1. Probing Supersymmetry with Neutral Current Scattering Experiments
Shufang Su • U. of Arizona

2. Sub-Z precision measurements
neutral current scattering
heavy quark physics
CP violation, EDM
Rare K-decay, CKM unitarity
muon g-2
lepton flavor violation …
polarized ee scattering (SLAC E158)
polarized ep scattering (JLab Qweak)
neutrino-nucleus scattering (NuTeV)
A. Kurylov, M. Ramsey-Musolf, SS
S. Su LOOPFESTIII

3. Outline motivation parity-violating electron scattering experiments
radiative corrections to weak charge QW
analysis of SUSY contributions to QW
MSSM contributions
RPV analysis
distinguish various new physics / SUSY
NuTeV experiment
conclusion
S. Su LOOPFESTIII

4. Motivation high precision low energy experiment available-
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/Qe,pW 10 more sensitive to new physics
need exp  “easier” experiment
indirect+direct: complementary information
consistency test of theory at loop level
size of loop effects from new physics: (/)(M/Mnew)2
Qe,pW  1-4 sin2W  0.1
probe new physics off the Z-resonance
- sensitive to new physics not mix with Z
S. Su LOOPFESTIII

5. Test of sin2W running sin2W(0) - sin2W(mZ2) = +0.007
QCsw: agree Q2=0
NuTeV: +3 Q2=20 (GeV)2
parity-violating electron
scattering (PVES)
ee Moller scattering (SLAC) QeW
ep elastic scattering (J-lab) QpW - -
 sin2W  at Q2=0.03 (GeV)2
clean environment: Hydrogen target
theoretically clean: small hadronic uncertainties
tree level  0.1  sensitive to new physics
S. Su LOOPFESTIII

6. Goal Develop consistency checks for theories of new physics-
Develop consistency checks for theories of new physics
using the low energy precision measurements
minimal Supersymmetric extension of SM (MSSM)
SUSY: most promising candidate for new physics
solution to Hierarchy problem
gauge coupling unification
provide a natural electroweak symmetry breaking
dark matter candidate ? (PVES)
with R-parity : loop corrections
without R-parity: tree-level contribution
low-energy precision measurements
PVES: weak charge QeW , QpW , ( QCsW ) - NuTeV: R() -
S. Su LOOPFESTIII

7. Weak charge QW A N+-N- ALR  QfW N++N- V geA = Ie3
weak charge QfW = 2gfV = 2 If3 -4Qfs2
ep Qweak exp QpW ee Moller exp QeW
Qe,pW tree 1-4s2 -(1-4s2)
Qe,pW loop
exp precision 4% 8%
 sin2W
SM running 10  8 
QCsW :  sin2W = NuTeV:  sin2W =
S. Su LOOPFESTIII

8. General structure of radiative corrections to QfW-
Including radiative corrections:
QfW =  (2If3 - 4  Qf s2) + f
, : universal, f: depend on fermion species
 = 1+SM+SUSY,  = 1+SM+SUSY, f= fSM+fSUSY
correction to muon life time 
S. Su LOOPFESTIII

9. Radiative contributions-
QfW =  (2If3 - 4  Qf s2) + f
correction to , G and mZs2  f
S. Su LOOPFESTIII

10. MSSM particle contents-
Spin differ by 1/2
SM particle superpartner
mass parameter
mqL2, 
mqR2, 
mqLR2 
mlL2, 
mlR2, 
mlLR2 
, tan=vu/vd M3 M2 M1
S. Su LOOPFESTIII

11. One loop SUSY contributions to PVES-
gauge boson
self-energies
external leg corrections
vertex corrections
box diagrams
S. Su LOOPFESTIII

12. 50 GeV < mq, ml, M1,2,  < 1000 GeV
Numerical analysis -
Model-independent analysis
MSSM parameter range: random scan
50 GeV < mq, ml, M1,2,  < 1000 GeV
1.4 < tan < 60 ~
hard to impose bounds on certain MSSM parameter
show the possible range of MSSM corrections
impose exp search limit on SUSY particles
impose S-T 95% CL constraints
impose g-2 constraints (2nd slepton LR mixing)
S. Su LOOPFESTIII

13. Correction to weak charge-
QfW =  (2Tf3 - 4Qf  s2) + f
QeW and QpW correlated
dominant :  (<0) 
negative shift in sin2W
 (QpW)SUSY / (QpW)SM < 4%,  (QeW)SUSY / (QeW)SM < 8%
S. Su LOOPFESTIII

14. Dominant contributions-
QfW =  (2Tf3 - 4Qf  s2) + f
non-universal corrections
vertex + wavefunction : cancel
box diagrams numerically suppressed
 contribution suppressed by (1-4 s2)
dominant contribution from 
 (<0)  negative shift in sin2W
S. Su LOOPFESTIII

15. R-parity General MSSM, including B,L-violating operators ijk ’ijk
dangerous  introduce proton decay
R-parity SM particle: even superparticle: odd
stable LSP as dark matter candidate
RPV: only look at L-violating operator
S. Su LOOPFESTIII

16. R-parity violating (RPV)
RPV operators contribute to Qe,pW at tree level
RPV
95% CL
MSSM
loop
Exp constraints
 decay: |Vud| = 
APV(Cs):  QWCs = 
Re/ :  Re/ = 
G:  G = 
QpW
No SUSY dark matter
I) Obtain 95% CL allowed region
in RPV coefficients
II) Evaluate  QWe and  QWp G
S. Su LOOPFESTIII

17. Correlation between QpW and QeW-
 QW (Z,N)=(2Z+N)  QuW +(2N+Z)  QdW
 QuW >0
 QdW <0
SUSY correction to heavy nuclei QW
  QW(Z,N) / QW(Z,N) < 0.2 % for Cs
Distinguish new physics
MSSM:
extra Z’:
leptoquark:
RPV SUSY
 QpW
 QeW
 QCsW
small
sizable
S. Su LOOPFESTIII

18. Additional PV electron scattering ideas-
Czarnecki, Marciano， Erler et al.
 N deep inelastic
Linear Collider e-e-
DIS-Parity, JLab
sin2W
DIS-Parity, SLAC
APV
e+e- LEP, SLD
SLAC E158 (ee)
JLab Moller (ee)
JLab Q-Weak (ep)
(GeV)
S. Su LOOPFESTIII

19. NuTeV experiment NC CC wrong-sign contribution! R=-0.0033  0.0015
Davidson et. al., JHEP 02, 037, 2002
MSSM
(N  X)
(N  l-(+)X)
R()  -
(-)
R= 
R=  -
S. Su LOOPFESTIII

20. R-parity violating (RPV)
RPV operators contribute to R() at tree level NC
either wrong sign or too small
hard to explain NuTeV deviation CC
S. Su LOOPFESTIII

21. Conclusion Parity-violating ee and ep scattering
could be used to test SM and probe new physics
MSSM contribution to QeW and QpW is 8% and 4%  1 exp need higher exp precision to constrain SUSY
correlation between QeW and QpW
distinguish various new physics
distinguish various SUSY scenario whether dark matter is SUSY particle ?
SUSY contribution to NuTeV result
MSSM with R-parity: wrong sign /small
negative gluino contribution:
size constrained by other considerations
hard to explain NuTeV in RPV
SUSY is not responsible for the NuTeV deviation
other new physics ?
hadronic effects ?
S. Su LOOPFESTIII