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
uct our focus Quarks dsb 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 IAnˆ 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 erMvr 2 22 RM IA LMrv v I e A r 2 e 2 r gLg 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
LrrvrdV matter
rJ rdV v J rrv rchearg
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 BBgS B sinsin 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
eeS gSg ss22MM
electron g 21.001 e “point” particles muon g 21.001
proton g p 22.79 composite particles neutron gn 21.91 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
UB
ge EBB22 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 2800 c 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 eeetc
strong gluons o quarks etc
weak WWZ e e etc
ee measure the g-factor anomaly to search for new physics
aaa"NEW" experimenttheory
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) (ehadronse ) (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 asc 2 M difference frequency g-2, not g, independent of ! Measuring the Spin Direction
e e Pe dN In the COM: nEAE 1cos 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