From Z0 to Zero:
A Precise Measurement of the Running
of the Weak Mixing Angle
SLAC E158
Steve Rock
University of Massachusetts
Zeuthen
For SLAC E158 Collaboration
Outline
• History
• Physics Motivation
• Technique for Precision Measurement





Beam
LH2 Target
Spectrometer
Detectors
Analysis
• Results
• Outlook
E158 Steve Rock Nov 04
SLAC E122 (1978)
e-D Inelastic Scattering
Detector
e
16 – 22 GeV
Liquid Deuterium
Measured Coupling of electron and nucleons
sin2W = 0.224 + 0.020
First definitive measurement of mixing between
the weak and electromagnetic interaction
Help Establish the Standard Model
E158 Steve Rock Nov 04
IMPROVEMENTS
•
•
•
•
•
•
HIGHER POLARIZATION (NLC)
BEAM STABILITY (SLC, FFTB)
50 GeV BEAM
5  LONGER TARGET
RADIATION RESISTANT DETECTOR (LHC)
LOW NOISE, HIGH RESOLUTION
ELECTRONICS
E158 Steve Rock Nov 04
Standard Model Electroweak Theory
Based on gauge group SU(2)L X U(1)
with isotriplet field W and isosinglet field B
SU(2)L coupling is g, U(1) coupling is g'
After spontaneous symmetry breaking via Higgs
mixing of W and B fields produces observed particles
Charged bosons
Neutral bosons
Vector couplings
Axial couplings
fermion weak isospin
fermion charge q/e
E158 Steve Rock Nov 04
Standard Model
W and g determine ALL couplings
LH coupling
RH coupling
e
W

g/ 2
0
Q f g sinW
Q f g sinW
( g 2  g '2 )1 / 2 ( I 3f  Q f sin 2 W )
( g 2  g '2 )1 / 2 ( Q f sin2 W )

f
f
f
Z0
f
E158 Steve Rock Nov 04
“High Energy” EW Data
• Spectacular precision at LEP, SLD



Quantum loop level (LO to NNLO)
Precise indirect constraints on top and Higgs masses
General consistency with the Standard Model
 Few smoking guns
 Leptonic and hadronic Z couplings seem inconsistent ?
• Direct searches have not yielded new physics
phenomena (so far)
• Complementary sensitivity at LOW ENERGIES



Rare or forbidden processes
Symmetry violations
Precision measurements
Belle, BaBar, E158, g-2,…
E158 Steve Rock Nov 04
Parity Violation at the Z-pole
(SLD at SLAC)
f
e
e
Z0
f
d
 v 2f  a 2f   [(1  Pe Ae )(1  cos2  ) 
d cos
2 A f ( Ae  Pe ) cos ]
g 2L  g R2 2v f a f
Af  2 2  2 2
gL  gR vf  a f
sin2W at Z pole
E158 Steve Rock Nov 04
Running of Weak Mixing Angle
sin2W = e2/g2
→ test gauge structure of SU(2)U(1)
3%
E158 Steve Rock Nov 04
Beyond the Standard Model
Find new physics by deviations from SM predictions
Precision EW via PV
New physics ~|amplitude|
Make high mass
APV ~
exchange visible
e
e

e
e
Z
e
+
e
?
Beat large against small to see new
E158 Steve Rock Nov 04
γ-Z INTERFERENCE
AT LOW Q2
2




2
2
4
 1
1
1 
Q
Q
Q

4 



Q
1




 2


2
2
4 
2
2


Q
M
M
M
M
M 

Z
X
Z


Z
X 
• Interference proportional to Q2
• Sensitive to Z’
E158 Steve Rock Nov 04
Precise Low Q2 PV Experiments
Moller- E158
e
e

e
DIS-Parity
e
Q-Weak(JLAB)
e
 Z
Z
e
p
e
e
e
Incoherent
isoscalar quarks
This Experiment Well understood
small corrections
No quarks
(2C1u-C1d)+Y(2C2u-C2d)

Cs133
 Z
Z
n
Pure leptonic,
Atomic Parity V
Coherent quarks
proton
Coherent quarks
entire nucleus
Results ~2008
Large syst. errors
atomic, nuclear
structure
-2(2C1u+C1d)
-376C1u- 422C1d
E158 Steve Rock Nov 04
Parity Violation in Møller Scattering
• Scatter polarized 50 GeV electrons
off unpolarized atomic electrons
• Measure
R L
APV 
 ALR
R L
• Small tree-level asymmetry
APV
GF 16 sin 2 
1
 mE
(  sin 2  )
W
2 ( 3  cos 2  )2 4
1-4sin2w ~ 0
A
 280  10 9
At tree level,
(smaller after radiative effects)
PV
• Raw asymmetry about 130 ppb
– Measure it with precision of 10%
– Most precise measurement of sin2W at low Q2
E158 Steve Rock Nov 04
E158 New Physics Reach
Compositeness
 ~ 10 TeV
Grand Unified Theories
MZ’ ~ 0.8 TeV
~ 0.01GF 0.01
E158 Steve Rock Nov 04
SLAC E-158
L~
1038
cm-2s-1
5x1011 e-/pulse
45 GeV
P=85%
integrating
flux counter
2 GHz
4-7 mrad
LH2
End Station A
E158 Steve Rock Nov 04
E158 Collaboration
•UC Berkeley
•Caltech
•Jefferson Lab
•Princeton
•Saclay
•SLAC
•Smith College 7 Ph.D. Students
60 physicists
•Syracuse
•UMass
•Virginia
Sep 97: EPAC approval
1998-99: Design and Beam Tests
2000:
Funding and construction
2001:
Engineering run
2002: Physics Runs 1 (Spring), 2 (Fall)
2003:
Physics Run 3 (Summer)
E158 Steve Rock Nov 04
TINY ASYMMETRY EXPRIMENT
9
A

130

10
( PV
)
(STABILITY AND INTENSITY)
• HIGH INTENSITY POLARIZID e BEAM
•
•
•
•
•
HIGH DENSITY ELECTRON TARGET (LH2)
BACKGROUND REMOVERS
MOLLER ELECTRON SELECTORS
DETECTORS
MONITORS
E158 Steve Rock Nov 04
Experimental Technique
• Scattering of polarized electrons off atomic electrons



High cross section (14 Barn)
High intensity electron beam, ~85% polarization
1.5m LH2 target


Luminosity 4*1038 cm-2s-1
High counting rates: flux-integrating calorimeter
• Principal backgrounds: elastic and inelastic ep
• Main systematics: beam polarization,
helicity-correlated beam effects, backgrounds
E158 Steve Rock Nov 04
Major Challenges
• Statistics !

Need to accumulate ~1016 scattered electrons
• Suppress Random noise


Want to be dominated by counting statistics
Beam pulse to pulse “random” fluctuations are major
(potential) source of additional “statistical error
• Systematics


False asymmetries
Backgrounds (Need to measure in situ)
E158 Steve Rock Nov 04
Statistics
# scattered e- per pulse
107/pulse
Rep rate (120 Hz)
109 /sec
Seconds/day
1014/day
100 days
1016
A ~ 10-8
E158 Steve Rock Nov 04
Control of Beam Systematics

Beam helicity is chosen pseudo-randomly at 120 Hz
•
•

sequence of pulse quadruplets
use electro-optical Pockels cell in Polarized Light Source
Reduce beam asymmetries by feedback
•
•
•
Control charge and position asymmetry at Source
Control Angle Asymmetry
Control Energy Asymmetry
E158 Steve Rock Nov 04
E-158 Beam
(and comparison with 500 GeV Linear Collider Design)
Parameter
E-158
NLC-500
Charge/Train
5 x 1011
14.4 x 1011
Repetition Rate
120 Hz
120 Hz
Energy
45 GeV
250 GeV
e- Polarization
85%
85%
Train Length
270ns
267ns
Microbunch spacing
0.3ns
1.4ns
Beam Loading
13%
22%
Energy Spread
0.15%
0.16%
E158 Steve Rock Nov 04
BEAM
•
•
•
•
HIGH INTENSITY 6×1011 /burst
HIGH POLARIZATION
“HIGH ENERGY” (Asymmetry  Q2 )
STABLE (Same Beam for L & R Polarization)





INTENSITY (acceleration, Target)
POSITION (Acceptance, backgrounds)
ANGLE (σ depends on θ)
ENERGY (σ depends on E)
TRANSVERSE SIZE (Target effects)
E158 Steve Rock Nov 04
Polarized Source
E158 Steve Rock Nov 04
Beam Diagnostics
Energy dithering
region
linac
A-Line
RF Cavity
BPM
Pulse-to-pulse monitoring of beam asymmetries
and resolutions:
energy  1 MeV
BPM  2 microns
BPM24 X (MeV)
toroid  30 ppm
Agreement (MeV)
Resolution
1.05 MeV
E158 Steve Rock Nov 04
BPM12 X (MeV)
BEAM VARIATIONS
• LONG TERM DRIFTS CONTROLLED WITH FEEDBACK

LASER OPTICS

LASER INTENSITY

POCKEL CELLS

ACCELERATING CAVITY

STEERING MAGNETS
E158 Steve Rock Nov 04
Beam Asymmetries
Charge asymmetry at
1 GeV
Charge asymmetry
agreement at 45 GeV
Energy difference
agreement in A line
Energy difference in A
line
Position differences < 20 nm
Position agreement ~ 1 nm
E158 Steve Rock Nov 04
BEAM VARIATIONS
• BEAM JITTER (OFFLINE CORRECTIONS)






ENERGY
ANGLES
POSITION (and correlation with time)
INTENSITY
BEAM SIZE
TARGET DENSITY
• MONITOR EFFECTS OF VARIATION


“NATURAL JITTER” (Linear Regression)
CONTROLLED VARIATION
• CORRECT PULSE BY PULSE
E158 Steve Rock Nov 04
Eliminating Beam Jitter
i Determined by Linear Regression
i Determined by Dithering
1
- -202128
Both Methods agree
E158 Steve Rock Nov 04
Moller Detector
Regression Corrections
In addition, independent analysis based on beam dithering
E158 Steve Rock Nov 04
Reversals and Checks
 Physics Asymmetry Reversals
•
•
Insertable Half-Wave Plate in Polarized Light Source
(g-2) spin precession in A-line (45 GeV and 48 GeV data)
 Reverse special laser optics
•

Insertable “-I/+I” Inverter in Polarized Light Source
“Null Asymmetry” Cross-check is provided by a
Luminosity Monitor
•
measure very forward angle e-p (Mott) and Møller scattering
E158 Steve Rock Nov 04
End Station A
E158 Steve Rock Nov 04
Experimental Layout in
ESA
Target chamber
Quadrupoles
Concrete Shielding Detector Cart
Precision
Beam
Monitors
Dipoles
Main
Collimators
Drift pipe
Luminosity
Monitor
60 m
E158 Steve Rock Nov 04
Liquid Hydrogen Target
CONSTANT
DENSITY
Refrigeration Capacity
Max. Heat Load:
- Beam
- Heat Leaks
- Pumping
Length
Radiation Lengths
Volume
Flow Rate
1000W
500W
200W
100W
1.5 m
0.18
47 liters
5 m/s
Disk 1
Disk 2
Disk 3
Disk 4
Wire mesh disks in target cell region
to introduce turbulence at 2mm scale
and a transverse velocity component.
Total of 8 disks in target region.
E158 Steve Rock Nov 04
SPECTROMETER & DETECTORS
• Separate Moller e- from other processes
• Accurately measure number of Moller e• Measure Q2
• Measure Backgrounds

Pions
e- p  e- p +? (BIGGIST CORRECTION)
 Neutrons, , …

E158 Steve Rock Nov 04
E158 Spectrometer
Forward background of e+ epairs
Line-of-sight shielding
requires a “chicane”
Emoller~25 GeV
Moller ring is 20 cm
from the beam
E158 Steve Rock Nov 04
Detectors
~1.5
~1.5omr
MOLLER, ep are copper/quartz fiber calorimeters
PION is a quartz bar Cherenkov
LUMI is an ion chamber with Al pre-radiator
All detectors have azymuthal segmentation,
and PMT readout to 16-bit ADC
E158 Steve Rock Nov 04
Profile Detector: Q²
4 Quartz Cherenkov detectors with PMT readout
insertable pre-radiators
insertable shutter in front of PMTs
Radial and azymuthal scans
 collimator alignment, spectrometer tuning
 background determination
 Q2 measurement
 Monte Carlo Tune
Cerenkov
detector
Linear
drive
Bearing
wheels
E158 Steve Rock Nov 04
e p Background
• MEASURE


e p Asymmetry in e p Detector
Shape of e p and e e in Profile Detector using Movable
Collimators
• MODEL ASYMMETRY(Q2,W2)


Monte Carlo using Detector Acceptance
Tuned with Profile Detector
 Quads on/off
 Collimator Positions
• CORRECTION ~ -25 ±5 ppb
E158 Steve Rock Nov 04
APV Measurement
1. Measure asymmetry for each pair of pulses
A
p
exp
σR - σL

σR  σL
2. Correct for difference in R/L beam properties,
charge, position, angle, energy
Apraw  Apexp  ai Δxi
R-L differences

coefficients determined experimentally by regression or from dithering coefficients
3. Sum over all pulse pairs,
Araw   A
p
raw
4. Obtain physics asymmetry:
1 A raw  fbkg A bkg
A PV 
Pb
fnorm
dilutions
beam polarization
backgrounds
E158 Steve Rock Nov 04
3 EXPERIMENTAL RESULTS
• e e TRANSVERSE ASYMMETRY

2 photon exchange physics
• e p LONGITUDINAL ASYMMETRY

Proton Structure
• e e LONGITUDINAL (main result)
E158 Steve Rock Nov 04
e e Transverse Asymmetries
Beam-Normal Asymmetry in elastic electron scattering
 Beam Polarization Perpendicular to Direction of motion
 Select by beam energy (number of spin rotations)
Azimuthal Dependence of Asymmetry
2 d (   )   
AT   
 S e  ( k e  k'e )
d
 


Interference between oneand two-photon exchange
AT 
me
s
 O( ppm)
E158 Steve Rock Nov 04
E158 e- e- Transverse Results
43 and 46 GeV
ee  ee
LH2 target
~ 24 hrs of data

(Azimuthal angle)
• Raw asymmetry!
• Publication by Fall
• Crosscheck E158 polarimetry at 3%?
 O(3) test of QED in E158 ?
 ~5% residual transverse polarization in
longitudinal data: carefully combine
detector channels to suppress this effect
E158 Steve Rock Nov 04
ep Detector Data (Run 1)
ARAW(45 GeV) = -1.36 ± 0.05 ppm (stat. only)
ARAW(48 GeV) = -1.70 ± 0.08 ppm (stat. only)
Ratio of asymmetries:
APV(48 GeV) /APV(45 GeV) = 1.25 ± 0.08 (stat) ± 0.03 (syst)
Consistent with expectations for inelastic ep asymmetry
E158 Steve Rock Nov 04
Møller Asymmetry (Blind Analysis)
• Over 330M pulse pairs over 3 separate runs (2002-2003) at
Ebeam=45 and 48 GeV
• Passively flip helicity of electrons wrt source laser light
~every day to suppress spurious helicity-correlated biases
E158 Steve Rock Nov 04
Raw Asymmetry Statistics
Asymmetry pulls per pulse pair:
150M pairs
Asymmetry pulls
per 10k pair “chunks”
E158 Steve Rock Nov 04
(A-<A>)/
Asymmetry Corrections and
Systematics
Correction
fbkg
fbkg)
Acorr (ppb)
Acorr) (ppb)
Beam asymmetries
-
-
-
4
Beam spotsize
-
-
0
1
Transverse asymmetry
-
-
-4
2
ep elastic
0.058
0.007
-8
2
ep inelastic
0.009
0.003
-22
6
High energy photons
0.004
0.002
+3
3
Synchrotron photons
0.0015
0.0005
0
2
Neutrons
0.0006
0.0002
-1
1
Brem and Compton electrons
0.005
0.002
0
1
Pions
0.001
0.001
1
1
TOTAL
0.082
0.009
-27
8
• Scale factors:
• Average Polarization 88 ± 5%
• Linearity 99 ± 1%
• Radiative corrections: 1.016 ± 0.005
E158 Steve Rock Nov 04
from APV to sin2Weff
APV
GF Q 2
1 y
2
eff



F


1

4
sin


brem
W
4
4
4 2 1  y  1  y 
where:
is an analyzing power factor; depends on
GF Q 2
1 y


4
kinematics and experimental geometry.
4 2 1  y 4  1  y 
2
Uncertainty is 1.7%. (y = Q /s)
E158 Steve Rock Nov 04
Running of the Weak Mixing Angle
7
E158 Steve Rock Nov 04
The Weak Mixing Angle
• General agreement between low Q2
experiments, although NuTeV is still
3 high compared to SM fit
• Stringent limits on new interactions at
multi-TeV scales
• Parameterize as limit on 4-fermion
contact term LL : 6-14 TeV limits for
E158 alone (95% C.L.)
• Limit on SO(10) Z' at 900 GeV
E158 Steve Rock Nov 04
Preliminary Results
APV (e-e- at Q2=0.026 GeV2) = 128  14 (stat)  12 (syst)
Significance of parity non-conservation in Møller scattering: 8 

sin2eff (Q2=0.026 GeV2) = 0.2403 ± 0.0010 (stat) ±0.0009 (syst)
Most precise measurement at low Q2
 Significance of running of sin2W: 7 

sin2WMS(MZ) = 0.2330 ± 0.0011 (stat) ±0.0010 (syst)

Standard Model pull: +1.2 
E158 Steve Rock Nov 04
Outlook
• Next set of precision measurements on the horizon

Neutrino-electron scattering
 Reactor experiments (in conjunction with 13): cross section
measurements to 0.7-1.3% would translate in (sin2W) down to
~0.001
 Ultimate measurements at the neutrino factory

Atomic parity violation
 Ratios of APV in isotopes and hydrogenic ions could reach sensitivity
of (sin2W) ~ 0.001

PV in electron scattering
 Active program planned for JLab: PV in elastic ep scattering (~2007),
Møller scattering, and DIS eD scattering (~2010) could reach below
(sin2W) ~ 0.001 per experiment

ee and ee at the Linear Collider
E158 Steve Rock Nov 04
Selected Future Measurements
sin2(W)
NuTev NeutrinoNucleon Scattering
168Yb
- 176Yb PNC
Isotopic Chain
SLAC E158
Møller Scattering
0.238
0.236
Linear Collider
In e+ e- and e- eModes
JLab Proton
Weak Charge
JLab DIS-parity
0.234
133Cs PNC
Single Isotope
0.232
LEP + SLAC
Measurements
At Z Pole
0.01GeV
0.1GeV
1GeV
10GeV
100GeV
1TeV
Q
E158 Steve Rock Nov 04
CONCLUSIONS
sin2W RUNS
• STANDARD MODEL STILL OK
• MANY MORE TESTS IN FUTURE
E158 Steve Rock Nov 04