The anomalous magnetic moment of the

Vladimir Tishchenko Brookhaven National Laboratory

ISU Colloquium 18 April, 2016 Outline

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

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

● … is a vector quantity characterizing magnetic interaction of an object

with a magnetic field spinning ball of charge the torque

orbiting charged particle

current loop

S – spin angular momentum (depends on mass distribution) γ - gyromagnetic ratio if charge distribution is not the same as the mass distribution, L – orbital angular momentum introduce g factor,

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 3 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 Unpublished.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".

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 4 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

μ turned out to be a harbinger of new physics! p Was finally explained, along with the g value of the BNL neutron, g =-3.8 om the 1960 by the quark model. proton substructure! n V. Tishchenko Idaho State University, Colloquium 18 April, 2016 5 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 6 anomalous magnetic moment

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 7 Present status: electron

● 2008 G. Gabrielse, Harvard

PRL 100 (2008) 120801 ● Take α from external measurements to test QED

PRA 73 (2006) 032504

PRL 106 (2011) 080801

● Or, assume ge and calculate α

PRL 100 (2008) 120801

μ gives the most precise determination of the fine structure constant! e

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 8 Theory

● th QED now calculated ae to 5 order in (12672 diagrams).

Kinoshita & collaborator., 2008, 2012 Schwinger 1948

Karplus & Kroll 1950; Petermann, Sommerfield 1957

Elend 1966 Fujikawa, Lee, Sanda 1972; Czarnecki, Krause, Marciano 1996; Knecht, Peris, Perrottet, Rafael, 2002; Czarnecki, Marciano, Vainshtein, 2003;

Nomura & Teubner, 2012; Lautrup, Peterman, de Rafael 1974; Laporta, Remiddi 1996; Kinoshita 1995 Prades, Rafael, Vainshtein, 2009 Samuel & Li, 1991

Samuel & Li, 1991

Samuel & Li, 1991

Kinoshita & collaborator., 1983, 2002, 2005, 2007, 2012 Sensitivity of ae to “new physics” at a mass scale Λ

Berestetskii, 1956

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 9 choice of heavy particles to probe NP

Only exist as complicated multi-body objects

Too fleeting or no electric charge

Neutral (and too light)

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 10 tauon

● mτ = 1777 MeV

● 7 (mτ/me)2 ≈ 1.2x10 ● τ meson has heightened sensitivity to higher-mass exchanges

● ττ ~ 0.29 ps ● Limits current precision to ­ 0.052 < aτ <0.013

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 11 muon

● mμ = 106 MeV

● 4 (mμ/me)2 ≈ 4x10

● ττ ~ 2.2 μs → convenient for exp. study

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 12 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 13 muon – “self analyzing polarimeter”

e+

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 14 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 15 Muon g-2 experiment in a nutshell

1) Take polarized (come naturally from pion decay)

2) Inject muons into a uniform magnetic field

– Momentum precession (cyclotron frequency) – Spin precession

momentum spin

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 16 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 17 1st CERN muon g-2 experiment 1958-1962

The first CERN g-2 team: Sens, Charpak, Muller, Farley, Zichichi (CERN/1959)

→ muon behaved so precisely as a structureless point-like QED particle; a heavy twin for the electron

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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 19 1st muon storage ring at CERN, 1962-1968

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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 20 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 21 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!

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 22 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 23 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, , and Frank Krienen. Kneeling from left: John Bailey, Vernon Hughes and Fred Combley

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 24 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 25 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 26 BNL g-2 experiment in a nutshell

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 27 BNL g-2 experiment in a nutshell

Determining the anomalous magnetic moment requires measuring 2001 data from E821 ● The spin precession frequency

muon decay is self-analyzing: higher energy positrons are emitted preferen-

tially in direction of muon spin wrapped around modulo 100 μs

● The magnetic field B ( )

375 fixed NMR probes 17 NMR trolley probes

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 28 Electric quads to contain the beam vertically

+HV

-HV -HV

+HV

E-field contribution vanishes

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 29 Equation of motion (relative to the ideal orbit) +

- -

+

`

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 30 Some numbers for the g-2 storage ring

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 31 Harmonic motion in the g-2 storage ring

E989 conditions

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 32 Small perturbation

E989 case

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 33 Resonances

bad case

http://www.regentsprep.orgV. Tishchenko Idaho State University, Colloquium 18 April, 2016 34 Resonances for BNL ring

F.J.M. Farley, W.M. Morse, Y.K. Semertzidis E821 notes # 106, 116, 149

http://www.scientificgamer.com

Y.K. Semertzidis et al., NIM A503 (2003) 458

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 35 Muons off-ideal momentum

+

- -

+

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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 36 ... 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.

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 37 BNL quadrupoles

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 38 Refined equations for discrete quads

W.M. Morse

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 39 CBO

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 40 How to avoid CBO

fill uniformly the phase space!

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 41 positrons from muon decay center of mass frame laboratory frame

y~0.58 (E=1.8 GeV)

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 42 Electric field correction

E821 CE = 470 ± 50 ppb

E989 goal for CE and Cp combo: 30 ppb

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 43 Pitch correction

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

E821 CP = 270 ± 40 ppb

E989 goal for CE and Cp combo: 30 ppb

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 44 Comparison of Experiment and Theory

● Theory uncertainty: 0.42 ppm

● Experimental uncertainty: 0.54 ppm E821 @ BNL

PDG 2013

● “interesting but not yet conclusive discrepancy” ● new physics signal?

A. Czarnecki and W.J. Marciano, PRD 64 (2001)

arXiv:1311.2198 [hep-ph] Fermilab E989 goal: 0.14 ppm

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 45 Muon g-2 Collaboration (E989)

• Domestic Universities • Italy England – Boston – Frascati University College – Cornell – Roma London – Illinois – Udine Liverpool Oxford – James Madison – Naples Rutherford Lab – Massachusetts – Trieste – Mississippi • China: – Kentucky – Shanghai Korea – Michigan • The Netherlands: KAIST – Michigan State – Groningen – Mississippi • Germany: – Northern Illinois – Dresden University • Japan: – Northwestern – Osaka – Regis • Russia: – Virginia – Dubna – Washington – PNPI – York College – Novosibirsk • National Labs – Argonne – Brookhaven – Fermilab Co-spokespersons: David Hertzog, Lee Roberts • Consultants Project Manager: Chris Polly – Muons, Inc.

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 46 uncertainties in E821 and E989 goals

statistical goal: x20 more muons

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 47 uncertainties in E821 and E989 goals

D. Kawall, UMass

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 48 396 CALORIMETER

Figure18.2: Front pictureof the7-crystal test array used in theFTBF. In this configuration, New calorimetersa SiPM is visible on the center channel, whil e PMTs are used on D.the r eHertzog,maining elements. UW pileup These crystals were wrapped in white millipore paper.

• Compact based on fixed space PbF2 crystals • 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)

3 Figure 18.3: Sample 3⇥ 3⇥ 14 cm PbF2 crystals together with a 16-channel Hamamatsu • Gain stability depends on electronics and calibrationSiPM mounted to our MarSiPMk VII, resist ivreadoute summing, voltage amplifier board. (Note, these system crystals are larger than in the conceptual design.) – Goal: Short term < 0.1% DG/G in 600 ms • The absorber must be dense to minimize the Moli`ere radius and radiation length. A short radiation length is critical to minimizethenumber of pXosit=0.93cm,rons entering Rthe=1.8cmside – Goal: Longer term < 1% DG/G in 24 h of the calorimeter while maintaining longitudinal shower containmen0 t. M • Pileup depends on signal speed and shower separation• The intrinsic signal speed must be very fast with no residual long-term tail, thus – Subdivide calorimeter minimizing pileup. – Use Cherenkov – Goal: 2-pulse separation by space: 2 out of 3 – Goal: 2-pulse separation by time: Dt > 5 ns

Crystal Calorimeter No lightguides! 1 Moliere R 2 Moliere R

Platform for Head on (high E) High angle (low E) Electronics

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 49 New electronics L. Gibbons, Cornell pileup

μTCA crate AMC13

MCH controller

● 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)

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 50 pileup + New DAQ T. Gorringe, UKY statistics

x24 calo x3 tracker aux detector frontend layer Frontends Frontends Frontends 8 GB/s samples ~1MB/s hits few MB/s hits on 10 GbE A on 1 GbE Aon VME→PCI TC TC E m m VM

mCPU+GPU mCPU mCPU calo FE tracker FE auxiliary FE

backend layer fragment fragment fragment buffer buffer buffer

event buffer

local disk array data analysis storage mCPU layer Analyzer FNAL local storage rolling copy histograms, run trees database

using CUDA, MIDAS, ROOT packages

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 51 Laser Calibration System gain G. Venanzoni, Frascati

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 52 beam, New Tracker EDM B. Casey, FNAL

Tracker

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). 9 independent Design: 5-mm-diameter 10-cm-long straw UV doublets at 7.5º. tracking modules straw walls: 6 μm Mylar sense wires: 25 μm gold-plated tungsten at 1500 V

gas: 80:20 Argon:CO2 readout: ASDQ chips

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 53 New Kicker D. Rubin, Cornell CBO

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 54 New Kicker D. Rubin, Cornell CBO

width of pulse is proportional to length of blumlein

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 55 Upgrade of Quadrupoles to higher HV CBO Lost Muons E989 goal 21 E8 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 56 New beam collimators Lost Muons

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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 57 Muon Campus at Fermilab

8 GeV protons from Booster

pion production target

Li lens

proton beam Recycler

120 ns

10 ms 12 Hz

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 58 Muon Campus at Fermilab

8 GeV protons from Booster

protons sent to Recycler g-2 `

Mu2e

delivery ring

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 59 MC1 (g-2) building

beneficial occupancy May 2014

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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 60 Storage ring at BNL in 2011 (E821)

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 61 September 2012: first yoke piece removed

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 62 30 September 2012

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 63 14 June 2013

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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 64 22 June 2013

Moving from Bldg. 919 to BNL Lab. gate

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 65 24 June 2013 unloading...

Craning onto the barge

Leaving Smith Point Marina on Long Island

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 66 journey from NY to IL

St. Louis

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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 67 20 July 2013

Arriving Lemont, IL

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 68 At Fermilab

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 69 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 70 Yoke assembly completed

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 71 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.

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 72 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!

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 73 backup slides

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 74 The Muon Anomalous Magnetic Moment

Quantum loop effects: where

- anomalous magnetic moment sensitivity to short distance physics: Berestetskii, 1956

=> muons ~40000 times more sensitive to new physics than electrons

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 75 Modify quadrupole Q1 beam losses

Goal: increase the number of stored muons (muon losses due to scattering in Q1 plate) Baseline plan: Displace Q1 outer plate by ~2cm radially

OPERA model

Q1 outer

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 76 Inflector

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 77 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

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 78 + - 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), (from F. Jegerlehner) form factor to 1-2% contribution error2 – All modes but 2π luminosity measured using Bhabha scattering

*Courtesy V. Logashenko, Tau 2008

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 79 Measuring B-field

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 80 Improvements at FNAL/BNL

parameter FNAL/BNL p / fill 0.25  / p 0.4  survive to ring 0.01  at magic P 50 Net 0.05

Stored Muons / POT

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 81 Summary of CERN and BNL results

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 82 NMR probes

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 83 BNL beam

V. Tishchenko Idaho State University, Colloquium 18 April, 2016 84