Measurement of Muon Dipole Moments

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1 Measurement of Muon Dipole Moments Gerco Onderwater KVI, University of Groningen, the Netherlands Lepton Moments 2010, Cape Cod, July

2 Outline Basic Properties : P-violation, dipole moments Nevis era : signal definition CERN era : ωa, decay in flight, pmagic, B-field BNL era : putting it all together Future : FNAL, J-PARC, PSI,...

Standard Model Properties Second generation charged

violation Muons are produced fully polarized Decay

3 Standard Model Properties Second generation charged lepton Mass : Charge : Lifetime : Production : Decay : mμ ~ 206 me ~ 105 MeV/c² qμ = qe = 1e τμ ~ 2.2μs π± μ±+νμ μ± e±+νμ+νe Weak interaction & parity violation Muons are produced fully polarized Decay electron distribution correlates with muon spin: asymmetry=1/3

4 EM Dipole Moments eℏ = g 2mc g=2 a 1 Anomaly e ℏ d = 2mc =0 P & T conservation This is where the physics is!

5 Nevis Stopped Muons

6 Larmor Precession d S = B dt eℏ = g B 2mc With B measured in terms of proton NMR frequency f m g = g p f p mp gp = 2x( (3)+1) (25) me Measure frequency ratio

7 1957 : First experiment π μ e g=2.0±0.1

8 Results with stopped muons π μ Year gμ σgμ Ref Garwin Cassels Cofn Lundy Lundy Garwin Precision e Δg/g = 150ppm Δa/a = 11% a= 2 Muon behaves as heavy electron!

More on λ=μμ/μp Year λ σλ Ref. 1963 1969 1970 1970 1972 1977 1982 1982 1999 0.00004 0.000048 0.000044 0.000013 0.0000082 0.0000044 0.0000011 0.0000017 0.

9 More on λ=μμ/μp Year λ σλ Ref Hutchinson Thompson; Hutchinson De Voe; Crowe Casperson; Mariam; Klempt Liu; muonium HFS muonium HFS muonium HFS muonium HFS muonium HFS dλ/λ = 120ppb with theory 35ppb Would need independent measurement of mμ/mp and gp to convert to gμ. μe/μp : 8x10-9 me/mp : 4x10-10 ge : 7x10-13 proton magnetic moment : dμp/μp ~ 10-8 daμ/aμ > 10-5

10 1958 : First EDM experiment d S d v B = B dt η < EDM S along B

11 CERN Muons in Flight

12 1961: On to the anomaly

13 Thomas-BMT Equation [ ] 1 a g a B B E d e = E B E ] [ dt mc e a = S =a B mc Instantly gain a factor ~1000 in precision... d s e = s dt mc

14 CERN I : Graded dipole field second-order QED μ π e

15 Muon Decay in Flight : Angle-to-Energy p L = E CM pcm cos CM, Emission angle in CM is correlated to spin direction BOOST e-energy in LAB is correlated to spin direction pt = pcm sin CM

16 CERN II : The first storage ring Proton injection Multi-turn storage Momentum 1.27 GeV/c Magnetic focussing third-order QED + almost hadronic correction p μ π e

17 The magic momentum [ ] e 1 a B a 2 E a = mc 1 Zero for γ=29.3, pμ=3.094 GeV/c Electric instead of magnetic focussing Use pure magnetic dipole for precise B measurement

18 Magnetic Field Uniformity Measure a a a = B= B g 2 a 1 p = p B R a = R { 2ppm contours a R= p = p If B(muons)=B(protons) Need homogenous field Need stable field Need λ 40 separately stabilized magnets Inflector to reduce non-uniformity Proton NMR probes outside vacuum Remove chambers to probe inside No need to (precisely) know where the muons are

19 CERN III : beyond QED π Confirms hadronic contribution e μ

20 CERN III : and a new EDM limit... e = a B m EDM up-down asymmetry 90º out of phase w.r.t. g-2

21 CERN III : and a new EDM limit... e [ a B ] = v B m EDM up-down asymmetry 90º out of phase w.r.t. g-2

22 BNL State of the Art

23 BNL 1984 Many improvements - muon injection - continuous storage ring - superconducting magnet - in-situ magnetometry - high-resolution calorimeters - WFDs - record intensity - circular aperture - calibration probe - and many more (a lot younger!) collaborators

24 Beam intensity & purity Move to most intense proton source: AGS 70TPOT in 12 bunches every 2.7s Use ~90m long pion decay line about 50% decay, cut pions before ring Directly inject muons using fast kickers ~200ns wide pulse

shims Ring cross section same as in λ measurement Calibration via spherical water probe

25 Homogenous B-field C-shaped iron yoke ρ=7m super-conducting coil Shielded SC inflector Precision iron poles Wedges to shim azimuthal variations & quadrupole moment Rose shims Current shims Ring cross section same as in λ measurement Calibration via spherical water probe Plunging probe to transfer calibration Fixed probes to track time variation NMR trolley to scan storage volume

26 Magnetic field tracking Beam profile weighing & time interpolation φ averaging & (x,y) multipole expansion

27 Improved electron detection Good energy resolution (few %) Fast response (few ns) Compact (half a shoebox) WFD readout (400MHz) Gated off during flash Detailed offline analysis possible ~1010 events

28 Double Blind Analysis a R= p R a = R = ωa and ωp analyzed independently unknown ofsets ω's analyzed independently by several groups (2-5) unknown ofsets require internal consistency ², insensitive to irrelevant variations,... require mutual consistency (incl. systematics) ω's equal within (highly correlated) statistics,... obtain all systematics (incl. E-feld, pitch,...) understand diferences,... remove ofset, do long-division and publish no room for discussion! p

29 Final result Combined average (μ+ and μ-) aμ(expt.) = 11,659,208.0(5.3)(3.3)x10-10(0.54ppm) (statistics limited)

30 Storage ring results QFD new? Ref Charpak Charpak Farley Henry Bailey Bailey Bailey Bailey Carey Brown Brown Bennett Bennett aμ(expt.) - aμ(th) = (30±8) x (3.6σ) Experiment: σa/a = 0.54 ppm Theory: δa/a 0.44 ppm CERN QCD σaμ BNL QED Year aμ

EDM @ BNL As at CERN, measure up-going vs down-going electron asymmetry NEW: reconstruct vertical angle (much better

31 BNL As at CERN, measure up-going vs down-going electron asymmetry NEW: reconstruct vertical angle (much better systematic, much less statistics) g-2 EDM Time modulo g-2 period 19 d e cm Bennett et al., PRD 80, (2009) 1017 to go for SM

32 FNAL Build on a proven formula

33 Aim + improve EDM limit by a factor 100

34 Why FNAL?

35 Using the pbar-accumulator Using a 900m long decay channel reduces pion content by 20 and gives 6-12 times more stored muons per proton

36 Timeline D v e r OE c s iew e l u hed n a l p d e l i a t e D u A r d fo g. 2 h c a o r p p a of

37 The big move : BNL FNAL Courtesy Chris Polly

38 Frozen Spin FNAL, PSI, J-PARC

39 Freezing the spin magnetic moment anomaly [ EDM e 1 E v B = a B a 2 v E m 2 1 ω ] ωa E=0, B=By (1) = a 2 2 /4 B (2) B= / 2a + frozens spin parasitic = v ωη Er abcβγ², B /2 B=B = y (1) (2) B=1 B

Ideas Post-(g-2) @ FNAL A. Silenko et al.

First-guess design p = 600MeV/c B = 0.45T, E = 5MV/m R = 4.2m Design: p = 500MeV/c B = 0.

around 10 24 e cm five orders below current limit Idea for PSI B.L. Roberts et al.

40 Ideas FNAL A. Silenko et al. (2003) J-PARC Letter of Intent: Search for the Permanent Muon Electric Dipole Moment at the e cm Level. First-guess design p = 600MeV/c B = 0.45T, E = 5MV/m R = 4.2m Design: p = 500MeV/c B = 0.25T E = 2MV/m R = 7m Estimated Sensitivity around e cm five orders below current limit Estimated Sensitivity around e cm five orders below current limit Idea for PSI B.L. Roberts et al. p = 125MeV/c N = 2 105/s P = 92% B = 1T E = 0.64MV/m R = 42cm Reach: 5x10-23 e cm / y 3-4 orders below current limit Table top experiment! See talks by Semertzidis & Ströher (for p & d) Adelmann, Kirch, Onderwater & Schietinger, J. Phys. G: Nucl. Part. Phys (2010)

41 Finale

42 Conclusion Over half a century of experience performing measurements of the dipole moments of the muon have taught us that performing a highly precise experiment requires extreme care & many clever ideas the muon is a lepton the muon behaves like a heavy electron QED, QCD & QFD corrections are correct there might be a hint for new physics And there is (much) more to come...

43 Many thanks to... Muon g-2 Collaborations BNL E821 FNAL P969 J-PARC Muon EDM Collaborations J-PARC PSI FNAL

Proposal to measure the muon electric dipole moment with a compact storage ring at PSI

Proposal to measure the muon electric dipole moment with a compact storage ring at PSI Klaus Kirch in collaboration with A. Adelmann, G. Onderwater*, T. Schietinger, A. Streun *Rijksuniversiteit Groningen