1. C3q Measurement Using Polarized e+/e- Beams at JLab
Xiaochao Zheng
Univ. of Virginia
March 27, 2009
Introduction — Standard Model of Electroweak Interaction
Neutral Weak Coupling Constants
C3q Measurements
Summary

2. Four Interactions of Our Nature
Electron scattering has been widely used to study
Structure of the nucleon — strong interactions, pQCD;
(Recently) parity violation electron scattering:
strange-quark content of the nucleon (elastic)
Electroweak interactions (DIS)

3. Electroweak Interaction – Charged Currents
1932, charged pion and muon decay indicate a fourth type of interaction:
π −. → μ −. ν μ ˉ
τ=2.6× 10 −8 𝑠
μ −. → 𝑒 −. ν 𝑒 ˉ ν μ
τ=2.2× 10 −6 𝑠
Much longer than strong (10-23 s) or electromagnetic (10-16 s) decays
1932, based on QED, Fermi proposed:
𝑀= 𝑒 𝑢 𝑝 ˉ γ μ 𝑢 𝑝   −1 𝑞 2  −𝑒 𝑢 𝑒 ˉ γ μ 𝑢 𝑒  =− 𝑒 2 𝑞 2  𝑗 μ 𝑒𝑚  𝑝  𝑗 𝑒𝑚,μ  𝑒
𝑀=𝐺  𝑢 𝑛 ˉ γ μ 𝑢 𝑝   𝑢 ν 𝑒 ˉ γ μ 𝑢 𝑒   𝑢 ν 𝑒 ˉ γ μ 𝑢 𝑒 
1956, when Parity violation was first proposed (and test by experiments), the only modification needed is:
γ μ → γ μ 1− γ 5

4. 𝑀 𝐶𝐶 = 4G 𝐽 μ 𝐽 μ +.
If further assume that weak interaction occurs by exchanging a (W) particle, similar to the photon in electromagnetic interactions, then
𝑀=  𝑔 𝑢 ˉ ν μ γ μ − γ 5 𝑢 μ  1 𝑀 𝑊 2 − 𝑞 2  𝑔 𝑢 ˉ e γ μ − γ 5 𝑢 ν 𝑒   𝑔 𝑢 ˉ e γ μ − γ 5 𝑢 ν 𝑒 
𝐺 2 = 𝑔 2 8 𝑀 𝑊 2
if q2<<MW2 then

5. Electroweak Interaction – Neutral Currents
1973, with developement of n beams, found:
ν ˉ μ 𝑒 −. → ν ˉ μ 𝑒 −.
ν μ 𝑁→ ν μ 𝑋
ν ˉ μ 𝑁→ ν ˉ μ 𝑋
cannot be explained by CC;
magnitude of strength indicate Neutral Currents.
𝑀 𝑁𝐶 = 4𝐺 ρ 𝐽 μ 𝑁𝐶 𝐽 𝑁𝐶,μ
𝐽 μ 𝑁𝐶 ν = 1 2  𝑢 ˉ ν γ μ − γ 5 𝑢 ν 
𝐽 μ 𝑁𝐶 𝑞 =  𝑢 ˉ 𝑞 γ μ 𝑐 𝑉 𝑞 − 𝑐 𝐴 𝑞 γ 5 𝑢 𝑞 
If further assume that weak interaction occurs by exchanging a (W) particle, similar to the photon in electromagnetic interactions, then
𝑀=  𝑔 𝑢 ˉ ν μ γ μ − γ 5 𝑢 μ  1 𝑀 𝑊 2 − 𝑞 2  𝑔 𝑢 ˉ e γ μ − γ 5 𝑢 ν 𝑒   𝑔 𝑢 ˉ e γ μ − γ 5 𝑢 ν 𝑒 

6. while experimentally observed NC couples to both R- and L-handed,
1961, construct a SU(2)L group using charged currents, quantum number: Weak isospin T.
Linear combination of the two is a neutral current, but it couples only to Left-handed fermions,
while experimentally observed NC couples to both R- and L-handed,
On the other hand, EM [U(1)g] also couple to both R- and L-H fermions.
Can combine NC from SU(2)L and UEM(1)g to construct:
𝑗 μ 𝑒𝑚 𝐽 μ 𝑁𝐶 ⇔ 𝐽 μ 3 𝑗 μ 𝑌
completes SU(2)L
U(1)Y, Y: weak hyper charge
𝑄= 𝑇 3 + 𝑌 2

7. 𝑊 μ 1 𝑊 μ 2 𝑊 μ 3 𝐵 μ ⇔ 𝑊 μ +. 𝑊 μ −. 𝐴 μ 𝑍 μ
𝐴 μ = 𝐵 μ cos θ 𝑊 + 𝑊 μ 3 sin θ 𝑊 𝑚=0
𝑍 μ =− 𝐵 μ sin θ 𝑊 + 𝑊 μ 3 cos θ 𝑊 𝑚≠0

8. ElectroWeak Standard Model
SM works well at present energy range;
Conceptual reasons for new physics:
What happens in the “high-energy desert”?
(250 GeV ~ x 1014 GeV ~ 2.4 x 1018 GeV)?
Data exist: cannot be explained by the SM ( mn, NuTeV anomaly...);

9. Exploring Nucleon Structure Using Electron Scattering Elastic, quasi-elastic, resonances, deep inelastic
(Quasi-) elastic – the nucleus (nucleon) appears as a rigid body
Resonance region – quarks inside the nucleon react coherently
Deep Inelastic Scattering (DIS):
Quarks start to react incoherently (start to see constituents of the nucleon)
(Can test pQCD)
𝑄 2 = 2M 𝑇 𝑁 ν

10. Weak Interaction in DIS (Parity Violating DIS)

11. Parity Violating Electron Scattering
Electromagnetic observables — s, A...
Weak observables — parity violating asymmetries (APV)
(polarized beam + unpolarized target)
APV = +
𝐴 𝐿𝑅 ≡  𝑟 −  𝑙  𝑟   𝑙 ≈ 𝑄 2 𝑀 𝑍 2 ≈120𝑝𝑝𝑚 𝑎𝑡 𝑄 2 =1  𝐺𝑒𝑉 𝑐  2
study hadron structure
elastic scattering: strange form factors A4(MAINZ), G0, HAPPEX (JLab), SAMPLE (MIT/Bates)
DIS: higher twist effects, charge symmetry violation PVDIS
test the electroweak standard model E158(SLAC), Qweak(JLab)

12. ElectroWeak Standard Model
SM works well at present energy range;
Conceptual reasons for new physics:
What happens in the “high-energy desert”?
(250 GeV ~ x 1014 GeV ~ 2.4 x 1018 GeV)?
Data exist: cannot be explained by the SM ( mn, NuTeV anomaly...);

13. ElectroWeak Standard Model
SM works well at present energy range;
Conceptual reasons for new physics:
What happens in the “high-energy desert”?
High energy direct searches:
LEP, LHC
indirect searches:
E158, NuTeV, Qweak, PVDIS
(250 GeV ~ x 1014 GeV ~ 2.4 x 1018 GeV)?
Search for Physics beyond the Standard Model

14. Testing the EW Standard Model – Running of sin2qW and the NuTeV Anomaly
(expected)

15. Current Knowledge on Weak Coupling Coeffecients
𝐶 1q = 𝑔 𝐴 𝑒 𝑔 𝑉 𝑞
𝐶 2q = 𝑔 𝑉 𝑒 𝑔 𝐴 𝑞
new
PDG2002 (best): (2C2u-C2d)=±0.24
J. Erler, M.J. Ramsey-Musolf, Prog. Part. Nucl. Phys. 54, 351 (2005)
R. Young, R. Carlini, A.W. Thomas, J. Roche, PRL 99, (2007) & priv. comm.
Some New Physics can affect C2q, but not C1q

16. Current Knowledge on C1,2q
all are 1 s limit
R. Young (combined)
PDG best fit
SAMPLE
PDG 2006 fit
C2u+C2d
1.25
1.5
1.75
1.0
0.75
0.5
0.25
-0.5
-0.75
C2u-C2d
- 0.2
0.4
0.2
- 0.4
0.10
0.125
0.15
0.175
C1u-C1d
- 0.4
- 0.6
- 0.8
C1u+C1d
SLAC/ Prescott
Tl APV
Cs APV
R. Young (PVES)
Qweak (expected)
R. Young (combined)
MIT/ Bates
SLAC/Prescott
Best: PDG2002 D(2C2u-C2d) = 0.24

17. Neutral Weak Couplings in Electron DIS
APV = +
1 2  𝑒 ˉ γ μ 𝑔 𝑉 𝑒 − 𝑔 𝐴 𝑒 γ 5 𝑒  𝑒 ˉ γ μ 𝑔 𝑉 𝑒 − 𝑔 𝐴 𝑒 γ 5 𝑒
1 2  𝑞 ˉ γ μ 𝑔 𝑉 𝑞 − 𝑔 𝐴 𝑞 γ 5 𝑞  𝑞 ˉ γ μ 𝑔 𝑉 𝑞 − 𝑔 𝐴 𝑞 γ 5 𝑞
axial electron * vector quark :
𝐿 𝑆𝑀 𝑃𝑉 = − 𝐺 𝐹 𝑒 ˉ γ μ γ 5 𝑒 𝑞 𝐶 1q 𝑞 ˉ γ μ 𝑞
vector electron * axial quark :
𝐿 𝑆𝑀 𝑃𝑉 = − 𝐺 𝐹 𝑒 ˉ γ μ 𝑒 𝑞 𝐶 2q 𝑞 ˉ γ μ γ 5 𝑞
𝐶 1u = 𝑔 𝐴 𝑒 𝑔 𝑉 𝑢 =− sin 2 θ 𝑊
𝐶 2u = 𝑔 𝑉 𝑒 𝑔 𝐴 𝑢 =− sin 2 θ 𝑊
𝐶 2d = 𝑔 𝑉 𝑒 𝑔 𝐴 𝑑 = 1 2 −2 sin 2 θ 𝑊
𝐶 1d = 𝑔 𝐴 𝑒 𝑔 𝑉 𝑑 = 1 2 − 2 3 sin 2 θ 𝑊

18. PVDIS Asymmetries + APV = Deuterium:
𝐴 𝑑 = 540𝑝𝑝𝑚 𝑄 2 2 𝐶 1u 1+ 𝑅 𝐶 𝑥 − 𝐶 1d 1+ 𝑅 𝑆 𝑥 +𝑌 2 𝐶 2u − 𝐶 2d 𝑅 𝑉 𝑥 5+ 𝑅 𝑆 𝑥 +4 𝑅 𝐶 𝑥

19. PVDIS Asymmetries APV = + + Deuterium: New physics sensitivity:
𝐴 𝑑 = 540𝑝𝑝𝑚 𝑄 2 2 𝐶 1u 1+ 𝑅 𝐶 𝑥 − 𝐶 1d 1+ 𝑅 𝑆 𝑥 +𝑌 2 𝐶 2u − 𝐶 2d 𝑅 𝑉 𝑥 5+ 𝑅 𝑆 𝑥 +4 𝑅 𝐶 𝑥
New physics sensitivity:
𝐿= 𝐿 𝑆𝑀 𝑃𝑉 + 𝐿 𝑁𝐸𝑊 𝑃𝑉
𝐿 𝑆𝑀 𝑃𝑉 = − 𝐺 𝐹 𝑒 ˉ γ μ 𝑒 𝑞 𝐶 2q 𝑞 ˉ γ μ γ 5 𝑞
𝐿 𝑁𝐸𝑊 𝑃𝑉 = 𝑔 2 4 Λ 2 𝑒 ˉ γ μ 𝑒 𝑓 ℎ 𝐴 𝑞 𝑞 ˉ γ μ γ 5 𝑞
g: coupling constant, L: mass limit, hAq: effective coefficient

20. PVDIS Asymmetries APV = + + Deuterium: New physics sensitivity:
𝐴 𝑑 = 540𝑝𝑝𝑚 𝑄 2 2 𝐶 1u 1+ 𝑅 𝐶 𝑥 − 𝐶 1d 1+ 𝑅 𝑆 𝑥 +𝑌 2 𝐶 2u − 𝐶 2d 𝑅 𝑉 𝑥 5+ 𝑅 𝑆 𝑥 +4 𝑅 𝐶 𝑥
New physics sensitivity:
𝐿= 𝐿 𝑆𝑀 𝑃𝑉 + 𝐿 𝑁𝐸𝑊 𝑃𝑉
𝐿 𝑆𝑀 𝑃𝑉 = − 𝐺 𝐹 𝑒 ˉ γ μ 𝑒 𝑞 𝐶 2q 𝑞 ˉ γ μ γ 5 𝑞
𝐿 𝑁𝐸𝑊 𝑃𝑉 = 𝑔 2 4 Λ 2 𝑒 ˉ γ μ 𝑒 𝑓 ℎ 𝐴 𝑞 𝑞 ˉ γ μ γ 5 𝑞
g: coupling constant, L: mass limit, hAq: effective coefficient
Sensitive to: Z' searches, compositeness, leptoquarks
Mass limit:
≈ 𝐺 𝐹 ∣Δ 2 𝐶 2u − 𝐶 2d ∣ −1 2

21. PV DIS and Other SM Test Experiments
E158/Moller (SLAC)
Atomic PV
NuTeV (FNAL)
Weak CC and NC difference
Nuclear structure?
Other hadronic effects?
Purely leptonic
Coherent Quarks in the Nucleus
- 376C1u - 422C1d
Nuclear structure?
Qweak (JLab)
PVDIS (JLab)
Different Experiments
Probe Different
Parts of Lagrangian,
PVDIS is the only one accessing C2q
2 (2C1u+C1d)
Coherent quarks in the proton
(2C1u-C1d)+Y(2C2u-C2d)
Isoscalar quark scattering
Cartoons borrowed from R. Arnold (UMass)

22. PVDIS Asymmetries APV = + Deuterium: Also sensitive to:
𝐴 𝑑 = 540𝑝𝑝𝑚 𝑄 2 2 𝐶 1u 1+ 𝑅 𝐶 𝑥 − 𝐶 1d 1+ 𝑅 𝑆 𝑥 +𝑌 2 𝐶 2u − 𝐶 2d 𝑅 𝑉 𝑥 5+ 𝑅 𝑆 𝑥 +4 𝑅 𝐶 𝑥
𝑅 𝑉 𝑥 = 𝑢 𝑉 𝑥 + 𝑑 𝑉 𝑥 𝑢 𝑥 + 𝑢 ˉ 𝑥 +𝑑 𝑥 + 𝑑 ˉ 𝑥
𝑅 𝑆 𝑥 = 2 𝑠 𝑥 + 𝑠 ˉ 𝑥 𝑢 𝑥 + 𝑢 ˉ 𝑥 +𝑑 𝑥 + 𝑑 ˉ 𝑥
𝑅 𝐶 𝑥 = 2 𝑐 𝑥 + 𝑐 ˉ 𝑥 𝑢 𝑥 + 𝑢 ˉ 𝑥 +𝑑 𝑥 + 𝑑 ˉ 𝑥
Also sensitive to:
quark-gluon correlations (higher-twist effects)
Charge symmetry violation
𝑢 𝑝 𝑥 ≠ 𝑑 𝑛 𝑥 𝑑 𝑝 𝑥 ≠ 𝑢 𝑛 𝑥

23. PVDIS Experiment – Past, Present and Future
1970's, result from SLAC E122 consistent with sin2qW=1/4, established the Electroweak Standard Model;
C.Y. Prescott, et al., Phys. Lett. B77, 347 (1978)
PVDIS asymmetry has the potential to explore New Physics, study hadronic effects/CSV However, hasn't been done since 1978.

24. PVDIS Experiment – Past, Present and Future
1970's, result from SLAC E122 consistent with sin2qW=1/4, established the Electroweak Standard Model;
C.Y. Prescott, et al., Phys. Lett. B77, 347 (1978)
PVDIS asymmetry has the potential to explore New Physics, study hadronic effects/CSV However, hasn't been done since 1978.
(Re)start PVDIS at JLab 6 & 12 GeV
Difficulty: separate New Physics and hadronic effects

25. PVDIS Experiment – Past, Present and Future
1970's, result from SLAC E122 consistent with sin2qW=1/4, established the Electroweak Standard Model;
C.Y. Prescott, et al., Phys. Lett. B77, 347 (1978)
PVDIS asymmetry has the potential to explore New Physics, study hadronic effects/CSV However, hasn't been done since 1978.
Do a first measurement at JLab 6 GeV:
If observe a significant deviation from the SM value, it will definitely indicate something exciting;
Indicate either electroweak new physics, or current understanding of strong interation is worse than we thought.
New electroweak Physics
Non-perturbative QCD (higher-twist) effects
Charge symmetry violation
At the 6 GeV precision:
Likely to be small, but need exp confirmation
Small from MRST fit (90% CL ~1%)

26. PVDIS Experiment – Past, Present and Future
1970's, result from SLAC E122 consistent with sin2qW=1/4, established the Electroweak Standard Model;
C.Y. Prescott, et al., Phys. Lett. B77, 347 (1978)
PVDIS asymmetry has the potential to explore New Physics, study hadronic effects/CSV However, hasn't been done since 1978.
Do a first measurement at JLab 6 GeV:
If observe a significant deviation from the SM value, it will definitely indicate something exciting;
Indicate either electroweak new physics, or current understanding of strong interation is worse than we thought.
At 12 GeV, a larger, well-planned PVDIS program could separate all three: New Physics, HT, CSV, important information for both EW and Strong interaction study.

27. JLab 6 GeV Experiment
Co-spokesperson & contact: X. Zheng
Co-spokesperson: P.E. Reimer, R. Michaels
(Hall-A Collaboration Experiment, approved by PAC27, re-approved by PAC33 for 32 days, rated A-)
Use 85mA, 6 GeV, 80% polarized beam on a 25-cm LD2 target;
Two Hall A High Resolution Spectrometers detect scattered electrons;
Measure PV asymmetry Ad at Q2=1.10 and 1.90 GeV2 to 2.7% (stat.);
Ad at Q2=1.10 will limit the higher twist effects;
If HT is small, can extract 2C2u-C2d from Ad at Q2=1.90 to ±0.04 (or with reduced precision if higher twists are un-expectedly large)

28. Current Knowledge on C1,2q
all are 1 s limit
R. Young (combined)
PDG best fit
SAMPLE
PDG 2006 fit
C2u+C2d
1.25
1.5
1.75
1.0
0.75
0.5
0.25
-0.5
-0.75
C2u-C2d
- 0.2
0.4
0.2
- 0.4
0.10
0.125
0.15
0.175
C1u-C1d
- 0.4
- 0.6
- 0.8
C1u+C1d
SLAC/ Prescott
Tl APV
Cs APV
R. Young (PVES)
Qweak (expected)
R. Young (combined)
MIT/ Bates
SLAC/Prescott
Best: D(2C2u-C2d) = 0.24

29. C2q from JLab E08-011 all are 1 s limit
R. Young (combined)
PDG best fit
SAMPLE
PDG 2006 fit
C2u+C2d
1.25
1.5
1.75
1.0
0.75
0.5
0.25
-0.5
-0.75
C2u-C2d
- 0.2
0.4
0.2
- 0.4
0.10
0.125
0.15
0.175
C1u-C1d
- 0.4
- 0.6
- 0.8
C1u+C1d
SLAC/ Prescott
Tl APV
Cs APV
R. Young (PVES)
JLab E (PDG fit)
Qweak (expected)
R. Young (combined)
JLab E (R. Young's fit)
MIT/ Bates
SLAC/Prescott
Best: D(2C2u-C2d) = (factor of six improvement);
New physics mass limit: →
≈ 𝐺 𝐹 ∣Δ 2 𝐶 2u − 𝐶 2d ∣ −1 2 ≈0.9TeV

30. PVDIS Program at JLab 12 GeV
Higher precision, possibly sensitive to 1) New Physics beyond the SM; 2) Charge Symmetry Violation (CSV)
Two approaches (conditionally approved):
Hall C “baseline” SHMS+HMS: PR (P.E. Reimer, X-C. Z, K. Paschke)
1% on Ad, extraction of C2q, sin2qW (if higher-twist and CSV are negligible);
Hall A large acceptance “solenoid” device: PR09-012
Measure Ad to 1% for a wide range of (x,Q2,y), clean separation of New Physics (via C2q and sin2qW), HT and CSV possible;
Extract d/u at large x from PVDIS on a proton target, free of nuclear effects;
Other hadronic physics study possible: A1n at large x, Semi-inclusive DIS.

31. PVDIS Program at JLab 12 GeV
Higher precision, possibly sensitive to 1) New Physics beyond the SM; 2) Charge Symmetry Violation (CSV)
Two approaches (conditionally approved):
Hall C “baseline” SHMS+HMS: PR (P.E. Reimer, X-C. Z, K. Paschke)
1% on Ad, extraction of C2q, sin2qW (if higher-twist and CSV are negligible);
Hall A large acceptance “solenoid” device: PR09-012
Measure Ad to 1% for a wide range of (x,Q2,y), clean separation of New Physics (via C2q and sin2qW), HT and CSV possible;
Extract d/u at large x from PVDIS on a proton target, free of nuclear effects;
Other hadronic physics study possible: A1n at large x, Semi-inclusive DIS.

32. PVDIS Program at JLab 12 GeV
Higher precision, possibly sensitive to 1) New Physics beyond the SM; 2) Charge Symmetry Violation (CSV)
Two approaches (conditionally approved):
Hall C “baseline” SHMS+HMS: PR (P.E. Reimer, X-C. Z, K. Paschke)
1% on Ad, extraction of C2q, sin2qW (if higher-twist and CSV are negligible);
Hall A large acceptance “solenoid” device: PR09-012
Measure Ad to 1% for a wide range of (x,Q2,y), clean separation of New Physics (via C2q and sin2qW), HT and CSV possible;
Extract d/u at large x from PVDIS on a proton target, free of nuclear effects;
Other hadronic physics study possible: A1n at large x, Semi-inclusive DIS.

33. Summary ( )
Measurement of neutron asymmetry A1n in the valence quark region at JLab 12 GeV
Flagship experiment
Will be one of the first experiments to run (~2014?)
PVDIS at 12 GeV
Ultimate goal: clean separation of New Physics and CSV (2015 or later?)