1. New Results from the HAPPEx Experiments at Q2= 0.1 GeV/c2
nucl-ex /
submitted to PRL
Robert Michaels
For the HAPPEX Collaboration
Thomas Jefferson National Accelerator Facility – Argonne National Laboratory – CSU, Los Angeles -William and Mary – Duke – DSM/DAPNIA/SPhN CEA Saclay - FIU – Harvard - INFN, Rome - INFN, Bari – IAE, Beijing – IPT Kharkov - Jozef Stefan Institute –
Kent State - MIT – NPIRAS, St. Petersburg – ODU – Rutgers - Smith College –
Syracuse – Temple – U. Blaise Pascal – U. of Illinois Urbana-Champagne –
UMass, Amherst – U. of Kentucky – U. of Virginia – UST, Heifei

2. Outline Parity-violation in electron scattering
Elastic Vector Strange Form Factors: GsE and GsM
Q2 = 0.1 (GeV/c)2 as/of early 2005
Results from 2005 data taking of HAPPEx-II:
HAPPEx-hydrogen and HAPPEx-Helium
The present situation at Q2 = 0.1 (GeV/c)2
Implications and Conclusions

3. Strangeness in the nucleon
Nucleon in QCD
« sea »
s quark: cleanest candidate to study the sea )
How much do virtual pairs contribute
to the structure of the nucleon ?
Momentum : 4 % (DIS)
Spin : 0 to -10% (polarized DIS)
Mass : 0 to 30 % (N -sigma term)
(large uncertainties on these contributions)
Goal: Determine the contributions of the strange quark sea ( ) to the charge and current/spin distributions in the nucleon :
“strange form factors” GsE and GsM

4. Parity Violating Electron Scattering  Weak NC Amplitudes
Interference:  ~ |MEM |2 + |MNC |2 + 2Re(MEM*)MNC
Interference with EM amplitude makes Neutral Current (NC) amplitude accessible
Tiny (~10-6) cross section asymmetry isolates weak interaction

5. Form Factors Adopt the Sachs FF:
(Roughly: Fourier transforms of charge and magnetization)
NC probes same hadronic flavor structure, with different couplings:
GZE/M provide an important new benchmark for testing
non-perturbative QCD structure of the nucleon

6. Charge Symmetry Gg,pE,M GsE,M GuE,M GdE,M Gg,nE,M GZ,pE,M GnE,M GpE,M
One expects the neutron to be an isospin rotation of the proton :
Gg,pE,M
GsE,M
GuE,M
GdE,M
Gg,nE,M
Charge symmetry
GZ,pE,M
<N| sgm s |N>
GnE,M
GpE,M
Shuffle
Well Measured
New : CSV could be as large as our stat. error: Kubis & Lewis PRC 74 (015204) 2006.

7. Isolating the form factors: vary the kinematics or target
For a proton:
~ few parts per million
Forward angle
Backward angle
For 4He: GEs alone
For deuterium:
enhanced GAe sensitivity

8. Theoretical Approaches to Strange Form Factors
Models - a non-exhaustive list:
kaon loops, vector dominance, Skyrme model, chiral quark model, dispersion relations, NJL model, quark-meson coupling model, chiral bag model, HBChPT, chiral hyperbag, QCD equalities, …
- no consensus on magnitudes or even signs of GsE and GsM !
a challenging problem in non-perturbative QCD
QCD on the lattice
- Dong, Liu, Williams PRD 58(1998)074504
- Lewis, Wilcox, Woloshyn PRD 67(2003)013003
- Leinweber, et al PRL 94(2005) and PRL 97(2006)

9. Strangeness Models (as/of 2000)
Leading moments of form factors:
s = GMs (Q2=0)
s = GEs/ (Q2=0)

10. World Data (early 2005) at Q2 ~ 0.1 GeV2
Note : SAMPLE result adopts
Zhu et al. calculation of GAe
PRD 62(2000)033008
GEs = ± 0.29
GMs = 0.62 ± 0.32 .
Would imply that 5-10% of nucleon magnetic moment is Strange
Caution: the combined fit is approximate. Correlated errors and assumptions not taken into account

11. Measurement of P-V Asymmetries
5% Statistical Precision on 1 ppm
-> requires 4x1014 counts
Rapid Helicity Flip: Measure the asymmetry at 10-4 level, 10 million times
High luminosity: thick targets, high beam current
Control noise (target, electronics)
High beam polarization and rapid flip
A (ppm)
Statistics: high rate, low noise
Systematics: beam asymmetries, backgrounds, Helicity correlated DAQ
Normalization: Polarization, Linearity, Dilution

12. HAPPEX (second generation)
E=3 GeV q=6° Q2= 0.1 (GeV/c)2
New 2005 results:
nucl-ex/
Submitted to PRL
Hydrogen : GsE + a GsM
4He: Pure GsE :

13. Hall A at Jefferson Lab
Polarized e-
Source
Hall A

14. High Resolution Spectrometer
Hall A at Jefferson Lab
Compton
1% syst
Continuous
Møller
2-3% syst
Polarimeters
Target
400 W transverse flow
20 cm, LH2
20 cm, 200 psi 4He
High Resolution Spectrometer
+ septum 5 mstr over 4o-8o

15. Summary of Data Runs: HAPPEX-II
June 2004
HAPPEX-He
about 3M pairs at 1300 ppm
=> dAstat ~ 0.74 ppm
June – July 2004
HAPPEX-H
about 9M pairs at 620 ppm
=> dAstat ~ 0.2 ppm
July-Sept 2005
about 35M pairs at 1130 ppm
=> dAstat ~ 0.19 ppm
Oct – Nov 2005
about 25M pairs at 540 ppm
=> dAstat ~ ppm
This talk

16. elastic events by HRS optics
High Resolution Spectrometers
Clean separation of
elastic events by HRS optics
Locate detector over elastic line
and integrate the flux 
Detector
Elastic Rate:
1H: 120 MHz
4He: 12 MHz
Detector
Cherenkov
cones
PMT
12 m dispersion
sweeps away
inelastic events
Brass-Quartz Integrating Cerenkov Shower Calorimeter
Large dispersion & heavy shielding reduce backgrounds at focal plane

17. Backgrounds Aluminum endcaps Inelastics Aluminum target windows
Shown is the single-particle momentum spectra.
Detector Footprint
Inelastics
Aluminum target windows
Inelastics and re-scattering
Poletip (negligible)
Aluminum endcaps
Detector Footprint

18. Correcting Beam Asymmetries
Araw = Adet - AQ + i=1,5ixi
natural beam jitter (regression)
beam modulation (dithering)
Slopes from
Independent methods provide a cross-check.
Each is subject to different systematic errors.
Regression:
Natural beam motion, measure dA/dDxi
Simultaneous fit establishes independent sensitivities
By definition, removes correlation of asymmetry to beam monitors
Sensitive to highly correlated beam motion and electronics noise
“Dithering”:
Induce non-HC beam motion with coils, measure dS/dCi, dxi/dCi
Relate slopes to dS/dxi
Not compromised by correlated beam motion
Robust, clear signals for failures
Sensitive to non-linearities

19. Beam Position Differences, Helium
Position difference goal: 3 nanometers!
All’s well that ends well
Problem clearly identified as beam steering from electronic cross-talk
No helicity-correlated electronics noise in Hall DAQ at < ppb level
Large position differences cancel in average over both detectors
X Angle BPM
micron
Helicity signal to driver removed
Raw ALL Asymetry
ppm
Helicity signal to driver reversed
Problem: Helicity signal deflecting the beam through electronics “pickup”
Large beam deflections even when Pockels cell is off

20. Beam Position Corrections, Helium
Raw Left Asymmetry
Corrected Left Asymmetry
Beam Asymmetries
Energy: -3ppb
X Target: -5 nm
X Angle: -28 nm
Y Target :-21 nm
Y Angle: 1 nm
ppm
ppm
Raw Right Asymmetry
Corrected Right Asymmetry
Total Corrections:
Left: -370 ppb
Right: 80 ppb
All: 120 ppb
ppm
ppm

21. Beam Position Corrections, Hydrogen
X Angle BPM
Surpassed Beam Asymmetry Goals for Hydrogen Run
Energy: ppb
X Target: 1 nm
X Angle: 2 nm
Y Target : 1 nm
Y Angle: <1 nm
micron
Corrected and Raw, Left arm alone,
Superimposed!
ppm
Total correction for beam position asymmetry on Left, Right, or ALL detector: 10 ppb

22. Araw = 6.40 ppm  0.23 (stat)  0.12 (syst)
4He Results
Slug
Asymmetry (ppm)
Raw Parity Violating Asymmetry
Araw correction ~ 0.3 ppm
Helicity Window Pair Asymmetry
Q2 = ± GeV2
Araw = 6.40 ppm  (stat)  0.12 (syst)

23. Araw = -1.58 ppm  0.12 (stat)  0.04 (syst)
Asymmetry (ppm)
Slug
1H Results
Raw Parity Violating Asymmetry
Araw correction ~3 ppb
Helicity Window Pair Asymmetry
Q2 = ± GeV2
Araw = ppm  (stat)  0.04 (syst)

24. Compton Polarimetry Hydrogen: 87.1 ± 0.9 % Continuous, non-invasive
Here : Electron Detector analysis
Cross-checked with Møller, Mott polarimeters
also: independent electron analysis
Helium: ± 0.8 %
Helium ran with lower beam energy, making the analysis significantly more challenging.
Breakthroughs in both photon and electron analyses obtained 1% systematic uncertainty

25. Miscellany Backgrounds: Dilutions: 2 % (4He) 0.8% (1H)
Systematic ppb (4He) ppb (1H)
Q2 & effective kinematics: Q2 < 1.0%
Two-photon exchange corrections:
small (no explicit correction made)
Transverse asymmetry:
measured directly in dedicated runs, cancels in left-right sum;
Systematic: 4 ppb (1H) 8 ppb (4He)
Electromagnetic Form Factors: use Friedrich & Walcher parameterization, Eur. Phys. J. A, 17, 607 (2003), and BLAST data for GEn
Axial Form Factor: highly suppressed for 1H (not present for 4He)
Vector Electroweak Radiative Corrections: Particle Data Group
Blinded Analysis

26. 4He: Nuclear Effects O+  O+ T=0 transition
Any one-body electroweak operator O: (eg Fetter and Walecka)
<J,T|O|J,T> =  J,T (,’) <’|O|> |> = complete set
one-body density matrix element single-particle matrix element
(nuclear structure) (nucleon structure)
Asymmetry involves ratio of weak/EM matrix elements (GEs and GET=0);
Single term in J,T in transition; O same in weak and EM except for couplings
 same one-body density matrix elements in numerator/denominator
 nuclear structure cancels, only nucleon form factors remain
This result is EXACT, if :
4He g.s. pure isospin state: Ramavataram, Hadjimichael, Donnelly PRC 50(1994)1174
No D-state admixture: Musolf & Donnelly PL B318(1993)263
Meson exchange corrections small: Musolf, Schiavilla, Donnelly PRC 50(1994)2173
Nuclear effects all << 1%, no explicit correction made.

27. Error Budget-Hydrogen
HAPPEx
Error Budget-Helium
2005 (this report)
2004 run
False Asymmetries
59 ppb
Polarization
51 ppb
Linearity
58 ppb
Radiative Corrections
6 ppb
Q2 Uncertainty
Al background
32 ppb
Helium quasi-elastic background
20 ppb
Total
120 ppb
False Asymmetries
103 ppb
Polarization
115 ppb
Linearity
78 ppb
Radiative Corrections
7 ppb
Q2 Uncertainty
66 ppb
Al background
14 ppb
Helium quasi-elastic background
86 ppb
Total
205 ppb
Error Budget-Hydrogen
2005 (this report)
2004 run
False Asymmetries
17 ppb
Polarization
14 ppb
Linearity
15 ppb
Radiative Corrections
3 ppb
Q2 Uncertainty
16 ppb
Al background
19 ppb
Rescattering Background
4 ppb
Total
37 ppb
False Asymmetries
43 ppb
Polarization
23 ppb
Linearity
15 ppb
Radiative Corrections
7 ppb
Q2 Uncertainty
12 ppb
Al background
16 ppb
Rescattering Background
32 ppb
Total
63 ppb

28. HAPPEX-II 2005 Results HAPPEX-4He:
Q2 = ± (GeV/c)2
APV =  0.23 (stat)  0.12 (syst) ppm
A(Gs=0) = ppm
GsE =  0.014(stat)  0.007(syst)
HAPPEX-H:
Q2 = ± (GeV/c)2
APV =  0.12 (stat)  0.04 (syst) ppm
A(Gs=0) = ppm  ppm
GsE GsM =  0.011(stat)  0.004(syst)  0.005(FF)

29. HAPPEX-II 2005 Results Three bands:
Inner: Project to axis for 1-D error bar
Middle: 68% probability contour
Outer: 95% probability contour
Caution: the combined fit is approximate. Correlated errors and assumptions not taken into account

30. World Data near Q2 ~0.1 GeV2 GMs = 0.28 +/- 0.20
GEs = /
~3% +/- 2.3% of proton magnetic moment
~0.2 +/- 0.5% of electric distribution
HAPPEX-only fit suggests something even smaller:
GMs = /- 0.24
GEs = /
Caution: the combined fit is approximate. Correlated errors and assumptions not taken into account

31. World data consistent with state of the art theoretical predictions
16. Skyrme Model - N.W. Park and H. Weigel, Nucl. Phys. A 451, 453 (1992).
17. Dispersion Relation - H.W. Hammer, U.G. Meissner, D. Drechsel, Phys. Lett. B 367, 323 (1996).
18. Dispersion Relation - H.-W. Hammer and Ramsey-Musolf, Phys. Rev. C 60, (1999).
19. Chiral Quark Soliton Model - A. Sliva et al., Phys. Rev. D 65, (2001).
20. Perturbative Chiral Quark Model - V. Lyubovitskij et al., Phys. Rev. C 66, (2002).
21. Lattice - R. Lewis et al., Phys. Rev. D 67, (2003).
22. Lattice + charge symmetry -Leinweber et al, Phys. Rev. Lett. 94, (2005) & Phys. Rev. Lett. 97, (2006)
[22]

32. Figures courtesy of R. Carlini, R. Young
A Global Fit: R.D. Young, et al. nucl-ex/
all data Q2 < 0.3, leading moments of GEs , GMS
Kelly’s EMF
Float GAe separately for neutron and proton
With HAPPEx-2005 data
Before HAPPEx-2005 data
Figures courtesy of R. Carlini, R. Young

33. Future: HAPPEX-3 (2007 or 8)

34. Conclusions
Marvelous consistency of data.
Q2 = 0.1 GeV2 : GsM and GsE consistent with zero; constraining axial FF to Zhu et al. theory favors positive GsM
4He: best fractional error in PV experiment to date (< 4%) no axial contamination  uniquely determines GsE
1H: < 100 ppb error on A, unprecedented “parity quality”
Still room (& hints?) for non-zero values at higher Q2
Future of Strangeness form factors:
G0 Backward: will allow GsM and GsE separation at two Q2
Mainz: PV-A4 backward-angle program well underway
HAPPEx-III: high precision Q2 = 0.6 GeV2

35. Backup Slides

36. Two Photon Exchange  and Z box and crossing diagrams.
Beyond single boson exchange in electroweak interference:
 and Z box and crossing diagrams.
effects appear small at large  and small Q2
not a concern at present experimental precision.
Electromagnetic Form Factors used to extract strange form factors:
which form factors to use?
Transverse Asymmetry/Beam normal asymmetry/Vector analyzing power:
 “background” to PV measurements, if electron beam not 100%
longitudinal and detectors not perfectly symmetric.
 interesting in its own right – imaginary parts of TPE.

37. Validity of charge symmetry assumption
Size of charge symmetry breaking effects in some n,p observables:
n - p mass difference  (mn - mp)/mn ~ 0.14%
polarized elastic scattering n + p, p+n A = An - Ap = (33 ± 6) x 10-4
Vigdor et al, PRC 46, 410 (1992)
Forward backward asymmetry n + p  d + 0 Afb ~ (17 ± 10)x 10-4
Opper et al., nucl-ex (2003)
 For vector FF: theoretical CSB estimates indicate < 1% violations Miller PRC 57, 1492 (1998) Lewis & Mobed, PRD 59, (1999)
Very recent : effects could be large as statistical error on our data!
Kubis & Lewis PRC 74, (2006)

38. EM Form Factors Electromagnetic form factors parameterized as by:
Friedrich and Walcher, Eur. Phys. J. A, 17, 607 (2003)
GEn from BLAST:
Claimed uncertainty at 7-8% FF
Error
GEp
2.5%
GMp
1.5%
GEn
10%
GMn
GA(3) -
GA(8)

39. HAPPEX (first generation)
Hydrogen Target: E=3.3 GeV, q=12.5°, Q2=0.48 (GeV/c)2
APV = ppm ± 0.98 (stat) ppm ± 0.56 (syst) ppm
GsE GsM = ± (exp) ± (FF)
Phys. Rev. Lett. 82,1096 (1999);
Phys. Lett. B509, 211 (2001);
Phys. Rev. C 69, (2004)
“Parity Quality” JLab
AA suppressed by ‘ (1 – 4 sin2w) where ‘ = [(1 + )(1 - 2)]½  (0.08)(0.08) here.

40. Background
Dedicated runs at very low current using track reconstruction of the HRS
Acceptance
Rolloff
Dipole field scan to measure the
probability of rescattering
inside the spectrometer
Helium
Helium QE in detector: /- 0.15%
Helium QE rescatter: /- 0.15%
Al fraction: /- 0.2%
Hydrogen:
Al fraction /- 25 %
Hydrogen Tail + Delta rescatter: <0.1%
Total systematic uncertainty contribution ~40 ppb (Helium), ~15ppb (Hydrogen)

41. Determining Q2 Asymmetry explicitly depends on Q2: Goal:
Q2 measured using standard HRS tracking package, with reduced beam current
Central scattering angle must be measured to dq < 0.5%
Asymmetry distribution must be averaged over finite acceptance

42. SAMPLE (MIT/Bates) GMs = 0.23  0.36  0.40
GeA(T=1) =  0.57  0.50
E.J. Beise et al., Prog Nuc Part Phys 54 (2005)
Results of Zhu et al commonly used to constrain GSM result:
GsM = 0.37  0.20Stat  0.36Syst  0.07FF

43. PV-A4 (MAMI/Mainz) GEs + aGMs
Q2 (GeV2)
A  stat  syst (ppm)
GEs + aGMs
0.230
-5.44  0.54  0.26
GEs GMs
=  0.034
0.101
-1.36  0.29  0.13
GEs GMs
=  0.036
“Evidence for Strange Quark Contributions to the Nucleon’s Form Factors at Q2 = 0.1 GeV2” PRL 94, (2006)
Back Angle runs underway to separate GsM, GA at additional points…

44. s and s have different spatial distributions in proton
What would non-zero GsE and GsM imply?
GsE  0
GsM  s and s have different magnetization distributions in proton -> contribute to magnetic moment, etc.
s and s have different spatial distributions in proton
Kaon = us
proton proton
Hyperon = uds
(naive model for illustration)

45. A Simple Fit (for a simple point)
GEs = r_s*t
GMs = mu_s
Includes only data Q2 < 0.3 GeV2
Includes SAMPLE constrainted with GA theory and HAPPEX-He 2004, 2005
G0 Global error allowed to float with unit constraint
Nothing intelligent done with form factors, correlated errors, etc.
Preliminary
Quantitative values should NOT be taken very seriously, but some clear, basic points:
The world data are consistent.
Rapid Q2 dependence of strange form-factors is not required.
Sizeable contributions at higher Q2 are not definitively ruled out. (To be tested by HAPPEX-III, G0 and A4 backangle.)