Lead (
208
Pb) Radius Experiment :
PREX
Elastic Scattering
Parity Violating Asymmetry
E = 1 GeV, θ = 5
electrons on lead
0
Spokespersons
•
Paul Souder
•
Krishna Kumar
•
Guido Urciuoli
•
Robert Michaels
208Pb
Run in March 2010 !
R. Michaels
PAVI 09
PREX
at
Idea behind
Z
0
PREX
of Weak Interaction :
Clean Probe Couples Mainly to Neutrons
( T.W. Donnelly, J. Dubach, I Sick )
In PWIA (to illustrate) :
⎛ dσ ⎞
⎛ dσ ⎞
⎜
⎟ −⎜
⎟
GF Q 2
⎝ dΩ ⎠ R ⎝ dΩ ⎠ L
=
A =
2πα 2
d
σ
d
σ
⎛
⎞
⎛
⎞
⎟ +⎜
⎜
⎟
⎝ dΩ ⎠ R ⎝ dΩ ⎠ L
F n (Q 2 )
⎡
⎤
2
−
−
1
4
sin
θ
⎢
W
⎥
FP (Q 2 ) ⎦
⎣
≈0
w/ Coulomb distortions (C. J. Horowitz) :
dA
= 3% →
A
R. Michaels
PAVI 09
dRn
d
= 1%
Rn
PREX
at
PREX
Physics
Output
Measured Asymmetry
Correct for Coulomb
Distortions
Weak Density at one Q 2
Mean Field
& Other
Models
Small Corrections for
Atomic
Parity
Violation
G
n
E
s
GE
MEC
2
Neutron Density at one Q
Assume Surface Thickness
Good to 25% (MFT)
Neutron
Stars
Slide adapted from
C. Horowitz
Rn
R. Michaels
PAVI 09
PREX
at
Fundamental Nuclear Physics
:
What is the size of a
nucleus ?
Neutrons are thought to determine
the size of heavy nuclei like 208Pb.
Can theory predict it ?
R. Michaels
PAVI 09
PREX
at
Reminder: Electromagnetic Scattering determines
ρ (r )
(charge distribution)
208
Pb
ρ (r )
dσ ⎛ mb
b⎞
⎜
⎟
dΩ ⎝ str ⎠
1
R. Michaels
PAVI 09
2
q
( fm )−1
3
PREX
at
0
Z of weak interaction : sees the
neutrons
Analysis is clean, like electromagnetic scattering:
1. Probes the entire nuclear volume
2. Perturbation theory applies
R. Michaels
PAVI 09
proton
t
neutron
t
Electric charge
1
0
Weak charge
0.08
1
PREX
at
Electron - Nucleus Potential
Vˆ (r ) = V (r ) + γ 5 A(r )
axial
electromagnetic
/
V (r ) = ∫ d r Z ρ (r ) | r − r |
3
208
/
/
A(r ) =
dσ
dσ
=
| FP (Q 2 ) | 2
dΩ dΩ Mott
FP (Q 2 ) =
1
4π
3
∫ d r j0 (qr ) ρ P (r )
2 2
[(1 − 4 sini
2
θ W ) Z ρ P (r ) − N ρ N (r )]
A ( r ) is small, best observed
by parity violation
Pb is spin 0
Proton form factor
GF
1 − 4 sin 2 θ W << 1 neutron weak
charge >> proton weak charge
Neutron form factor
FN (Q 2 ) =
1
4π
∫d
3
r j 0 (qr ) ρ N (r )
Parity Violating Asymmetry
⎛ dσ ⎞
⎛ dσ ⎞
⎜
⎟ −⎜
⎟
GF Q 2
⎝ dΩ ⎠ R ⎝ dΩ ⎠ L
=
A =
2πα 2
⎛ dσ ⎞
⎛ dσ ⎞
⎜
⎟ +⎜
⎟
⎝ dΩ ⎠ R ⎝ dΩ ⎠ L
R. Michaels
PAVI 09
⎡
FN (Q 2 ) ⎤
2
⎢ 1 − 4 sin θ W −
⎥
2
(
)
F
Q
P
⎣
⎦
≈0
PREX
at
PREX:
2
Measurement
easu e e t at one
o e Q iss sufficient
su c e t to measure
easu e R
N
0.3
Skyrme
covariant meson
covariant point coupling
0.28
Why only
Wh
l one
parameter ?
0.27
(next slide…)
2
Fn(Q )/N
/N
0.29
( R.J. Furnstahl )
0.26
0.25
proposed error *
5.6
5.65
rn in
R. Michaels
PAVI 09
5.7
5.75
5.8
208
Pb (fm)
* 2/3
this error if
100 uA, dPe/Pe = 1%
PREX
at
Slide adapted from J. Piekarewicz
Nuclear Structure: Neutron density is a fundamental
observable that remains elusive.
Reflects poor understanding of
symmetry energy of nuclear
matter = the energy cost of N ≠ Z
E (n, x) = E (n, x = 1 / 2) + Sυ (n) (1 − 2 x 2 )
n=
x=
n.m. density
ratio
proton/neutrons
• Slope unconstrained by data
208
• Adding R N from
Pb
will eliminate the
dispersion in plot.
R. Michaels
PAVI 09
PREX
at
Thanks, Alex Brown
Skx-s15
PREX Workshop 2008
E/N
ρN
R. Michaels
PAVI 09
PREX
at
Thanks, Alex Brown
PREX Workshop 2008
R. Michaels
PAVI 09
Skx-s20
PREX
at
Thanks, Alex Brown
PREX Workshop 2008
R. Michaels
PAVI 09
Skx-s25
PREX
at
Interpretation
p
of
PREX
Acceptance
R. Michaels
PAVI 09
PREX
at
Application: Atomic Parity Violation
2
• Low Q test of Standard Model
• Needs RN
H PNC ≈
[− N
∫
2
GF
2
Isotope Chain Experiments
e.g. Berkeley Yb
(or APV measures RN )
ρ N (r ) + Z (1 − 4 sin 2 θ W ) ρ P (r )] ψ e/ γ 5 ψ e d 3 r
r
r
≈0
APV
R. Michaels
PAVI 09
PREX
at
Application :
Neutron
Stars
What is the nature
of extremely dense
matter ?
Do collapsed stars form
“exotic” phases of
matter ? ((strange
g stars,,
quark stars)
Crab Nebula
R. Michaels
PAVI 09
(X-ray, visible, radio, infrared)
PREX
at
Inputs:
Eq. of state (EOS)
P( ρ )
PREX helps
h l h
here
Hydrostatics (Gen. Rel.)
Astrophysics Observations
Luminosity L
Temp. T
Mass M from pulsar timing
L = 4πσ B R 2 T 4
(with corrections … )
Mass - Radius
di
relationship
l i
hi
Fig from: Dany Page.
J.M. Lattimer & M. Prakash, Science 304 (2004) 536.
R. Michaels
PAVI 09
PREX
at
PREX
&
Neutron Stars
( C.J. Horowitz, J. Piekarewicz )
R N calibrates EOS of
Neutron Rich Matter
Crust Thickness
Explain Glitches in Pulsar Frequency ?
Combine PREX R N with
Obs. Neutron Star Radii
Phase Transition
Ph
T
iti
tto “E
“Exotic”
ti ” C
Core ?
Strange star ? Quark Star ?
Some Neutron Stars
seem too Cold
Cooling by neutrino emission (URCA)
Crab Pulsar
R. Michaels
PAVI 09
Rn − R p > 0.2 fm
URCA probable, else not
PREX
at
PREX Design
Spectometers
Lead Foil
Target
Pol. Source
Hall A
CEBAF
R. Michaels
PAVI 09
PREX
at
Hall A at Jefferson Lab
Polarized eSource
R. Michaels
PAVI 09
Hall A
PREX
at
High Resolution Spectrometers
Spectrometer Concept:
Resolve Elastic
1st excited state
Pb
2.6 MeV
Elastic
detector
Inelastic
Quad
Left-Right symmetry to
control transverse
polarization systematic
target
Dipole
Q Q
R. Michaels
PAVI 09
PREX
at
50 Septum magnet augments the
High Resolution Spectrometers
HRS-L
Increased Figure of Merit
HRS-R
collimator
collimator
target
L / R HRS control
vertical A_T.
What about horizontal ?
R. Michaels
PAVI 09
PREX
at
Collimator at entrance to spectrometer
Æ Suppressing A_T systematics
Paul Souder
A T hole
A_T
Be degrader
Aligned in
spectrometers to
define identical
Left / Right
scattering angles
as well as good
up / down
symmetry
Insertable blocker
to block Be
R. Michaels
PAVI 09
PREX
at
Events from A_T hole (Be plug)
Main detector
A_T detector
Measures
horizontal A_T
systematic.
(Vertical is
measured from
Left/Right
spectrometers)
Thanks:
Dustin McNulty
Krishna Kumar
P lS
Paul
Souder
d
R. Michaels
PAVI 09
PREX
at
Measure θ from Nuclear Recoil
δE=Energy loss
E B
E=Beam
energy
MA=Nuclear mass
θ=Scattering angle
δE θ
2
E
=
E 2 MA
Scattered Electron Energy (GeV)
Recoil is large for H, small for nuclei
(3X better accuracy than survey)
R. Michaels
PAVI 09
PREX
at
Important Systematic :
PITA
Effect
Polarization Induced Transport Asymmetry
Intensityy Asymmetry
y
y AI = ε Δ sin((θ )
Tx − Ty
where ε =
Tx + Ty
Transport Asymmetry
Asymmetric
Transport System
y'
45o
x
Fast/
Slow
Axes
x'
θ
Δ drifts, but slope is
z
R. Michaels
PAVI 09
Initial Linear
Polarization
y
Pockels Cell
(Imperfect λ/4 Plate)
Polarization
Ellipses
Δ=0
R
L
Laser at
Pol. Source
~ stable.
Feedback on Δ
See talk by
Gordon Cates
PREX
at
(NEW for PREX)
Double Wien Filter
Crossed E & B fields to rotate the spin
• Two Wien Spin Manipulators in series
• Solenoid rotates spin +/‐90 degrees (spin rotation as B but focus as B2). Flips spin without moving the beam !
Flips spin without moving the beam !
Electron
Beam
SPIN
R. Michaels
PAVI 09
See talk by
Riad Suleiman
PREX
at
Beam Asymmetries
Araw = Adet - AQ + αΔ
ΔE+ ΣβiΔx
Δ i
p from
Slopes
R. Michaels
PAVI 09
•natural beam jitter (regression)
•beam modulation (dithering)
PREX
at
The Corrections Work !
X Angle BPM
ppm
With corrections
micro
on
Heelicity-corr.. Position diff
Shown : period
Sh
i d off data
d t d
during
i
HAPPEX (4He)
H ) when
h
b
beam h
had
d a
helicity-correlated position due to a mistake * in electronics.
Helicity signal to
driver reversed
Helicity signal to
driver removed
R
Raw
ALL A
Asymetry
t
* The mistake: Helicity signal deflecting the beam through electronics “pickup”
pickup
R. Michaels
PAVI 09
PREX
at
Final Beam Position Corrections (HAPPEX-H)
X Angle BPM
Beam Asymmetry Results
micro
on
Energy: -0.25 ppb
X Target: 1 nm
X Angle: 2 nm
Y Target : 1 nm
Y Angle: <1 nm
Corrected and Raw, Left spectrometer
arm alone, Superimposed!
ppm
Total correction for beam position
asymmetry on Left, Right, or ALL
detector: 10 ppb
Spectacular results
from HAPPEX-H show
we can do PREX.
R. Michaels
PAVI 09
PREX
at
Redundant position measurements at the ~1 nm level
(i) Stripline monitors (2 pairs of wires)
(ii) Resonant microwave cavities
Helicity Correlated Position Differences -avity Diff (nm)
X Cav
nm
nm
60
Y (cavity)
X (cavity))
40
20
0
-20
m)
Y Cavity Diff (nm
(Helicity – correlated differences averaged over ~1 day)
80
80
60
40
20
0
-20
-40
-40
-60
-60
-80
-80
-80 -60 -40 -20 0 20 40 60 80
X Stripline Diff (nm)
X (stripline)
R. Michaels
PAVI 09
nm
HAPPEX 2005
-80 -60 -40 -20 0 20 40 60 80
Y Stripline Diff (nm)
Y (stripline)
PREX
at
nm
PREX Integrating Detectors
UMass / Smith
DETECTORS
R. Michaels
PAVI 09
PREX
at
Lead Target
g
208
Pb
Successfully tested at 100 μA !! (2 x I in proposal)
Liquid Helium
Coolant
12
beam
C
Diamond Backing:
• High Thermal Conductivity
• Negligible Systematics
R. Michaels
PAVI 09
PREX
at
Target Assembly
R. Michaels
PAVI 09
PREX
at
Momentum of Electron Scattering from Lead
6000
208
Num
m. events
5000
4000
Lead Target Tests
Elastic
Pb Elastic
Low
Detector
Rate
Detector
at
3000
2000
E = 1.1 GeV
θ = 60
First
excited stateState
1st Excited
(~0.1% rate)
(2.6 MeV)
2.6 MeV
1000
0
-30
-25
-20
X-Y Tracks for Lead
-15
0.1
0.05
Num. events
N
R. Michaels
PAVI 09
-5
0
5
MeV
10
Momentum (MeV)
σA ∝ 1
4000
3500
3000
2500
2000
1500
1000
500
0
0.2
0.15
-10
-0
-0.05
-0.1
-0.15
-0.2 -1
•
Check rates
•
Backgrounds (HRS is clean)
•
Sensitivity to beam
parameters
•
Width of asymmetry
I
-0.8
-0.6
-0.4
-0.2
-0
0.2
σA ∝ 1
•
HRS resolution
•
Detector resolution
0.4
PREX
at
I
Noise
•
•
•
.
(integrating at 30 Hz)
PREX: ~120 ppm
Want onlyy counting
g
statistics noise, all
others << 120 ppm
New 18-bit ADCs
Æ improve
p
beam noise.
Careful about cable runs,
PMTs, grounds loops.
Test:
(HAPPEX data)
Use the “Luminosity Monitor” to demonstrate noise
(next slide)
R. Michaels
PAVI 09
PREX
at
Luminosity Monitor
A source of
extremelyy high
g
rate
Æ Established
noise floor of
50 ppm
R. Michaels
PAVI 09
PREX
at
PREX : Summary
• Fundamental Nuclear Physics with
many applications
• HAPPEX & test runs have
demonstrated technical aspects
• Polarimetry Upgrade critical
• 2 month run starting March 2010
R. Michaels
PAVI 09
PREX
at
Extra Slides
R. Michaels
PAVI 09
PREX
at
“What
What if ’’ Scenarios
Assuming other systematics are negligible
50 uA
30 days
dRN/RN
Æ
100 uA
60 days
dRN/RN
R. Michaels
PAVI 09
-Æ
dPe/Pe
= 1%
dPe/Pe
= 2%
1%
12 %
1.2
0.6 %
0.8 %
PREX
at
Optimum Kinematics for Lead Parity:
<A> = 0
0.5
5 ppm
ppm.
E = 1 GeV if
Accuracy in Asy 3%
Fig. of merit
Min. error in R n
maximize:
1 month run
1% in R
n
(2 months x
100 uA
Æ 0.5% if no
y
)
systematics)
R. Michaels
PAVI 09
PREX
at
Polarimetry Accuracy :
1% from 2 methods
Hydrogen:
y
g
86.7% ± 2%
Møller
(New High-field design )
Compton
e−γ
Helium: 84.0% ± 2.5%
HAPPEX
Compton
P l i
Polarimety
Measuremens
R. Michaels
PAVI 09
PREX
at
(slide from C. Horowitz)
Pb Radius vs Neutron Star Radius
• The 208Pb radius constrains the pressure of neutron
matter at subnuclear densities
densities.
• The NS radius depends on the pressure at nuclear
density and above.
• Most
M t interested
i t
t d in
i density
d
it d
dependence
d
off equation
ti off
state (EOS) from a possible phase transition.
p
to have both low density
y and high
g density
y
• Important
measurements to constrain density dependence of EOS.
– If Pb radius is relatively large: EOS at low density is stiff with
high P. If NS radius is small than high density EOS soft.
– This softening of EOS with density could strongly suggest a
transition to an exotic high density phase such as quark matter,
strange matter, color superconductor, kaon condensate…
R. Michaels
PAVI 09
PREX
at
Asymmetries in Lumi
Monitors
after beam noise subtraction
~ 50 ppm noise per pulse
Æ milestone for
electronics
( need << 120 ppm)
Jan
2008
D t
Data
R. Michaels
PAVI 09
PREX
at
Neutron Star Crust vs
Pb Neutron
N t
Skin
Ski
Liquid/Solid Transition Density
C.J. Horowitz, J. Piekarawicz
Liquid
q
FP
Neutron
Star
•
•
R. Michaels
PAVI 09
208Pb
b
Solid
TM1
Thicker neutron skin in Pb means energy rises
rapidly with density Æ Quickly favors uniform phase.
Thick skin in Pb Æ low transition density in star.
PREX
at
PREX: pins down the symmetry energy
E
⎛ N −Z ⎞
≈ − av + a4 ⎜
⎟
A
A
⎝
⎠
( R.J. Furnstahl )
2
+ as / A
1/ 3
+ ...
(1 parameter)
energy cost for unequal #
protons & neutrons
PREX
error
bar
(1σ )
208
Actually, it’s the
density dependence of
a4 that we pin down.
Pb
PREX
R. Michaels
PAVI 09
PREX
at
(slide from C. Horowitz)
PREX Constrains Rapid
p Direct
URCA Cooling of Neutron Stars
•
•
•
•
•
Proton fraction Yp for matter in
beta equilibrium depends on
symmetry energy S(n).
Rn in Pb determines density
dependence of S(n).
The larger Rn in Pb the lower
the threshold mass for direct
URCA cooling.
If Rn-Rp<0.2 fm all EOS models
do not have direct URCA in
1 4 M¯ stars.
1.4
stars
If Rn-Rp>0.25 fm all models do
have URCA in 1.4 M¯ stars.
R. Michaels
PAVI 09
Rn-Rp in 208Pb
If Yp > red line NS cools quickly via
direct URCA reaction n p+e+ν
p+e+
PREX
at
How to Measure
Neutron Distributions, Symmetry Energy
•
•
•
•
•
Proton-Nucleus Elastic
Pi
Pion,
alpha,
l h d S
Scattering
i
Pion Photoproduction
Heavy ion collisions
Rare Isotopes (dripline)
(d l )
•
Magnetic scattering
•
PREX
•
Theory
R. Michaels
PAVI 09
Involve strong probes
Most spins couple to zero.
(weak interaction)
MFT fit mostly by data other
than neutron densities
PREX
at
Hall A
Cherenkov
cones
PMT
Polarimeters
Compton
Moller
Target
R. Michaels
PAVI 09
Spectro: SQQDQ
PREX
at
Heavy Ions
((adapted
p
from Bettyy Tsang,
g, PREX Workshop)
p)
R. Michaels
PAVI 09
Isospin Diffusion (NSCL)
Probe the symmetry
energy in 124Sn + 112Sn
PREX
at
At 50 the new Optimal FOM is at 1.05 GeV (+/- 0.05)
(when accounting for collimating small angle, not shown)
1% @ ~1 GeV
R. Michaels
PAVI 09
PREX
at
Corrections to the Asymmetry are
Mostly Negligible
• Coulomb Distortions ~20% = the biggest correction.
• Transverse Asymmetry (to be measured)
• Strangeness
• Electric Form Factor of Neutron
• Parity Admixtures
• Dispersion Corrections
• Meson Exchange Currents
• Shape Dependence
Horowitz, et.al. PRC 63 025501
• Isospin Corrections
• Radiative Corrections
• Excited States
• Target Impurities
R. Michaels
PAVI 09
PREX
at
Successful Results of beam tests Jan 2008
Good energy resolution
R. Michaels
PAVI 09
⎛ ΔE ⎞
1+ ⎜
⎟
⎝ E ⎠
σ = σ0
PREX
at
2
Intensity
y Feedback
Adjustments
for small phase shifts
to make close to
circular polarization
HAPPEX
Low jitter and high accuracy allows sub-ppm
cumulative charge asymmetry in ~ 1 hour
~ 2 hours
R. Michaels
PAVI 09
In practice, aim for 0.1 ppm over
duration of data-taking.
PREX
at
Optimization for Barium -- of possible direct use for Atomic PV
Ba
Cross Section
at E=1.0 GeV
Asymmetry
A (ppm)
dσ/dΩ (mbarn)
138
q (fm -1)
ε = dA/A
q (fm -1)
Sensitivity
to R_n
FOM x ε2
1 GeV
G V optimum
i
6
Θ
R. Michaels
PAVI 09
q (fm -1)
10
1
V)
e
G
(
E
PREX
at
0.5
Warm Septum
p
Existing superconducting septum won’t work at high L
Warm low energy
gy (1 GeV) magnet
g
designed.
g
Grant proposal in preparation (~100 k$) [Syracuse / Smith College]
Delta = 0.0035 (3 MeV / 850 MeV)
Delta = 0 (Elastic)
0.03
Transverse Direc
rection (m)
0.03
TOSCA design
0.0
P resolution ok
−0.03
−0.03
0.04
R. Michaels
PAVI 09
0.02
0.0
Dispersive Direction (Meters)
PREX
at