1. Electroweak Physics at the EIC
1. WEAK NC PARITY VIOLATION
AND NEW PHYSICS
i) APV vs Pol Electron Scattering (ARL)
ii) QWEAK(ep), Moller(ee), DIS(eNeX), …
2. Preliminary EIC requirements
For Competitive ARL Program
~100fb-1 (K. Kumar et al.; R. Holt)
eg 1034cm-2s-1x107s
William J. Marciano
Oct 21, 2009

2. BNL LDRD FY2010 (Funded) Electroweak Physics with an Electron-Ion Collider Deshpande, Kumar, Marciano, Vogelsang
STUDY GOALS
DIS & Nuclear Structure Functions (,Z,W) (Beyond HERA)
 L(HERA)=1031cm-2s-1  >1033cm-2s-1
ARL, sin2W(Q2), Radiative Corrections, “New Physics”
requires roughly 100fb-1(1034cm-2s-1)
Lepton Flavor Violation: eg epX
requires roughly one inverse attobarn=1000fb-1!
To be competitive with BR(eX)~10-10
Rates & Backgrounds Need Thorough Study

3. SOME ISSUES What are the Machine and Detector Requirements?
“New Physics Effects” (Z’, Leptoquarks, SUSY, S&T, LFV…)
sin2W(Q2) Running Weak Mixing Angle
Inclusion of Electroweak Radiative Corrections (Important?)
High Precision & Polarization(0.5%?, 0.25%?)
Nucleon vs Nuclear Asymmetries (EMC Effect, CSV?)
Proton & Deuteron Polarization (Spin Content-Peff?)
Various Issues That Need Thorough Study

4. 1) PV Weak Neutral Currents (Past, Present and Future)
The SU(2)LxU(1)Y Weinberg-Salam Model: weak neutral current coupling
g/cosWZf(T3f-2Qfsin2W -T3f5)f
T3f=1/2, Qf=electric charge
A New Form of Parity Violation!
-Z Interference  Parity Violation Everywhere!
Depends on sin2W

5. Atomic Parity Violation (APV)
QW(Z,N) =Z(1-4sin2W)-N Weak Charge
W=Weak Mixing Angle
QW(p)=1-4sin2W0.08
QW(209Bi83) = sin2W =-126
Bi Much Larger but Complicated Atomic Physics
Originally APV not seen in Bi  SM Ruled Out?
(Later seen: Tl, Bi, Cs…)
QW(133Cs55)= sin2W
=-73.16(34)
Recent(2008) Atomic Theory Improvement

6. Confirmed SU(2)LxU(1)Y SM! ±10% Determination of sin2W Precision!
1978 SLAC Polarized DIS eD Asymmetry
(Prescott, Hughes…)
e+De+X -Z Interference
ARL= R-L/R+L2x10-4Q2GeV-2(1-2.5sin2W)
~10-4Expected
Exp. Gave ARLexp=1.5x10-4sin2W=0.21(2)
Confirmed SU(2)LxU(1)Y SM!
±10% Determination of sin2W Precision!

7. sin2W(mZ)MS=3/8[1-109/18ln(mX/mZ)+…]
Seemed to agree with GUTS (SU(5), SO(10)…)
sin2W=3/8 at unification =mX2x1014GeV
sin2W(mZ)MS=3/8[1-109/18ln(mX/mZ)+…]
0.21! (Great Desert?)
But later, minimal SU(5) ruled out by proton decay
exps (pe+)>1033yr mX>5x1015GeV
SUSY GUT UnificationmX1016GeV p1035yr
For mSUSY(TeV)
sin2W(mZ)MS=0.232 (Good Current Agreement!)

8. sin2W needed better than 1% determination
1980s - Age of EW Precision
sin2W needed better than 1% determination
Renormalization Prescription Required
EW Radiative Corrections Computed
Finite and Calculable: DIS N, ve, APV (A. Sirlin &WJM)
mZ, mW, Z, ALR, AFB
Define Renormalized Weak Mixing Angle: sin2WR
sin20W=1-(m0W/m0Z)2=(e0/g0)2 Natural Bare Relation
sin2W1-(mW/mZ) On Shell Definition, Popular in1980s
Induces large (mt/mW)2 corrections
Now Largely Abandoned
sin2W()MSe2()MS/g2()MS Good for GUT running
No Large RC Induced
Theoretically Nice/ But Unphysical

9. sin2Wlep = Z coupling at the Z pole
very popular at LEP
= sin2W(mZ)MS (best feature)
sin2W(Q2) = Physical Running Angle
Continuous
Incorporates Z mixing loops: quarks, leptons, W
Precision measurements at the Z Pole (e+e-Zff)
Best Determinations
sin2W(mZ)MS = (26) ALR(1-4sin2W) (SLAC)
sin2W(mZ)MS = (29) AFB(bb) (CERN)
(3 sigma difference!)
World Average: sin2W(mZ)MS= (16)
IS IT CORRECT?

10. + mW=80.398(25)GeVsin2W(mZ)MS = 0.23104(15)
-1= , G= x10-5Gev-2, mZ= GeV
+ mW=80.398(25)GeVsin2W(mZ)MS = (15)
Implications: 114GeV<mHiggs<150GeV.
New Physics Constraints From: mW, sin2W, ,& G
S=ND/6 (ND=# of heavy new doublets, eg 4th generationND=4)
mW*= Kaluza-Klein Mass (Extra Dimensions)
GG( S+O(1)(mW/mW*)2+…)
sin2W(mZ)MS S ND&mW*
Average (16) (11) (2), mW*3TeV
ALR (26) (15) (SUSY)
AFB(bb) (29) (17) 9(3)! Heavy Higgs, mW*~1-2TeV
Very Different Interpretations. We failed to nail sin2W(mZ)MS!

12. What about low energy measurements?
DIS  Scattering: R(NX)/(NX)
Loop Effects  mt heavy! (Currently 173GeV)
Early sin2W(mZ)MS=0.233SUSY GUTS
NuTeV sin2W(mZ)MS=0.236(2) High?
Nuclear-Charge Symmetry Violation?
Radiative Corrections?
Other?

13. Atomic Parity Violation Strikes Back
1990 QW(Cs)exp=-71.04(1.38)(0.88) C. Wieman et al.
Electroweak RCQW(Cs)SM=PV( PV(0)sin2W(mZ)MS)
=-73.19(3)
1999 QW(Cs)exp=-72.06(28)(34) Better Atomic Th.
2008 QW(Cs)exp=-72.69(28)(39)sin2W(mZ)MS=0.2290(22)
2009 QW(Cs)exp=-73.16(28)(20)sin2W(mZ)MS=0.2312(16)!
0.5%  Major Constraint On “New Physics”
QW(Cs)=QW(Cs)SM( S-0.9(mZ/mZ)2+…)
eg S=0.00.4 mZ>1.2TeV, leptoquarks, Anapole Moment …

14. Radiative Corrections to APV (eN Interaction)
QW(Z,N)= PV(-N+Z(1-4PVsin2W(mZ)MS)
PV=1-/2(1/s2+4(1-4s2)(ln(mZ/M)2+3/2)+….)0.99
PV(0)=1-/2s2((9-8s2)/8s2+(9/4-4s2)(1-4s2)(ln(mZ/M)2+3/2)
-2/3(T3fQf-2s2Qf2)ln(mZ/mf)2+…)1.003
s2sin2W(mZ)MS= , M=Hadronic Mass Scale
Radiative Corrections to APV small & insensitive to hadronic unc.
Same Corrections Apply to elastic eN scattering as Q20, Ee<<mN

15. E158 at SLAC Pol eeee Moller) Ee50GeV on fixed target, Q2=0.02GeV2
ALR(ee)=-131(14)(10)x10-9  (1-4sin2W)
EW Radiative Corrections -50%! (Czarnecki &WJM)
Measured to 12% sin2W to 0.6%
sin2W(mZ)MS=0.2329(13) slightly high
Best Low Q2 Determination of sin2W
APV(Cs) & E158 sin2W(Q2) running
ALR(ee)exp=ALR(ee)SM(1+0.24T-0.33S+7(mZ/mZ)2…)
Constrains “New Physics” eq mZ>0.6TeV, H--,S, Anapole Moment, …

17. Goals of Future Experiments
High Precision: sin2W or better
Low Q2 Sensitivity to “New Physics”
mZ’ >1TeV, S< , SUSY Loops, Extra Dim., Compositeness….

18. Future Efforts QWEAK exp at JLAB being prepared
Will measure forward ALR(epep)  (1-4sin2W)=QW(p)
E=1.1GeV, Q20.03GeV2, Pol=0.801%ARL(ep)3x10-7
small ARL requires long running
Goal sin2W(mZ)MS= via 4% measurement of ALR
Will be best low energy measurement of sin2W
ALR(ep)exp=ALR(ep)SM(1+4(mZ/mZ)2+…)
eg mz~0.9TeV Sensitivity (Not as good as APV)
The Gorchtein - Horowitz Problem (PRL)
Z box diagrams: O(2Ee/mp) 6% of QW(p)!
RC Estimate needs to be checked
Proposed Qweak Theory Uncertainty < 2%?
JLAB Flagship Experiment

19. ALR(eeee) to 2.5% Future Efforts: Polarized Moller at JLAB
After 12GeV Upgrade
ALR(eeee) to 2.5%
sin2W(mZ)MS= !
Comparable to Z pole studies!
ALR(ee)exp=ALR(ee)SM(1+7(mZ/mZ)2+…)
Explores mZ1.5TeV Better than APV, S0.08 etc.
Future JLAB Flagship Experiment (difficult!)
Complementary to LHC Discoveries

20. Comparison of QW(p) & QW(Cs)
HPV=G/2[(C1uuu+C1ddd)e5e+
(C2uu5u+C2dd5d)ee+…]
QW(p)=2(2C1u+C1d)
QW(Cs)=2(188C1u+211C1d)
What about the C2q?

21. What About C2u and C2d? Renormalized at low Q2 by Strong Interactions
Measure in Deep-Inelastic Scattering (DIS), eD & ep
ARL(eDeX)2x10-4GeV-2Q2[(C1u-C1d/2)+f(y)(C2u-C2d/2)]
f(y)=[1-(1-y)2]/[1+(1-y)2]
Standard Model: C1u= (1-8sin2W/3)/2  0.20
C1d=-(1-4/sin2W/3)/2 -0.32
C2u= (1-4sin2W)/2 0.04
C2d =-(1-4sin2W)/2-0.04
C2q sensitive to RC & “New Physics” eg Z (SO(10))
Measure ARL to 0.25%?
Measure C2q to 1-2%? Theory (loops)?

22. JLAB 6 GeV DIS eDeX On the books
JLAB 12 GeV DIS eD Proposed (Likely)
Goals: Measure C2qs, “New Physics”, Charge Sym. Violation …
Effective Luminosity (Fixed Target) 1038cm-2sec-1!
What can ep and eD at e-Ion contribute?
Asymmetry F.O,M,A2N, AQ2, N1/Q2 (acceptance?)
High Q2 Better (but Collider Luminosity?)
K. Kumar Talk 100fb-1 Needed
Program can be started with lower luminosity
Do DIS ep, eD, eN at factor of 10 lower

23. Single and Double Polarization Asymmetries
Polarized e: AeRL=(RR+RL-LR-LL)/(RR+RL+LR+LL)Pe
Polarized p: ApRL=(RR+LR-RL-LL)/(RR+LR+RL+LL)Pp
Polarized D: Pu=Pd=PD
Use to determine quark polarizations
Polarized e&p or D AepRRLL= (RR-LL)/(RR+LL)Peff
Peff=(Pe+Pp)/(1+PePp)
like relativistic velocities addition1
eg Pe=0.85, Pp=0.70 Peff=0.972!
uncertainty: Peff/Peff=0.17Pe/Pe+0.08Pp/Pp small
If we determine (see above) Pp=0.700.014
Peff=0.972 Superb!
How to best utilize Peff?

24. Use polarized e & polarized p or D at EICARR,LLto 0.25%
Preliminary Comments
Use polarized e & polarized p or D at EICARR,LLto 0.25%
Systematics?
Peff determined to  % via ApRL & ADRL (possible?)
Other?
ADRR,LL(1-3.2sin2W) sin2W/sin2W=-0.4ADRR.LL/ADRR.LL
0.25% measurement of ADRR.LLsin2W=
Sensitive to “New Physics” eg S=0.05
Summary: Measure DIS RR, RL, LR, LL
Determine: Pquarks, Peff. sin2W precisely

25. LDRD ARL GOALS Elucidate Physics Case
Examine Machine and Detector Requirements For 0.1%
sin2W Determination
Include Full EW Radiative Corrections to DIS
Is 100fb-1 Sufficient? Doable?
Utility of Proton (Deuteron) Polarization? Precision sin2W
Stage 1 e-Ion Goals?
Study Pol. Quark dist. & Nuclear Effects (EMC, CSV)
Important Secondary EIC Goal? Expands Proposal?