The Tiny Muon versus the Standard Model. Paul Debevec Physics 403 November 14 th, 2017

Transcription

1 The Tiny Muon versus the Standard Model Paul Debevec Physics 403 November 14 th, 2017

2 BNL E821 Muon g-2 Collaboration

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5 Standard Model of Particle Physics

6 Components of the Standard Model of Particle Physics Quarks Leptons Gauge Bosons u c t d s b e e e e g W o Z g our focus Muon properties 207 electron mass point particle decays in 2.2 s charged intrinsic spin

7 Standard Model of Particle Physics

8 magnetic moment of a current loop ˆn N A I in classical electricity and magnetism current loop has a magnetic dipole moment ˆ I An magnetic dipole creates a magnetic field S

9 current from orbital motion of a charge r e IA v v I e A r 2 r 2 magnetic moment proportional to orbital angular momentum v e 2 R 2M 2 e r Mvr L Mr v e g L g 2M 1 g constanct of proportionality is gyromagnetic ratio or g-factor

10 quantization of angular momentum from atomic structure-- quantum numbers E orbital angular momentum azimuthal angular momentum integral quantum numbers 0,1,2,... m 0, 1, 2,..., 2 unit of angular momentum Planck s constant 0 1 unit of magnetic moment Bohr magneton e 2M

11 spin angular momentum and spin magnetic moment S s 1 2 m 12 s intrinsic spin quantum number is half-integral e gs S g 2M s 2 spin g-factor is 2 e 1 e 2 2 M 2 2 M magnetic moment is one Bohr magneton

12 spin g-factor is beyond classical physics arbitrary matter/charge distribution gives g = 1 L r r v r dv matter v r J r dv r v r J r charg e r e M charg e matter r e L g 1 2M

13 spin g-factor is quantum mechanical Schrodinger equation Dirac equation point particle with spin 1/2 in E and B fields has g = 2 Field theory (these results are not elementary)

14 magnetic moment in a magnetic field potential energy U B torque B

15 magnetic moment precesses in magnetic field d B S dt e B B sin gs S B sin 2M d S dt s sin S g s s e B 2M precession (angular) frequency proportional to B and g s measure B and s to determine g s

16 magnetic moments and g-factors of selected particles g e s S g e S s 2M 2M electron muon proton neutron g g g g e p n point particles composite particles

17 g-factor anomaly anomaly defined a g 2 2 anomaly explained all particles are surrounded by virtual particles and fields (this figure is a cartoon)

18 spin direction is quantized N S S N

19 g - 2 > 0 potential energy U B g e E 2B 2 B 22 M add perturbation of virtual fields and particles with perturbation energy levels repel so g must increase

20 g-factor anomaly (this figure is a Feynman diagram) virtual photon a lowest order contribution Schwinger (1947) 2 1 e 1 2 c / e / e external magnetic field fine structure constant 2 e c 1 137

21 Standard Model contributions to g-factor anomaly QED + hadronic + weak Interaction Field Particles QED photons e e etc strong gluons o quarks etc weak W W Z e e e e etc

22 measure the g-factor anomaly to search for new physics "NEW" experiment theory a a a QED + WEAK + HADRONIC What is the sensitivity to new physics? How accurate is the experiment? How accurate is the theory?

23 muon anomaly versus electron anomaly Electron is stable and common Electron anomaly ha been measured to 4 parts in 1,000,000,000 Hadronic contribution only 2 ppb Weak contribution only 0.03 ppb M Coupling to virtual particles is M X So, muon anomaly is 40,000 more sensitive 2 e /

24 Standard Model calculation of muon anomaly - QED QED contribution is well known and understood dominant contribution % of anomaly a(qed)= (0.29)10-10 (0.025 ppm) e+ e- e + e + e + e - e - e - representative diagrams--hundreds more

25 Standard Model calculation of muon anomaly - Weak Weak contribution is also well known and understood 1.3 parts per million contribution a(weak)=15.1(0.4)10-10 (0.03 ppm) Z o W W representative diagrams--many more

26 Standard Model calculation of muon anomaly - Hadronic Hadronic contribution cannot be calculated from QCD (yet) hadrons dominant contribution theory needs virtual hadrons e + e - real hadrons available from experiment

27 Standard Model calculation of muon anomaly - Hadronic R E cm (GeV) H (s) obtained by: R(s) (e e hadrons ) ( ee ) a had 1 ( ) 3 H ( s) K( s) ds 4 2 4m

28 Speculations of physics beyond the Standard Model W, Z structure W W gw Muon substructure Supersymmetry W W µ µ chargino-sneutrino one-loop a 2 M 4Tev 2 Z µ µ neutralino-smuons one-loop

29 Polarized muons Elements of g-2 experiment pion decay produces polarized muons Precession gives (g-2) in a storage ring the spin precesses relative to the momentum at a rate (g-2) Parity violation positron energy indicates the direction of the muon spin P The magic momentum at one special momentum, the precession is independent of the electric focussing fields

30 Polarized Muons Pion decay is the source of polarized muons spin momentum Pions are produced in proton nucleus collisions AGS p

31 Precession in Uniform Field of Storage Ring in flight at rest 2 s g e B M s g e B m 1 c e B M B cyclotron frequency

32 Difference Frequency a spin momentum simulation a s c g 2 2 e B M difference frequency g-2, not g, independent of!

33 Measuring the Spin Direction P e In the COM: e e dn n E ded A E 1 cos High energy positrons in the LAB frame are emitted at forward angles in the CM frame cut on these We measure / ( ) t N t Ne 1 Acos at

34 Storing the Muons The Magic Momentum Problem: Orbiting particles hit the top or bottom Solution: Build a trap with electric quadrupoles Moving muons see electric field like another magnetic field and their spins react... e 1 v a a B a E 2 2 M 1 c = s vanishes at GeV/c

35 Precession frequency a Getting the Answer Magnetic field map TIME p B p 2 p a a e B m

36 BNL E821 Analysis Strategy Magnetic Field Secret Offsets Secret Offsets Data Production Fitting / Systematics

37 Storage Ring / Kicker Radius Aperture Field P m 7112 mm 90 mm 1.45 T GeV/c

38 BNL Storage Ring 100 kv KICK ns Quads

39 Fast Rotation Momentum distribution

40 Magnetic Field Measured in situ using an NMR trolley Continuously monitored with > 360 fixed probes mounted above and below the storage region

41 Field Contours Averaged around Ring 1999 Regardless of muon orbit, all muons see the same field to < 1ppm 2000 inflector shield problem 2001

42 Systematic Errors for p Size [ppm] 1) absolute calibration ) trolley probe calibration ) trolley measurement of B ) interpolation with fixed probe ) muon distribution ) others 0.15 Total Systematic Error d p = 0.24 ppm

43 Counts Measuring the difference frequency a e ns samples < 20 ps shifts < 0.1% gain change Time

44 4,000,000,000 e + with E > 2 GeV / ( ) t N t Ne 1 Acos at

45 One Analysis Challenge: Pileup Subtraction Phase shift can be seen here Two are close; we can still separate these With two software deadtimes, we extrapolate to zero deadtime and make a pileup-free histogram low rate deadtime corrected Energy Spectrum with deadtime

46 Systematic Errors for a Size [ppm] 1) coherent betatron oscillations ) pileup ) gain changes ) lost muons ) binning and fitting procedure ) others 0.06 Total Systematic Error d a = 0.31 ppm

47 Results from the 2000/2001 runs & World Average a x World average a = (6) x 10-10

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49 The Big Move from Brookhaven to Fermilab

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