the anomalous magnetic moment of the muon · 2nd muon storage ring at cern, 1969-1976 excellent...

The anomalous magnetic moment of the muon

Vladimir TishchenkoBrookhaven National Laboratory

ISU Colloquium 18 April, 2016

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 2

Outline

● Magnetic moment● History of the magnetic moments● Future muon g-2 experiment at

Fermilab


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,


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 Unpublished.● 1925 G. E. Uhlenbeck (25) and S. A. Goudsmit (23): hypothesis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".


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.


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


anomalous magnetic moment


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!


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


choice of heavy particles to probe NP

Only exist as complicated multi-body objects

Too fleeting or no electric charge

Neutral (and too light)


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


muon

● mμ = 106 MeV

● (mμ/me)2 ≈ 4x104 ● ττ ~ 2.2 μs

convenient for exp. study→


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


muon – “self analyzing polarimeter”

e+


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


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


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


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)


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


1st muon storage ring at CERN, 1962-1968

… after an error in QED LBL calculations was correctedJ. Aldins et al., PRD 1 (1970) 2378


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



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!



● 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


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


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


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


BNL g-2 experiment in a nutshell


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


Electric quads to contain the beam vertically

E-field contribution vanishes

+HV

+HV

-HV -HV


Equation of motion (relative to the ideal orbit)

`

+

+

--


Some numbers for the g-2 storage ring


Harmonic motion in the g-2 storage ring

E989 conditions


Small perturbation

E989 case


Resonances

bad case

http://www.regentsprep.org


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


Muons off-ideal momentum

+

+

--

maximum momentum of stored muons for 4.5-cm-radius aperture:


... 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.


BNL quadrupoles


Refined equations for discrete quads

W.M. Morse


CBO


How to avoid CBO

fill uniformly the phase space!


positrons from muon decay

center of mass frame laboratory frame

y~0.58 (E=1.8 GeV)


Electric field correction

E821 CE = 470 ± 50 ppbE989 goal for CE and Cp combo: 30 ppb


Pitch correction

F.J.N. Farley, Phys. Lett. 42 (1972) 66

E821 CP = 270 ± 40 ppbE989 goal for CE and Cp combo: 30 ppb


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


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


uncertainties in E821 and E989 goals

statistical goal: x20 more muons


uncertainties in E821 and E989 goalsD. Kawall, UMass


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


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


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


Laser Calibration SystemG. Venanzoni, Frascati

gain


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


New Kicker D. Rubin, CornellCBO


New Kicker D. Rubin, Cornell

width of pulse is proportional to length of blumlein

CBO


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


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


Muon Campus at Fermilab

pion production target

8 GeV protons from Booster

Recycler

Li lensprotonbeam

120 ns

10 ms 12 Hz


Muon Campus at Fermilab

`

delivery ring

g-2

Mu2e

protons sent to Recycler

8 GeV protons from Booster


MC1 (g-2) building

beneficial occupancy May 2014

● Hall temperature stability +/- 1ºC● Stable floor (reinforced concrete, 84-cm-thick)


Storage ring at BNL in 2011 (E821)


September 2012: first yoke piece removed


30 September 2012


14 June 2013

The transport fixture and coils are outside Bldg. 919 at BNL. The superconducting coils are attached to the transport fixture.


22 June 2013

Moving from Bldg. 919 to BNL Lab. gate


24 June 2013

Leaving Smith Point Marina on Long Island

Craning onto the barge

unloading...


journey from NY to IL

more photos and info: http://muon-g-2.fnal.gov/bigmove

St. Louis


20 July 2013

Arriving Lemont, IL


At Fermilab


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


Yoke assembly completed


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.


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!


backup slides


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


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


Inflector


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


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)


Measuring B-field


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


Summary of CERN and BNL results


NMR probes


BNL beam

the anomalous magnetic moment of the muon · 2nd muon storage ring at cern, 1969-1976 excellent...

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