# Presentation: 014173

## Deuteron Polarimetry

- for an EDM Search:
- Ideas and Concepts

- Ed Stephenson
- Indiana University Cyclotron Facility
- Bloomington, IN

- for the EDM/g-2 Workshop
- RHIC/AGS Users’ Meeting - 2006

- Other talks have discussed producing an EDM effect.
- Here I will discuss measuring that effect.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

- But spin precesses in plane due
- to magnetic moment in **B**-field.

**B**

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

- But spin precesses in plane due
- to magnetic moment in **B**-field.

**B**

**B**

**E**

- spin

- v

- At some later time, the
- spin is pointing backward.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

- But spin precesses in plane due
- to magnetic moment in **B**-field.

**B**

**B**

**E**

- spin

- v

- At some later time, the
- spin is pointing backward.

- During this part of the
- cycle, an EDM will
- precess the spin back
- into the plane.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

- But spin precesses in plane due
- to magnetic moment in **B**-field.

**B**

**B**

**E**

- spin

- v

- At some later time, the
- spin is pointing backward.

- During this part of the
- cycle, an EDM will
- precess the spin back
- into the plane.

- The EDM precession on these
- two parts of the cycle cancel,
- leaving no net effect from an EDM.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

**B**

**E**

- spin

- v

- During this part of the
- cycle, an EDM will
- precess the spin back
- into the plane.

- Add a _synchrotron oscillation_
- that is in phase with the in-plane
- spin precession.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

**B**

**E**

- spin

- v

- During this part of the
- cycle, an EDM will
- precess the spin back
- into the plane.

- Add a _synchrotron oscillation_
- that is in phase with the in-plane
- spin precession.

- This increases the velocity
- and precession here.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

**B**

**E**

- spin

- v

- During this part of the
- cycle, an EDM will
- precess the spin back
- into the plane.

- Add a _synchrotron oscillation_
- that is in phase with the in-plane
- spin precession.

- This increases the velocity
- and precession here.

- The spin starts
- higher here.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

**B**

**E**

- spin

- v

- During this part of the
- cycle, an EDM will
- precess the spin back
- into the plane.

- Add a _synchrotron oscillation_
- that is in phase with the in-plane
- spin precession.

- This increases the velocity
- and precession here.

- The spin starts
- higher here.

- But the velocity is now lower,
- so the EDM precession is less.

## What is the effect in a “resonant” storage ring?

**B**

**E**

- velocity

- spin

- Polarization is initially along the momentum direction.
**v** × **B** generates **E**-field in frame of particle.

- An EDM will precess the spin out of the orbit plane.

**B**

**E**

- spin

- v

- During this part of the
- cycle, an EDM will
- precess the spin back
- into the plane.

- Add a _synchrotron oscillation_
- that is in phase with the in-plane
- spin precession.

- This increases the velocity
- and precession here.

- The spin starts
- higher here.

- But the velocity is now lower,
- so the EDM precession is less.

- Now there is a net
- precession from the
- EDM on each cycle.

- Repeat 109 times and measure vertical polarization!

## How big is the effect?

- Suppose:

- For  d = 10–29 e·cm,

- ωEDM = 5.7 × 10–10 rad/s.

- average rate of rise is

## How big is the effect?

- Suppose:

- For  d = 10–29 e·cm,

- ωEDM = 5.7 × 10–10 rad/s.

- In-plane polarization is inherently unstable, so the polarization will decay
- with a characteristic lifetime τ (consistent with a Gaussian spread of spins).

- Time dependence
- of EDM signal

- p

- t

- τ

- pmax = 1.3 × 10-7

- Similar sensitivities are obtained
- in hadronic parity violation experiments.

- Do not extend store
-     much beyond τ.
- Fit shape to data.

- for p0 = 0.6
- and τ = 1000 s.

- average rate of rise is

## Polarimeter requirements:

- High efficiency
- High spin sensitivity
- Continuous measurement
- Vertical and in-plane components
- Bunch timing resolution (<<4 ns)

## Polarimeter requirements:

- High efficiency
- High spin sensitivity
- Continuous measurement
- Vertical and in-plane components
- Bunch timing resolution (<<4 ns)

- Best choice:

- deuteron scattering from
- a thick carbon target

- Forward angle elastic
- cross sections are large.

- Spin-orbit forces make
- substantial spin dependence.

## Polarimeter requirements:

- _Polarimeter requirements_:

- High efficiency
- High spin sensitivity
- Continuous measurement
- Vertical and in-plane components
- Bunch timing resolution (<<4 ns)

- Best choice:

- deuteron scattering from
- a thick carbon target

- Forward angle elastic
- cross sections are large.

- Spin-orbit forces make
- substantial spin dependence.

- _How does it work_?

- beam

- ●

- spin up

- target

- detectors:

- Left

- Right

- Relative rates (left/right)
- depend on degree of polarization.

- spin sensitivity

- θ

- Asymmetries:
-    L/R – EDM signal
-    D/U – g-2 precession

## Data from Saturne show a

- significant value of *iT**11**(**θ**)*
- at small laboratory angles.

- work
- here

- Bonin *et al.,* NIM **A288**, 389 (’90)

- The range of
- momenta covering
- p = 1.0 – 1.5 GeV/c
- is 250 – 526 MeV.

- Data across energies is used to
- optimize polarimeter performance.

- Points correspond to acceptance
- ranges of about 5°.

- number of
- deuterons used
- to measure
- polarization as
- a fraction of all
- deuterons in
- the beam

- best spot

- angle

- nuclear

- Coulomb

- useful for
- spin (17 mb)

- lost to ring
- acceptance
- (2 kb)

- cross
- section

- 40 MeV: 10-5
- 1 GeV: 6x10-4

- IDEA:
-  make thick target defining aperture
-  scatter into it with thin target

- D

- L

- U

- R

- R

- D

- Δ

- “extraction”
- target - gas

- “defining aperture”
- primary target

- detector
- system

- Target could be
- Ar gas (higher Z).

- Target “extracts” by
- Coulomb scattering
- deuterons onto thick
- main target.  There’s
- not enough good
- events here to
- warrant detectors.

- Events must imbed far
- enough from hole to
- not multiple scatter out
- of primary target, thus
- Δ << D.  Δ, which is a
- large fraction of the
- deuteron range, sets
- scale for polarimeter.

- Hole is large
- compared to
- beam.  Every-
- thing that goes
- through hole
- stays in the
- ring.  (It may
- take several
- orbits to stop
- scattered
- particle.)

- Detector is far enough
- away that doughnut
- illumination is not an
- acceptance issue:
- Δ < R.

- Primary target may
- need to be iris to
- allow adjustment of
- position and inner
- radius.  It may also
- need to be removed
- during injection.

- (POMME efficiency
- several percent)

- L, R, D, and U
- functional
- subdivisions

## Optimization of polarimeter performance

- Adjust target thickness to
- maximize useful rate without
- degrading performance.

- 1

- Adjust Fe absorber to
- remove breakup protons
- (no spin dependence)
- and leave elastic
- deuterons.

- 2

- Segment scintillator
- to yield two transverse
- asymmetries and
- check systematics.

- 3

- Sample spectra, 110 MeV, 27°

- DEUTERON

- PROTON

- detected particle energy  (MeV)

- iT11

- rates (50 elements) ~ 2e7 /s

## Statistical Precision

- estimated error in EDM precession

- NOTE:

- For

- e·cm

- rad/s

- Reaching the 1σ limit requires 1.7 years.

- Polarimeter properties

- efficiency

- target:  15 cm C at 1.7 g/cm3

- θ range = 3.5° – 8.5°

- s

- momentum

- GeV/c

- T

- Measurement time is polarization lifetime.
- Extraction rate is constant.

- Data acquisition time
- Nrep = 5.2 × 104

## Dealing with systematic errors

- The Toolbox:
-    spin reversal (at source, in different bunches)
-          combined with cross-ratio calculations
-    correct time dependence
-          depolarization confirmed from in-plane values

- _An illustration:_

- angle error

- position error

- θ

- θ

- both represented by θ

- Fix problem with spin-flip and cross ratio:

- Systematic effects come at higher order
- and constrain allowed size of θ.

- ~0.1

- ~ –0.07

- asymmetry
- ~ 0.01
- (residual py)

- requires θ < 0.02°
- difference + to –

- u = p+ + p–

## R&D Issues

- better elastic scattering data
-      Bonin data contains much proton contamination, iT11 too low
-      run at RIKEN/COSY and/or optical model analysis

- better model of polarimeter (Monte Carlo simulation)
-      explore target/absorber thickness
-      explore acceptance (statistics and systematics)
-      develop systematic error strategies

- develop suitable fast detectors

- test prototype for beam/polarimeter interactions