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Angular Momentum and Magnetic Moments

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Angular Momentum and Magnetic Moments The Tiny Muon versus the Standard Model Paul Debevec Physics 403 November 14th , 2017 BNL E821 Muon g-2 Collaboration Standard Model of Particle Physics Components of the Standard Model of Particle Physics u c t our focus Quarks d s b Muon properties e 207 electron mass Leptons “point” particle eee decays in 2.2 s g charged W intrinsic “spin” Gauge Bosons o Z g Standard Model of Particle Physics magnetic moment of a current loop nˆ in classical electricity and magnetism A current loop has a magnetic dipole moment I I Anˆ N magnetic dipole creates a magnetic field S current from orbital motion of a charge magnetic moment proportional to orbital angular momentum r v ve e e r2 Mvr 22 RM IA L Mr v v I e A r 2 e 2 r g L g 1 2M constanct of proportionality is g gyromagnetic ratio or g-factor quantization of angular momentum from atomic structure-- quantum numbers orbital angular momentum 0,1,2,... azimuthal angular momentum m 0, 1, 2,..., integral quantum numbers E unit of angular momentum 2 Planck’s constant 1 unit of magnetic moment Bohr magneton e 0 2M spin angular momentum and spin magnetic moment S s 12 intrinsic spin quantum number is half-integral ms 12 e gss S g 2 spin g-factor is 2 2M ee1 2 magnetic moment is 2MM 2 2 one Bohr magneton spin g-factor is beyond classical physics arbitrary matter/charge distribution gives g = 1 L matter r r v r dV r J r dV v J r charg e r v r e rr charg eM matter e Lg 1 2M spin g-factor is quantum mechanical Schrodinger equation point particle with spin 1/2 Dirac equation in E and B fields has g = 2 Field theory (these results are not elementary) magnetic moment in a magnetic field potential energy UB torque B magnetic moment precesses in magnetic field d BS dt e B Bsin g S B sin s 2M d SS sin dt s e gB ss2M precession (angular) frequency proportional to B and gs measure B and s to determine gs magnetic moments and g-factors of selected particles e e S g S g ss22MM electron g 2 1.001 e “point” particles muon g 2 1.001 proton g p 2 2.79 composite particles neutron gn 2 1.91 g-factor anomaly g 2 anomaly defined a 2 anomaly explained all particles are surrounded by virtual particles and fields (this figure is a cartoon) spin direction is quantized N S g - 2 > 0 potential energy UB ge EBB 22 22M add perturbation of virtual fields and particles with perturbation energy levels repel so g must increase g-factor anomaly (this figure is a Feynman diagram) virtual photon lowest order contribution Schwinger (1947) / e / e 11e2 a 0.001 2 c 800 external magnetic field e2 1 fine structure constant c 137 Standard Model contributions to g-factor anomaly QED + hadronic + weak Interaction Field Particles QED photons e e etc strong gluons o quarks etc weak WWZ e e etc ee measure the g-factor anomaly to search for new physics a"NEW" aexperiment a theory QED + WEAK + HADRONIC What is the sensitivity to new physics? How accurate is the experiment? How accurate is the theory? 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 2 M •Coupling to virtual particles is e / M X •So, muon anomaly is 40,000 more sensitive Standard Model calculation of muon anomaly - QED QED contribution is well known and understood dominant contribution 99.9930% of anomaly a(QED)=11 658 470.57(0.29)10-10 (0.025 ppm) e+ e+ - e e+ e+ e - e- e- representative diagrams--hundreds more 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) o Z W W representative diagrams--many more Standard Model calculation of muon anomaly - Hadronic Hadronic contribution cannot be calculated from QCD (yet) hadrons dominant contribution theory needs virtual hadrons e+ available from experiment e- real hadrons Standard Model calculation of muon anomaly - Hadronic 5 4 R 3 2 2 3 4 5 6 7 Ecm (GeV) (ee hadrons ) (s) obtained by: R(s) H ()ee had 1 a()()()3 H s K s ds 4 4m2 Speculations of physics beyond the Standard Model g 2 W 0.02 •W, Z structure 2 W W •Muon substructure M 2 a 4Tev 2 •Supersymmetry ˜ Z W ˜ µ ˜ µ µ µ ˜ neutralino-smuons one-loop chargino-sneutrino one-loop Elements of g-2 experiment • Polarized muons 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 Polarized Muons •Pion decay is the source of polarized muons spin momentum •Pions are produced in proton nucleus collisions p AGS Precession in Uniform Field of Storage Ring at rest in flight B ge ge 21 s B 1 B 2 M s 2 m cyclotron frequency e 1 B c M Difference Frequency a spin momentum ge 2 B simulation a s c 2 M difference frequency g-2, not g, independent of ! Measuring the Spin Direction e e Pe dN In the COM: n E1 A E cos dEd 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 A cos a t 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... ev1 = 29.3 a a B a 22 E Mc 1 64 s vanishes at 3.094 GeV/c Getting the Answer Precession frequency a Magnetic field map TIME p a p a B e 2p B m BNL E821 Analysis Strategy Magnetic Field Secret Offsets Secret Offsets Data Production Fitting / Systematics Storage Ring / Kicker Radius 7112 mm Aperture 90 mm Field 1.45 T Pm 3.094 GeV/c 100 BNL Storage Ring kV KICK 0 500 ns Quads Fast Rotation Momentum distribution Magnetic Field Measured in situ using an NMR trolley Continuously monitored with > 360 fixed probes mounted above and below the storage region Field Contours Averaged around Ring Regardless of muon orbit, all muons see the same 1999 field to < 1ppm 2000 inflector shield problem 2001 Systematic Errors for “p” Size [ppm] 1) absolute calibration 0.05 2) trolley probe calibration 0.15 3) trolley measurement of B0 0.10 4) interpolation with fixed probe 0.10 5) muon distribution 0.03 6) others 0.15 Total Systematic Error dp = 0.24 ppm Measuring the difference frequency “a” e+ 2.5 ns samples < 20 ps shifts < 0.1% gain change ounts C Time 4,000,000,000 e+ with E > 2 GeV t / N( t ) Ne 1 A cos a t One Analysis Challenge: Pileup Subtraction Phase shift can be seen here Two are close; we can still separate these with deadtime With two software low rate deadtimes, we deadtime extrapolate to zero corrected deadtime and make a pileup-free histogram Energy Spectrum Systematic Errors for “a” Size [ppm] 1) coherent betatron oscillations 0.21 2) pileup 0.13 3) gain changes 0.13 4) lost muons 0.10 5) binning and fitting procedure 0.06 6) others 0.06 Total Systematic Error da = 0.31 ppm Results from the 2000/2001 runs & World Average 10 - 11659000 10 x 11659000 - a -10 World average a = 11659208(6) x 10 The Big Move from Brookhaven to Fermilab http://muon-g-2.fnal.gov/bigmove/gallery.shtml .
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