Muon (and electron) Anomalous Magnetic Moment

Muon (and electron)
Anomalous Magnetic
Moment
Luis Pesántez
May 17 th ,2001

Why?
• Explain discrepancies between
theory and experiment.
• Precision achieved is very high.
• Very sensitive to new physics.
2

• Introduction
Outline
– Measurement in electrons vs. muons
• Radiative corrections
– QED, HVP, EW
• Experiments
– Historical overview
• E821 at Brookhaven
– Achievements
– Latest results
• The future
• Summary
3

Magnetic moment
• Intrinsic property of charged
particles:
• Pauli-Schroedinger equation predicts
g s =2
4

The anomaly
• Early experiments show small
disagreement:
• Redefine g s as:
Radiative corrections:
5

Theory: corrections
6

Muons vs. electrons
• Uncertainty in muon
• But corrections go as
7

Muons vs. electrons
8

Radiative corrections
• Three types of contributions:
– QED: photons and leptons (~100%)
– HVP (~ 60 ppm)
– EW: gauge bosons (~ 1.3 ppm)
• Calculated both analytically and
numerically, also relies on
experimental measurements.
9

QED
• C1 comes from Schwinger correction
• Values computed up to 4 th order and
estimated 5 th order.
10

• Two-loop
QED: some Feynman
• Three-loop
(72 diagrams)
diagrams
11

Hadronic
• Cannot be calculated from first
principles.
• All lowest order calculations related to:
• Lattice QCD
• Loops containing hadrons
and leptons.
12

Hadronic Vacuum Polarization
13

Electroweak
• Contribution is very small compared
to QED and Hadronic.
• Not sensitive to mass of Higgs
(150 - 500 GeV).
• Only one and two loop contribute,
three loops in neglected O(10 -12 ).
14

Electroweak
15

Summary of theory
16

Experimental history
• 1947 anomaly observed in H
hyperfine splitting (electrons).
• 1948 Schwinger correction.
• 1957 Nevis cyclotron: anomaly
observed in muon, found to be
~equal to anomaly in electron.
17

CERN experiments
• 1962: sensitive to order .
• 1968: sensitive to order .
• 1979: sensitive to order + had.
18

E821 at Brookhaven
19

E821 at Brookhaven
• 1984: reach 0.35 ppm, test EW.
• Muons are stored in a ring (very
uniform and stable Bfield).
• Count number of electrons product
of muon decay.
20

Experimental idea
21

Muon decay
• Muons produced from
π decay are polarized
(weak decay).
• Muon spin precesses
faster than
momentum.
22

Slow electron
Fast electron
Muon decay
• Fast electrons are emitted with
their momentum anti-parallel to
muon spin.
23

What is measured?
• Spin precession frequency
(interaction with Bfield):
• Cyclotron frequency:
• Anomaly:
if
24

Magic momentum
• Electrostatic focusing changes the
frequency:
• Easy!
25

Magic momentum
• Electrostatic focusing changes the
frequency:
• Magic momentum:
26

Detection
• 24 electromagnetic calorimeters
• Detect electrons above E th = 1.8 GeV.
– Remember, we want fast electron
• We get more events depending on
direction of muon spin.
27

Determination of
28

Calculating anomaly
• B field determined with NMR (proton
Larmor frequency)
• And with λ measured from muonium
hfs:
• The anomaly is then:
29

Dealing with errors
• Different teams determining and
.
• Blind data analysis.
30

E821 results
14 times more accurate than CERN
experiment.
Test of CPT in muons
31

E821 results
32

Current status
33

Theoretical challenge
• Find alternatives to explain
discrepancy:
– Leptons substructure
– Supersymmetry
34

Future experiments
• E989 @ Fermilab
– Reduce uncertainty to 0.16 ppm:
5 - 6σ deviation.
– Factor of 20 increase in statistics.
– Significant reduction on systematic
uncertainties.
35

Future experiments
36

What to remember
• Muons are “better” than electrons.
• Precise test of SM.
• All the physics is present in one
number.
• discrepancy, new physics?
37

Light-by-light scattering
39

Setup
40

Electron anomaly
41

Electron anomaly
42

Electron anomaly
43