1. Shufang Su • U. of Arizona
Parity Violation
and determination of sin2W
Shufang Su • U. of Arizona
Hall C 2006 summer workshop

2. Outline Determination of sin2eff Neutral current measurements-
Determination of sin2eff
Neutral current measurements
parity violating electron scattering (PVES)
ee Moller scattering (SLAC E158, Jlab 12 GeV)
ep elastic scattering (Jlab Qweak)
- Parity violation deep inelastic scattering (DIS-parity)
atomic parity violation (APV)
neutrino-nucleus deep inelastic scattering (NuTeV)
probe new physics beyond SM
some QCD issue
Conclusion
S. Su

3. Low energy precision measurements
address questions difficult to study at high energy
weak interactions (parity violation)
high precision low energy experiment available
- muon g-2: M=m , new  2x10-9, exp < 10-9
-decay, -decay: M=mW , new  10-3, exp  10-3
parity-violating electron scattering: M=mW , new  10-3,
1/QWe,p 10 more sensitive to new physics
need exp  “easier” experiment -
size of loop effects from new physics: (/)(M/Mnew)2
QWe,p  1-4 sin2W  0.1
probe new physics off the Z-resonance
- sensitive to new physics not mix with Z
S. Su

4. Møller Scattering DIS-ParityZ
Møller Scattering
Purely Leptonic e g Z
Q-Weak (JLab)
Coherent quarks in P
Results in ~2008
2(2C1u+C1d) e g Z p n
DIS-Parity
Isoscaler quark scattering
(2C1u-C1d)+Y(2C2u-C2d) e g Z
Cs133
Atomic Parity Violation
Coherent quarks in entire nucleus
Nuclear structure uncertainties
-376 C1u – 422 C1d n m W Z +
Neutrino Scattering
Quark scattering (from nucleus)
Weak charged and neutral current difference
S. Su
Courtesy of P. Reimer and R. Arnold

5. Test of sin2W running Weak mixing angle sinW g sinW = g’ cosW = e-
Weak mixing angle sinW
g sinW = g’ cosW = e
Jlab Moller
QWe
Qweak
SLAC E158
NuTeV
Standard Model Prediction
Erler, Kurylov & Ramsey-Musolf,
Phys. Rev. D 72, (2005)
Cs APV
DIS-parity
S. Su

6. Precision of sin2W determination-
Measurement
Δsin2θW/sin2θW
Δsin2θW
Z-pole
0.07%
0.5% Qw(Cs)
0.7%
0.0016
NuTeV
13.1% Qw(e)SLAC
0.5%
0.0013
2.5% Qw(e)Jlab
0.1%
(on par with Z pole)
4% QW(p)
0.3%
0.8% DIS-parity
0.45%
0.0011
Talk by D. Mack
Talk by K. Paschke
S. Su

7. Sensitivity to new physics scale-
Ramsey-Musolf(1999)
O(1)
: new physics scale
courtesy of Carlini
Take  QWp=4%
probe new physics scale comparable to LHC
confirmation of LHC discovery (couplings, charges)
S. Su

8. NC exp as a indirect probe of new physics-
SM is a low energy approximation of a more fundamental theory
SUSY: minimal Supersymmetric extension of SM (MSSM)
each SM particle superpartner
- with R-parity : loop corrections
- without R-parity: tree-level contribution
extra Z’
- exists in extension of SM
- constraints from Z-pole observable (mix with Z)
leptoquark
extra-dimension …
spin differ by ½
S. Su

9. M(ZΧ) M(ZLR) (TeV) (TeV)
Misc. model sensitivities (non-SUSY) -
Courtesy of D. Mack
Experiment Z’
M(ZΧ) M(ZLR) (TeV) (TeV)
Leptoquarks
MLQ(up) MLQ(down)
(TeV) (TeV)
Compositeness (LL)
e-q e-e
(TeV) (TeV)
Colliders
(LEP2, CDF,Hera)
“1.5” “1.5”
0.5% Qw(Cs)
exists!
13.1% Qw(e)
2.5% Qw(e)
4% Qw(p)
under construction
scaled from R-Musolf, PRC 60 (1999), Collider limits from Erler and Langacker, hep-ph/
S. Su

10. Moller and Qweak - A V
weak charge QWf = 2gfV = 2 If3 -4Qfs2
S. Su

11. Moller and Qweak QWp (Qweak) QWe (SLAC) QWe (Jlab)-
QWp (Qweak) QWe (SLAC) QWe (Jlab)
QWe,p tree 1-4s2 -(1-4s2)
QWe,p loop
q GeV GeV GeV2
ALR ppm ppm ppm
exp precision 4% 13% 2.5%
 sin2W
clean environment: Hydrogen target
theoretically clean: small hadronic uncertainties
tree level  0.1  sensitive to new physics
S. Su

12. MSSM correction to weak charge-
QWf =  (2Tf3 - 4Qf  s2) + f
Kurylov, Ramsey-Musolf, Su (2003)
QWe and QWp correlated
dominant :  (<0) 
negative shift in sin2W
MSSM
 (QWp)SUSY / (QWp)SM < 4%,  (QWe)SUSY / (QWe)SM < 8%
S. Su

13. R-parity violating (RPV)
RPV operators contribute to QWe,p at tree level
Kurylov, Ramsey-Musolf, Su (2003)
RPV 95% CL
MSSM
loop
No SUSY DM
Exp constraints
 decay: |Vud| = 
APV(Cs):  QWCs = 
Re/ :  Re/ = 
G:  G = 
Future 2.5% Moller
QpW
4% Qweak
I) Obtain 95% CL allowed region
in RPV coefficients
II) Evaluate  QWe and  QWp G
S. Su

14. Correlation between QWp , QWe-
Distinguish new physics
Erler, Kurylov and Ramsey-Musolf (2003)
exp
MSSM:
extra Z’:
RPV SUSY
leptoquark
 QWp
 QWe SM  SM 
Distinguish
via APV QWCs
Combinations of NC exps could be used to distinguish various new physics
S. Su

15. ? Extract QWp use kinematics to simplify: at forward angle -
use kinematics to simplify: at forward angle  ?
Musolf et. al., (1994)
measure F(,q2) over finite range in q2, extrapolate F
to small q2
existing PVES: SAMPLE, HAPPEX, G0, A4
minimize effect of F by making q2 small
q2  0.03 GeV2, still enough statistics   QpW / QpW | hadronic effects  2 %
S. Su

16. QCD correction to ep scattering-
Box diagram contribution to QWP
Erler, Kurylov and Ramsey-Musolf (2003) e p Z  e p W e p Z e p Z 
suppression
non-calculable
Similar to nuclear -decay e e- n p  W
 QWP
26% 3% 6%
kloop » O(mW)
kloop » O(mZ)
QCD  kloop  O(mZ)
|CW|  (CKM unitarity)
|CZ|  2
non-perturbative
using OPE (pQCD)
 QWP (QCD)
0.7%
0.08%
0.65%
Total theoretical uncertainty » 0.8%
S. Su

17. DIS-parity: eD scattering
Longitudinally polarized electrons
on unpolarized deuterium target
— Cahn and Gilman, PRD (1978).
S. Su

18. Sensitivity to sin2W Large asymmetry Q2 = 3.7 GeV2, Ad = 0.0003-
Large asymmetry
Q2 = 3.7 GeV2, Ad =
“Easy experiment”
 Ad/Ad = 0.8%   sin2 W/sin2W = 0.45%
S. Su

19. Ranges of C1u, C1d, C2u, C2d -
Courtesy of P. Reimer
S. Su

20. SUSY contributions -
DIS-parity
S. Su

21. Atomic parity violation-
Two approaches
rotation of polarization plane of linearly polarized light
apply external E field  parity forbidden atomic transition
Boulder group: cesium APV 0.35% exp uncertainty wood et. Al. (1997)
QW(Z,N)=(2Z+N)QWu+(Z+2N)QWd
¼ Z(1-4 sin2W)-N ¼ -N
finite nuclear size
nucleon substructure
nuclear spin-dependent term
 »  0.15%
Pollock and Wieman (2001)
Musolf (1994)
Erler, Kurylov and Ramsey-Musolf (2003)
atomic structure
1% Blundell et. al. (1990, 1992)
Dzuba et. Al. (1989)
reduced error 0.6% (exp + theory)
via transit dipole amplitude measurement
Bennett and Wieman (1999)
+ 2.5  deviation (2002)
Breit interaction  Derevianko (2000), Dzuba et. al. (2001)
Uehling potential  Johnson et. al. (2001), Milstein et. al. (2002)
QED self-energy and vertex 
Dzuba et. Al. (2002), Kuchiev and Flambaum (2002), Milstein et. al. (2002)
QWCs (exp) =  QWCs(SM)= agree
S. Su

22. Sensitivity to new physics-
Distinguish new physics
 QW (Z,N)=(2Z+N)  QWu +(2N+Z)  QWd
 QWu >0
 QWd <0
  QW(Z,N) / QW(Z,N) < 0.2 % for Cs
MSSM
exp
MSSM:
extra Z’:
 QWCs
small
sizable
 QWp SM 
 QWe 
Erler, Kurylov and Ramsey-Musolf (2003)
S. Su

23. Outlook -- APV Paris group: more precise Cs APV
Seattle group: Ba+ APV 6S1/2  5D3/2
Berkeley group: isotope Yb APV
eliminate large atomic structure theory uncertainties
0.2% uncertainties
comparable to QWp in sensitivity to new physics
Ramsey-Musolf(1999)
S. Su

24. NuTeV experiment NC CC gL,R2=(uL,R)2+(dL,R)2- NC CC
gL,R2=(uL,R)2+(dL,R)2
R=  R=  -
exp fit: (gLeff)2=0.30050.0014, (gReff)2=0.03100.0011
SM EW fit: (gLeff)2=0.3042, (gReff)2=0.0301
S. Su

25. NuTeV anomaly … exp fit (=1): sin2Won-shell = 0.2277  0.0016
SM fit to Z-pole: sin2Won-shell =  (3  away)
To explain NuTeV anomaly
nuclear shadowing
Miller and Thomas (2002), Zeller et. Al. (2002), Kovalenkov, schmidt and Yang (2002)
asymmetry in strange sea distribution
Davidson, Forte, Gambino, Rius and Strumia (2002), Goncharov et. al. (2001)
isospin symmetry breaking
Bodek et. al. (1999), Zeller et. Al. (2002)
QCD corrections
Dobrescu and Ellis (2003), Kretzer et. al. (2003), Davidson et. al. (2002) …
S. Su

26. New physics explanation-
Difficult !
Supersymmetry:  R,   0
Kurylov, Ramsey-Musolf, Su (2003), Davidson, Forte, Gambino, Rius and Strumia (2002)
Extra Z’ : family non-universal, finetuning
Langacker and Plumacher (2000)
Leptoquark: tune mass splitting
Davidson, Forte, Gambino, Rius and Strumia (2002)
 mixing with extra heavy neutrino:
constraints from other observables
Babu and Pati (2002), Loinaz et. al. (2003) -
MSSM
RPV
S. Su

27. Conclusion precision measurements of sin2W at low energy-
precision measurements of sin2W at low energy
- PV ee, ep scattering (E158, Jlab Moller, Qweak)
- eD DIS-parity
- APV measurements
- NuTeV
consistency check of SM
sensitive to new physics
complementary to direct searches
combinations of several exp
 distinguish various new physics
uncertainties caused by QCD
- extract from experimental measurements
- SM predictions
S. Su

28. Talks in this workshop Talk in parity violation K. Paschke: DIS-parity
D. Mack: Moller Parity
Talk in parity violation
S. Su