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(eNeX), … 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

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, sin2W(Q2), Radiative Corrections, “New Physics” requires roughly 100fb-1(1034cm-2s-1)• Lepton Flavor Violation: eg epX requires roughly one inverse attobarn=1000fb-1! To be competitive with BR(eX)~10-10

Rates & Backgrounds Need Thorough Study

SOME ISSUES

What are the Machine and Detector Requirements?

“New Physics Effects” (Z’, Leptoquarks, SUSY, S&T, LFV…)

sin2W(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

1) PV Weak Neutral Currents (Past, Present and Future)

• The SU(2)LxU(1)Y Weinberg-Salam Model: weak neutral current coupling

g/cosWZf(T3f-2Qfsin2W -T3f5)f

T3f=1/2, Qf=electric charge

A New Form of Parity Violation!

-Z Interference Parity Violation Everywhere!

Depends on sin2W

Atomic Parity Violation (APV)

• QW(Z,N) =Z(1-4sin2W)-N Weak Charge

W=Weak Mixing Angle

QW(p)=1-4sin2W0.08

QW(209Bi83) = -43 -332sin2W =-126 Bi Much Larger but Complicated Atomic Physics Originally APV not seen in Bi SM Ruled Out? (Later seen: Tl, Bi, Cs…)

QW(133Cs55)=-23-220sin2W

=-73.16(34) Recent(2008) Atomic Theory Improvement

1978 SLAC Polarized DIS eD Asymmetry (Prescott, Hughes…) e+De+X -Z Interference

ARL= R-L/R+L2x10-4Q2GeV-2(1-2.5sin2W) ~10-4Expected

Exp. Gave ARLexp=1.5x10-4sin2W=0.21(2)

Confirmed SU(2)LxU(1)Y SM!

±10% Determination of sin2W Precision!

Seemed to agree with GUTS (SU(5), SO(10)…)

sin2W=3/8 at unification =mX2x1014GeV

sin2W(mZ)MS=3/8[1-109/18ln(mX/mZ)+…] 0.21! (Great Desert?)

But later, minimal SU(5) ruled out by proton decay

exps (pe+)>1033yr mX>5x1015GeV

SUSY GUT UnificationmX1016GeV p1035yr

For mSUSY(TeV)

sin2W(mZ)MS=0.232 (Good Current Agreement!)

1980s - Age of EW Precision

sin2W needed better than 1% determination Renormalization Prescription Required EW Radiative Corrections Computed

Finite and Calculable: DIS N, ve, APV (A. Sirlin &WJM)

mZ, mW, Z, ALR, AFB

Define Renormalized Weak Mixing Angle: sin2WR

sin20W=1-(m0

W/m0Z)2=(e0/g0)2 Natural Bare Relation

sin2W1-(mW/mZ)2 On Shell Definition, Popular in1980s

Induces large (mt/mW)2 corrections Now Largely Abandoned

sin2W()MSe2()MS/g2()MS Good for GUT running No Large RC Induced

Theoretically Nice/ But Unphysical

sin2Wlep = Z coupling at the Z pole

very popular at LEP

= sin2W(mZ)MS+0.00028 (best feature)

sin2W(Q2) = Physical Running Angle Continuous Incorporates Z mixing loops: quarks, leptons, W

Precision measurements at the Z Pole (e+e-Zff) Best Determinations

sin2W(mZ)MS = 0.23070(26) ALR(1-4sin2W) (SLAC)

sin2W(mZ)MS = 0.23193(29) AFB(bb) (CERN) (3 sigma difference!)

World Average: sin2W(mZ)MS=0.23125(16) IS IT CORRECT?

•

-1=137.035999, G=1.16637x10-5Gev-2, mZ=91.1875GeV

+ mW=80.398(25)GeVsin2W(mZ)MS = 0.23104(15)

Implications: 114GeV<mHiggs<150GeV.

New Physics Constraints From: mW, sin2W, ,& G

S=ND/6 (ND=# of heavy new doublets, eg 4th generationND=4)

mW*= Kaluza-Klein Mass (Extra Dimensions)

GG(1+0.0085S+O(1)(mW/mW*)2+…) sin2W(mZ)MS S ND&mW*

Average 0.23125(16) +0.11(11) 2(2), mW*3TeV

ALR 0.23070(26) -0.18(15) (SUSY)

AFB(bb) 0.23193(29) +0.46(17) 9(3)! Heavy Higgs, mW*~1-2TeV

Very Different Interpretations. We failed to nail sin2W(mZ)MS!

What about low energy measurements?

• DIS Scattering: R(NX)/(NX)

Loop Effects mt heavy! (Currently 173GeV)

Early sin2W(mZ)MS=0.233SUSY GUTS

NuTeV sin2W(mZ)MS=0.236(2) High?

Nuclear-Charge Symmetry Violation?

Radiative Corrections?

Other?

Atomic Parity Violation Strikes Back

1990 QW(Cs)exp=-71.04(1.38)(0.88) C. Wieman et al.

Electroweak RCQW(Cs)SM=PV(-23-220PV(0)sin2W(mZ)MS) =-73.19(3)

1999 QW(Cs)exp=-72.06(28)(34) Better Atomic Th.

2008 QW(Cs)exp=-72.69(28)(39)sin2W(mZ)MS=0.2290(22)

2009 QW(Cs)exp=-73.16(28)(20)sin2W(mZ)MS=0.2312(16)! 0.5% Major Constraint On “New Physics”

QW(Cs)=QW(Cs)SM(1+0.011S-0.9(mZ/mZ)2+…)

eg S=0.00.4 mZ>1.2TeV, leptoquarks, Anapole Moment …

Radiative Corrections to APV (eN Interaction)

QW(Z,N)= PV(-N+Z(1-4PVsin2W(mZ)MS)

PV=1-/2(1/s2+4(1-4s2)(ln(mZ/M)2+3/2)+….)0.99

PV(0)=1-/2s2((9-8s2)/8s2+(9/4-4s2)(1-4s2)(ln(mZ/M)2+3/2)

-2/3(T3fQf-2s2Qf2)ln(mZ/mf)2+…)1.003

s2sin2W(mZ)MS=0.23125, M=Hadronic Mass Scale

Radiative Corrections to APV small & insensitive to hadronic unc.

Same Corrections Apply to elastic eN scattering as Q20, Ee<<mN

E158 at SLAC Pol eeee Moller)Ee50GeV on fixed target, Q2=0.02GeV2

ALR(ee)=-131(14)(10)x10-9 (1-4sin2W)

EW Radiative Corrections -50%! (Czarnecki &WJM)

Measured to 12% sin2W to 0.6%

sin2W(mZ)MS=0.2329(13) slightly high

Best Low Q2 Determination of sin2W

APV(Cs) & E158 sin2W(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, …

Goals of Future Experiments

• High Precision: sin2W0.00025 or better

• Low Q2 Sensitivity to “New Physics”

mZ’ >1TeV, S<0.1-0.2, SUSY Loops, Extra Dim., Compositeness….

Future Efforts

QWEAK exp at JLAB being prepared

Will measure forward ALR(epep) (1-4sin2W)=QW(p)

E=1.1GeV, Q20.03GeV2, Pol=0.801%ARL(ep)3x10-7

small ARL requires long running

Goal sin2W(mZ)MS=0.0008 via 4% measurement of ALR

Will be best low energy measurement of sin2W

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(2Ee/mp) 6% of QW(p)!

RC Estimate needs to be checked

Proposed Qweak Theory Uncertainty < 2%?

JLAB Flagship Experiment

Future Efforts: Polarized Moller at JLAB

After 12GeV Upgrade ALR(eeee) to 2.5%

sin2W(mZ)MS=0.00025! Comparable to Z pole studies!

ALR(ee)exp=ALR(ee)SM(1+7(mZ/mZ)2+…)

Explores mZ1.5TeV Better than APV, S0.08 etc.

Future JLAB Flagship Experiment (difficult!) Complementary to LHC Discoveries

Comparison of QW(p) & QW(Cs)

• HPV=G/2[(C1uuu+C1ddd)e5e+

(C2uu5u+C2dd5d)ee+…]

QW(p)=2(2C1u+C1d)

QW(Cs)=2(188C1u+211C1d)

What about the C2q?

What About C2u and C2d?

• Renormalized at low Q2 by Strong Interactions

Measure in Deep-Inelastic Scattering (DIS), eD & ep

ARL(eDeX)2x10-4GeV-2Q2[(C1u-C1d/2)+f(y)(C2u-C2d/2)]

f(y)=[1-(1-y)2]/[1+(1-y)2]

Standard Model: C1u= (1-8sin2W/3)/2 0.20

C1d=-(1-4/sin2W/3)/2 -0.32

C2u= (1-4sin2W)/2 0.04

C2d =-(1-4sin2W)/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)?

JLAB 6 GeV DIS eDeX 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, AQ2, N1/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

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 addition1

eg Pe=0.85, Pp=0.70 Peff=0.972!

uncertainty: Peff/Peff=0.17Pe/Pe+0.08Pp/Pp small

If we determine (see above) Pp=0.700.014

Peff=0.9720.0018 Superb!

How to best utilize Peff?

Preliminary Comments

Use polarized e & polarized p or D at EICARR,LLto 0.25%

Systematics?

Peff determined to 0.1-0.2% via ApRL & AD

RL (possible?)

Other?

ADRR,LL(1-3.2sin2W) sin2W/sin2W=-0.4AD

RR.LL/ADRR.LL

0.25% measurement of ADRR.LLsin2W=0.00023

Sensitive to “New Physics” eg S=0.05

Summary: Measure DIS RR, RL, LR, LL

Determine: Pquarks, Peff. sin2W precisely

LDRD ARL GOALS

Elucidate Physics Case

Examine Machine and Detector Requirements For 0.1%

sin2W Determination

Include Full EW Radiative Corrections to DIS

Is 100fb-1 Sufficient? Doable?

Utility of Proton (Deuteron) Polarization? Precision sin2W

Stage 1 e-Ion Goals?

Study Pol. Quark dist. & Nuclear Effects (EMC, CSV)

Important Secondary EIC Goal? Expands Proposal?