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The Tiny Muon versus the Standard Model

Paul Debevec 403 November 14th , 2017 BNL E821 Muon g-2 Collaboration

Standard Model of Components of the Standard Model of Particle Physics

uct our focus  dsb Muon properties

e      207  Leptons       “point” particle eee      decays in 2.2 s g charged W  intrinsic “” Gauge Bosons   o  Z  g Standard Model of Particle Physics of a current loop

nˆ in classical electricity and A current loop has a magnetic moment

I   IAnˆ N

magnetic dipole creates a

S current from orbital of a charge

magnetic moment proportional to orbital angular 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 or g-factor quantization of

from atomic structure-- numbers

orbital angular momentum  0,1,2,... azimuthal angular momentum m 0,1,2,..., quantum numbers E

unit of angular momentum  2 Planck’s constant

1 unit of magnetic moment e  0 2M spin angular momentum and spin magnetic moment

S s 12 intrinsic spin 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 arbitrary matter/charge distribution gives g = 1

LrrvrdV matter    

   rJ rdV  v J rrv  rchearg    

e rr    charg eM matter e  Lg  1 2M spin g-factor is quantum mechanical

Schrodinger equation point particle with spin 1/2 in E and B fields has g = 2

Field theory

(these results are not elementary) magnetic moment in a magnetic field

potential

UB

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

g p 22.79 composite particles 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... ev1  = 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

p

a p a  B   e 2p 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 dp = 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 da = 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