 2014
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Yoke assembly completed
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Present Status
● MC1 building beneficial occupancy in May 2014.Ring reassembly started.
● Diagnosed and repaired E821 He Cold Leak.● Magnet successfully cold-power tested to 60%
of nominal operating current, June 2015.● Passed CD2/3 DOE review in June 2015.
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In conclusion
● The very successful muon g-2 program at BNL ended with a statistics-limited >3σ discrepancy in Δaμ (exp-thy)
● To test the discrepancy the new muon (g-2) experiment at Fermilab will reduce the experimental uncertainty by a factor of about four
● The experimental setup has been successfully moved from Brookhaven to Fermilab
● Reassembly of the g-2 storage ring completed, the magnet is power on and the field shimming progresses well.
● New/upgraded calorimeters, electronics, DAQ, kicker, quadrupoles, collimators, electron trackers, field measurement and instrumentation to reduce systematic uncertainties completed.
● First beam in 2017!
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backup slides
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The Muon Anomalous Magnetic Moment
Quantum loop effects:
- anomalous magnetic moment
where
sensitivity to short distance physics: Berestetskii, 1956
=> muons ~40000 times more sensitive to new physics than electrons
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Modify quadrupole Q1
Q1 outer
OPERA model
Goal: increase the number of stored muons (muon losses due to scattering in Q1 plate)Baseline plan: Displace Q1 outer plate by ~2cm radially
beam losses
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Inflector
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Most difficult part of theory comes from hadronic sector
● Theory error dominated by QCD piece● Common to divide hadronic loops into 3
categories...
– aμ(had,LO) = 6923 ± 42
– aμ(had,HO) = -98 ± 1
– aμ(had,LBL) = 105 ± 26*Courtesy E. De Rafael, arXiv 0809.3025
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Reducing δaμ(had,LO) requires precision e+e- → hadrons
● Experiments have reduced error such that 2π region no longer dominates error
● Data from Novosibirsk (CMD2 and SND)
– For 2π, ratio N(2π)/N(ee), form factor to 1-2%
– All modes but 2π luminosity measured using Bhabha scattering
*Courtesy V. Logashenko, Tau 2008
contribution error2(from F. Jegerlehner)
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Measuring B-field
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Improvements at FNAL/BNL
Stored Muons / POT
0.05Net
50 at magic P
0.01 survive to ring
0.4 / p
0.25p / fill
FNAL/BNLparameter
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Summary of CERN and BNL results
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NMR probes
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BNL beam