Muon g 2. Physics 403 Advanced Modern Physics Laboratory Matthias Grosse Perdekamp. Slides adapted from Jörg Pretz RWTH Aachen/ FZ Jülich

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1 Muon g 2 Physics 403 Advanced Modern Physics Laboratory Matthias Grosse Perdekamp Slides adapted from Jörg Pretz RWTH Aachen/ FZ Jülich 1 /53

2 Outline Introduction & Motivation Method Experiment & Analysis Results Summary & Outlook 2 /53

3 Introduction & Motivation 3 /53

4 Magnetic Moment and g-factor g = magnetic moment (eħ/ 2mc) angular momentum n = 2 for Dirac particle 4 /53

5 Magnetic Moment and g-factor g = magnetic moment (eħ/ 2mc) angular momentum n = 2 for Dirac particle higher order corrections: e e l lead to an x B anomalous magnetic moment a = g 2 2 α π 5 /53

6 Electron a e (exp) = (0.28) (0.2ppb) D. Hanneke, S. Fogwell Hoogerheide, and G. Gabrielse, Phys. Rev. A 83, (2011) a e (th) = (0.86) (0.7ppb) Aoyama et al., arxiv: [hep-ph] a e (exp) a e (th) = 0.4(1.3) /53

7 Contributions to a e : Electron a had a e = a em e + e + aweak e = (( 1) ppb ppb) a e electro-mag. hadronic weak e e l e + e l e Z 0 e l - x B x B x B a e tests QED but it is not sensitive to hadronic and weak contributions! 7 /53

8 Some 4 loop Corrections T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Phys. Rev. D 85 (2012) [arxiv: [hep-ph]]. includes 5 loop corrections as well 8 /53

9 Muon a µ (th) = (49) 10 9 (0.42ppm) K. Hagiwara et al., J. Phys. G G 38 (2011) [arxiv: [hep-ph]]. Contributions to a µ : a µ = aµ em + had a µ + weak a µ = (( 1 ) + 60 ppm ppm ) a µ Error of experiment: σ aµ a µ ± 1.3 ppb ± 0.4 ppm ± 0.02 ppm = 0.5ppm (stat. and syst.) a µ is sensitive to hadronic and weak contributions, because had,weak,bsm ahad,weak,bsm µ (m µ /m e ) 2 a e (BSM: beyond Standard Model) 10 / 53

hadronic contribution: a had µ e + - e l is related to and x B e + e - + - W + + 0 R

10 hadronic contribution: a had µ e + - e l is related to and x B e + e W R had = σe+ e hadrons σ e+ e µ + µ Error on a had limited by µ experimental data 10 / 53

11 Contributions beyond Standard Model \ 2 Muon substructure: a substr ( m µ µ Λ sensitivity Λ 5 TeV (similar to LHC) SUSY models: a SUSY µ GeV 2 tan β M SUSY (1.7 ppm) for M SUSY = 500GeV and tan β = m t /m b 11 / 53

12 Method 12 / 53

13 Method Observe µ spin precession in storage ring: ω a = d ϑ = e dt m c µ a µ B ω a from e + time spectrum µ + e + ν e ν µ: due to parity violation: correlation between nb. of e + and spin of µ + s p ϑ a e + detector () B B_ 1.5T ring radius R 7m and T c = 150ns 2π T a = ω a = 4.4µs τ = 64µs 13 / 53

14 events/a.u. Method decay spectrum: dr(y, t ) e t /τ n(y ) (1 + A(y ) sin(ϑ a )) y = E e E µ, ϑ a = ω a t t/ s 14 / 53

15 Experiment 15 / 53

16 Experiment Components: Beamline (get polarized muons) Magnet (measurement of B) Detectors (measurement of ω a ) 20 / 53

Beamline AGS bunch width: 27 ns bunch separation: 33 ms 24 GeV proton beam (6 Bunches/2.5 s,7 10 12 p/bunch) momentum selection π (p m + 0.

17 Beamline AGS bunch width: 27 ns bunch separation: 33 ms 24 GeV proton beam (6 Bunches/2.5 s, p/bunch) momentum selection π (p m + 0.5%) > µ (p m ) + ν Q1 production target(10 8 π /Bunch) D1 D4 + momentum selection decay path (70m) P1 inflector detectors magnet 10000µ + /Bunch muon per 10 protons! 21 / 53

19 Magnet Superferric Magnet (B=1.45 T) 4 Nb/Ti coils, I=5200 A Radius m Shimming: edge shims wedges iron strips surface coils 19/53

20 1 eb ω p = g 2 p m p c B field measurement field measurement by NMR difficulty is not to measure B at one point to < 1 ppm but over a large volume/ time scale 300 fixed NMR probes on top and bottom of the vacuum chamber, read out continuously Trolley with 17 NMR probes, which measures the field in the storage region every 2-3 days Standard probe for calibration note that NMR measures B difference between B and B measured to be < 0.01ppm 20/53

21 3 c 0 '-J IDV> 0 O r l <C ;;; <C 0 :l 21/53

22 B-field in transverse direction 1ppm contour lines 22/53

23 Systematic Error B Source of error Size[ppm] Absolute calibration of standard probe 0.05 Calibration of trolley probes 0.09 Trolley measurements of B Interpolation with fixed probes 0.07 Uncertainty from muon distribution 0.03 others 0.1 higher multipoles, trolley temperature eddy currents from kicker Total /53

24 24 detectors inside the ring e + -Detectors Lead/Scintillating Fibers energy resolution σ 10%/ E (GeV) 15 radiation lengths PMT analog signals are digitized every 2.5 ns rate changes from 1 MHz to a few Hz from t=0 to t=10τ time stability on average 60 ps/10τ = 0.1 ppm laser system to check time and gain stability 24/53

25 e+ pulse to 25/53

26 Determination of ω a Fit time spectrum with e + with E > 2 GeV for ω a : N(t ) = N 0 (t )e t / τ (1 + A(t ) cos(ω a t + φ(t ))) correct for/ include in fitting pile-up (by looking at double pulses) µ losses, (looking for coincidences in several detectors) gain changes of PMT (looking at laser pulses) betatron oscillation (N 0, A, φ modulated by 1 + A b e t /τ 2 2 b cos(ωb t + Φ b ) ) 15 parameters depending on fitting method only Φ correlates strongly with ω a χ 2 of reached as expected for 4000 degrees of freedom 26/53

27 Counts per 150 ns Time [us]

28 3000 :, :; time (JlS) time s) -0o.C<- 3BI53

29 Systematic Error ω a Source of error Size[ppm] Pileup 0.08 Lost Muons 0.09 horiz. betatron oscillations 0.07 Gain changes 0.12 others 0.11 AGS background, timing shifts E field and vertical betatron oscillations Beam debunching/ randomization, binning & fitting procedure Total /53

30 Final Result 30 / 53

31 Putting everything together a µ = ω µ ω a ω p ω a ω p ωp ω a (this experiment) p ω µ = µ µ = (10) (muonium) ω p µ p a µ (exp) = (5.4)(3.3) combination of results (0.54ppm) 3 σ away from SM-expectiation! 31 / 53

32 CERN BNL CERN( ) 4300 ppm muon is heavy electron CERN( ) 270 ppm a µ /= a e CERN( ) 7 ppm sensitive to hadronic contribution BNL( ) FNAL 0.54 ppm goal: 0.14 ppm sensitive to weak contribution and BSM (?) 32/53

33 Summary & Outlook Comparison of theoretical and measured anomalous magnetic of muon allows stringent test of Standard Model Situation since 10 years: 3 σ difference between theory and experiment New efforts at Fermilab and in Japan with factor 4 smaller error BNL Experiment set also limit on muon EDM: d µ = ( 0.1 ± 0.9) e cm d µ < e cm (95% CL) 33/53

34 Time Magazine, Feb W I N N E R S & L O S l R S 17.."'. 34/53

Muon (g 2) at JPARC. Five to Ten Times Better than E821. B. Lee Roberts. Department of Physics Boston University BOSTON UNIVERSITY

Muon (g 2) at JPARC. Five to Ten Times Better than E821. B. Lee Roberts. Department of Physics Boston University BOSTON UNIVERSITY Muon (g 2) at JPARC Five to Ten Times Better than E821 B. Lee Roberts roberts@bu.edu http://physics.bu.edu/roberts.html Department of Physics Boston University B. Lee Roberts, JPARC LOI Presentation, 26