robert michaels prex at trento prex workshop 09 physics interpretation of prex 208 pb e = 1 gev,...

Trento PREX Workshop 09

Robert MichaelsPREX at

Physics Interpretation of PREX

208Pb

E = 1 GeV,

electrons on lead

05Elastic Scattering

Parity Violating Asymmetry

• Physics Analysis

• Can one Q2 determine RN ?

• Follow-up measurements

other Q2 , other nuclei

• Theory Questions

Trento PREX Workshop 09

Robert MichaelsPREX at

neutron weak charge >> proton weak charge

is small, best observed by parity violation

)()()(ˆ 5 rArVrV

||)()(/

//3 rrrZrdrV )()()sin41(22

)( 2 rNrZG

rA NPWF

22 |)(| QFd

d

d

dP

Mott

)()(4

1)( 0

32 rqrjrdQF PP )()(

4

1)( 0

32 rqrjrdQF NN

)(

)(sin41

22 2

22

2

QF

QFQG

d

d

d

d

d

d

d

d

AP

NW

F

LR

LR

Electron - Nucleus Potential

electromagnetic axial

Neutron form factor

Parity Violating Asymmetry

)(rA

1sin41 2 W

Proton form factor

0

Pb is spin 0208

Trento PREX Workshop 09

Robert MichaelsPREX at

Measured Asymmetry

Weak Density at one Q2

Neutron Density at one Q2

Correct for CoulombDistortions

Small Corrections forG

nE G

sE MEC

Assume Surface Thickness Good to 25% (MFT)

Atomic Parity Violation

Mean Field & Other

Models

Neutron

Stars

R n

PREX Physics Analysis

from C.J. Horowitz

Trento PREX Workshop 09

Robert MichaelsPREX at

str

mb

d

d

1fmq

Reminder: Electromagnetic Scattering determines

r

r

Pb208

(charge distribution)

1 2 3

Trento PREX Workshop 09

Robert MichaelsPREX at

( R.J. Furnstahl )

Measurement at one Q is sufficient to measure R

2

N

proposed error *

Why only one parameter ?

(next slide…)

PREX:

* 2/3 this error if 100 uA, dPe/Pe = 1%

Trento PREX Workshop 09

Robert MichaelsPREX at

PREX: pins down the symmetry energy (1 parameter)

( R.J. Furnstahl )

energy cost for unequal # protons & neutrons.../ 3/1

2

4

AaA

ZNaa

A

Esv

PREX

Pb208

)1(

Actually, it’s the density dependence of a4 that we pin down.

Trento PREX Workshop 09

Robert MichaelsPREX at

Skx-s15Thanks, Alex Brown

PREX Workshop 2008

E/N

N

Trento PREX Workshop 09

Robert MichaelsPREX at

Skx-s20Thanks, Alex Brown

PREX Workshop 2008

Trento PREX Workshop 09

Robert MichaelsPREX at

Skx-s25Thanks, Alex Brown

PREX Workshop 2008

Trento PREX Workshop 09

Robert MichaelsPREX at

Relationship of Measured Asymmetry to Theory

),(

),(

dd

d

Add

dA

physics

measured

dd

),(

theoryA

Differential Cross Section

Acceptance Function will be measured, presently simulated

Theoretical Asymmetry

PREX Expt provides these

to be compared

Trento PREX Workshop 09

Robert MichaelsPREX at

Simulated AcceptanceIt will also be measured !

(integrated over azimuth)

Trento PREX Workshop 09

Robert MichaelsPREX at

Acceptance

Examples of Theoretical Models Calculations by C. J. Horowitz

Trento PREX Workshop 09

Robert MichaelsPREX at

Simulation of Observed Asymmetry for various Models

Thanks, C.J. Horowitz

Trento PREX Workshop 09

Robert MichaelsPREX at

Application: Atomic Parity Violation• Low Q test of Standard Model

• Needs RN (or APV measures RN )

2

rdrZrNG

H eePWNF

PNC35/2 )()sin41()(

22

0

Isotope Chain Experiments e.g. Berkeley Yb

• Shape dependence enters APV similarly to PVES.

• Nearly a direct application.

(lucky accident of PVES kinematics)

Analysis by Steve Pollock PRC 63, 025501 (2001).

Trento PREX Workshop 09

Robert MichaelsPREX at

Theory Questions : Corrections to the Asymmetry

• Coulomb Distortions ~20% = the biggest correction. Under control

• Transverse Asymmetry (to be measured)

• Two – photon exchange effects --

including Dispersion Corrections (intermediate excited state)

• Strangeness

• Electric Form Factor of Neutron

• Parity Admixtures

• Meson Exchange Currents

• Shape Dependence

• Isospin Corrections

• Radiative Corrections

• Excited States

• Target Impurities

Horowitz, et.al. PRC 63

025501

How well do we really know these ?

Trento PREX Workshop 09

Robert MichaelsPREX at

Optimum Kinematics for Lead Parity: E = 1 GeV if <A> = 0.5 ppm. Accuracy in Asy 3%

n

Fig. of merit

Min. error in R

maximize:

1 month run

1% in R

n

(2 months x 100 uA 0.5% if no systematics)

5

Trento PREX Workshop 09

Robert MichaelsPREX at

Fine-Tuning: At 50 the Optimal FOM is at 1.05 GeV (+/- 0.05)

1% @ ~1 GeV

Trento PREX Workshop 09

Robert MichaelsPREX at

Optimization for Barium -- of possible direct use for Atomic PV

1 GeV optimum

Trento PREX Workshop 09

Robert MichaelsPREX at

Higher Q2 Point ? ( e.g. E = 1.3 GeV, 80, q = 0.92 fm-1 )

5

Here ?

For Lead

Trento PREX Workshop 09

Robert MichaelsPREX at

Time to make measurements

IPT

2

7days

strAIP 007.0~,50~,85.0~ JLab Spectrometers (2 HRS)

For PREX (optimal) 1% in RN

Higher Q2 point ( E = 1.3 GeV, q = 0.92 fm-1 ) 2% in RN

IPT

2

19days

Trento PREX Workshop 09

Robert MichaelsPREX at

Estimates for Other Nuclei: 48Ca 120sn

• Forward angle use 50 septum

• Want thick target 10% X0 = practical maxbt

E

Radiative losses estimated ~ ~ 0.4 - 0.5

48Ca 1.6 10.2 6.6

120Sn 6 9.1 1.6

208Pb 11.4 6.3 0.5

3cm

g20 cm

gX Tlen (mm)

Trento PREX Workshop 09

Robert MichaelsPREX at

48Ca 120sn

48Ca 1.7 2.0 3.4 % 25 3.5

120Sn 1.2 1.0 2.9 % 125 2.6

22 ARFOM

E (GeV)

max

Appm

Sensitivity to RN

Rate(MHz / arm)

Each a 2 month run

% Error

A

dA

These should match

for 1% in RN

For effectively 1% in RN

Trento PREX Workshop 09

Robert MichaelsPREX at

PREX : Summary of Future Options

• Do PREX better RN to ~ 0.6 % ?!

• Higher Q2 point 208Pb -- marginal

• 138 Ba

• 48 Ca

• 120 Sn

~ 2 month beam (each)

Thanks:

C. J. Horowitz, P. Souder, K. Kumar