Precision sin 2 θ W (Q 2 ) & Electroweak Physics at The EIC (Electron-Ion Collider) Based on talks at: W&M, Rockefeller, BNL and U.

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1 Precision sin 2 θ W (Q 2 ) & Electroweak Physics at The EIC (Electron-Ion Collider) William J. Marciano (October 26, 2010) Based on talks at: W&M, Rockefeller, BNL and U. Washington

2 Outline 1. General Discussion 2. WEAK NC PARITY VIOLATION i) APV vs Pol Electron Scattering ii) QWEAK, Moller, DIS (ed&ep) 3. sin 2 θ W (Q 2 ) Collider Requirements For Competitive A RL Program ~100fb -1 (K. Kumar et al.) 2009 Talk Y. Li (Recent) Δsin 2 θ W /sin 2 θ W =±0.2% *4. Utility of Both Beams Polarized

3 1. General Discussion Current US On Shore Collider Programs 1) SLAC e + e - b b factory (Ended!) 2) Fermilab 2TeV p p Collider Still Higgs Hunting (1-4 More Years?) (8fb -1 16fb -1 ) Future µ + µ - Collider? Needs lots of R&D (20+yrs) Meanwhile high intensity ν and µ physics 3) BNL RHIC & Polarized pp for Nuclear Physics Luminosity and Detector Upgrades ( 10 yr program) Last Collider Standing! Future polarized ep/eion collider? L ~10 34 cm -2 s -1

4 4) JLAB Fixed Target polarized ep, en scattering E e =6GeV 12GeV? L~10 38 cm -2 s -1! Mainly QCD/Nuclear Physics But Flagship A LR ep, ee, ed Experiments Precision sin 2 θ W and New Physics Effects Future Polarized ep, ed, e 3 He, eion Collider Goal L~10 35 cm -2 s -1! US has room for (at most) one EIC Cost $ M Affordable if the Physics Case is strong (In my view, EIC has a good chance to happen) Partly Because The US Needs a Collider!

5 EIC Physics Case Must be primarily a Nuclear/QCD Facility Structure functions (pol., PV)), small x gluons Properties of quarks in nuclei (EMC effects) Sum rules (Bj) etc, α(q 2 ) QCD HERA(ep): L~10 31 cm -2 s ,34,35 cm -2 s -1 polarized e,p,d, 3 He; Heavy Ions What about Electroweak Physics? Second Detector? Complementary Program!

6 BNL/LDRD Proposal 2009 Electroweak Physics with an Electron-Ion Collider (Deshpande, Kumar, Marciano, Vogelsang) Postdoc: Yingchuan Li DIS & Nuclear Structure Functions (γ,z,w) (Beyond HERA) Bjorken Sum Rule, Polarized EMC, PV Structure Functions A RL, sin 2 θ W (Q 2 ), Radiative Corrections, New Physics Lepton Flavor Violation: eg ep τx (1000fb -1!) Also, en µx vs µn en (Coherent Conversion) Various Issues That Need Thorough Study What are the Machine and Detector Requirements? Inclusion of Electroweak Radiative Corrections (Important?) Weak Ampitudes Squared vs Photon-Z Interference High Precision & Polarization(±0.5%?, ±0.25%?) Proton, D, 3 HE Polarization (Spin Content-Other?)

7 2. WEAK NC PARITY VIOLATION Atomic Parity Violation (APV) Q W (Z,N) =Z(1-4sin 2 θ W )-N Weak Charge θ W =Weak Mixing Angle Q W (p)=1-4sin 2 θ W =0.07 Q W ( 209 Bi 83 ) = sin 2 θ W =-127 Bi Much Larger but Complicated Atomic Physics Originally APV not seen in Bi SM Ruled Out? (Later seen in Tl, Bi, Cs ) 1978 SLAC Polarized ed Asymmetry (Prescott, Hughes ) e+d e+x γ-z Interference A RL = σ R -σ L /σ R +σ L 2x10-4 Q 2 GeV -2 (1-2.5sin 2 θ W )~10-4 Expected Exp. Gave A RL =1.5x10-4 sin 2 θ W =0.21(2)

8 Confirmed SU(2) L xu(1) Y SM! ±10% Determination of sin 2 θ W Precision! Seemed to agree with GUTS (SU(5), SO(10) ) sin 2 θ 0 W=3/8 at unification µ=m X 2x10 14 GeV sin 2 θ W (m Z ) MS =3/8[1-109α/18πln(m X /m Z )+ ] 0.21! (Great Desert?) But later, minimal SU(5) ruled out by proton decay exps τ(p e + π 0 )>10 33 yr m X >3x10 15 GeV SUSY GUT Unification (m susy ~1TeV) m X GeV τ p yr sin 2 θ W (m Z ) MS =0.233 (Good Current Agreement!)

9 1980s - Age of EW Precision sin 2 θ W needed better than ±1% determination Renormalization Prescription Required EW Radiative Corrections Computed Finite and Calculable: DIS ν µ N, v µ e, APV (A. Sirlin &WJM) m Z, m W, Γ Z, A LR, A FB Define Renormalized Weak Mixing Angle: sin 2 θ W R sin 2 θ 0 W=1-(m 0 W/m 0 Z) 2 =(e 0 /g 0 ) 2 Natural Bare Relation sin 2 θ W 1-(m W /m Z ) 2 On Shell Definition, Popular in1980s Induces large α(m t /m W ) 2 corrections Now Largely Abandoned sin 2 θ W (µ) MS e 2 (µ) MS /g 2 (µ) MS Good for GUT running No Large RC Induced Theoretically Nice/ But Unphysical

10 sin 2 θ W lep = Z µµ coupling at the Z pole very popular at LEP = sin 2 θ W (m Z ) MS (best feature) sin 2 θ W (Q 2 ) = Physical Running Angle Continuous Incorporates γz mixing loops: quarks, leptons, W ± Precision measurements at the Z Pole (e + e - Z ff) Best Determinations sin 2 θ W (m Z ) MS = (26) A LR (SLAC) sin 2 θ W (m Z ) MS = (29) (3.2 sigma difference!) A FB (b b) (CERN)

11 Leptonic vs Hadronic Z Pole Averages sin 2 θ W (m Z ) MS = (21) sin 2 θ W (m Z ) MS = (27) (Also differ by > 3sigma) Leptonic Hadronic World Average: sin 2 θ W (m Z ) MS = (16) IS IT CORRECT? (Major Implications)

12 α -1 = , G µ = (7)x10-5 Gev -2, m Z = GeV + m W =80.398(25)GeV sin 2 θ W (m Z ) = (15) Implications: 114GeV<m Higgs <150GeV. New Physics Constraints From: m W, sin 2 θ W, α,& G µ S=N D /6π (N D =# of heavy new doublets, eg 4th generation N D =4) m W* = Kaluza-Klein Mass (Extra Dimensions) G µ G µ ( S+O(1)(m W /m W* ) 2 + ) sin 2 θ W (m Z ) M S S N D &m W* Average (16) +0.11(11) 2(2), m W* 3TeV A LR (26) -0.18(15) (SUSY) A FB (b b) (29) +0.46(17) 9(3)! Heavy Higgs, m W* ~1-2TeV Very Different Interpretations. We failed to nail sin 2 θ W (m Z ) MS!

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14 What about low energy measurements? DIS ν Scattering: R ν σ(ν µ N ν µ X)/σ(ν µ N µx) loops m t heavy, sin 2 θ W (m Z ) MS =0.233 SUSY GUTS NuTeV sin 2 θ W (m Z ) MS =0.236(2) High? Rad. Corr.? Nuclear-Charge Symmetry Violation? Meanwhile: Atomic Parity Violation: 1990 Q W (Cs) exp =-71.04(1.38)(0.88) C. Wieman et al. Electroweak RC Q W (Cs) SM =ρ PV ( κ PV (0)sin 2 θ W (m Z ) MS ) =-73.19(3) 1999 Q W (Cs) exp =-72.06(28)(34) Better Atomic Th Q W (Cs) exp =-72.69(28)(39) sin 2 θ W (m Z ) MS =0.2290(22) 2009 Q W (Cs) exp =-73.16(28)(20) sin 2 θ W (m Z ) MS =0.2312(16)! ±0.5% Major Constraint On New Physics Q W (Cs)=Q W (Cs) SM ( S-0.9(m Z /m Zχ ) 2 + ) eg S=0.0±0.4 m Zχ >1.2TeV, leptoquarks,

15 Radiative Corrections to APV Q W (Z,N)= ρ PV (-N+Z(1-4κ PV sin 2 θ W (m Z ) MS ) ρ PV =1-α/2π(1/s 2 +4(1-4s 2 )(ln(m Z /M) 2 +3/2)+.) 0.99 κ PV (0)=1-α/2πs 2 ((9-8s 2 )/8s 2 +(9/4-4s 2 )(1-4s 2 )(ln(m Z /M) 2 +3/2) -2/3 (T 3f Q f -2s 2 Q f2 )ln(m Z /m f ) 2 + ) s 2 sin 2 θ W (m Z ) MS = , M=Hadronic Mass Scale Radiative Corrections to APV small and insensitive to hadronic unc. Same Corrections Apply to elastic en scattering as Q 2 0, E e <<m N

16 E158 at SLAC Pol ee ee Moller) E e 50GeV on fixed target, Q 2 =0.02GeV 2 A LR (ee)=-131(14)(10)x10-9 α (1-4sin 2 θ W ) EW Radiative Corretions -50%! (Czarnecki &WJM) Measured to ±12% sin 2 θ W to ±0.6% sin 2 θ W (m Z ) MS =0.2329(13) slightly high Best Low Q 2 Determination of sin 2 θ W A LR (ee) exp =A LR (ee) SM (1+0.13T-0.20S+7(m Z /m Zχ ) 2 ) Constrains New Physics eq m Zχ >0.6TeV, H --,S, Anapole Moment, Together APV(Cs) & E158 sin 2 θ W (Q 2 ) running sin 2 θ W (m Z ) MS =0.232(1) about ±0.5%

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18 Goals of Future Experiments High Precision: Δsin 2 θ W or better Low Q 2 Sensitivity to New Physics m Z >1TeV, S < , SUSY Loops, Extra Dim., 4th Generation.

19 Other A LR Experiments Strange Quark Content Program: Bates, JLAB, MAMI Proton strange charge radius and magnetic moment consistent with 0. Axial Vector effects and RC cloud strangeness. PREX Experiment: Neuton distribution Preparing the way for future experiments, pushing technology and instrumentation, polarization

20 Future Efforts QWEAK exp at JLAB Will measure forward A LR (ep ep) α (1-4sin 2 θ W )=Q W (p) E=1.1GeV, Q GeV 2, Pol=0.80±1% A RL (ep) 3x10-7 small A RL requires long running Goal Δsin 2 θ W (m Z ) MS = via ±4% measurement of A LR Will be best low energy measurement of sin 2 θ W A LR (ep) exp =A LR (ep) SM (1+4(m Z /m Zχ ) 2 + ) eg m zχ ~0.9TeV Sensitivity (Not as good as APV) The Gorchtein - Horowitz Nightmare (PRL) γz box diagrams: O(2αE e /πm p ) 6% of Q W (p)! Recently Confirmed (Improved): Sibirtev et al.; Gorchtein et al. Proposed Qweak Theory Uncertainty < 2% JLAB Flagship Experiment

21 Other Future Efforts: Polarized Moller at JLAB After 12GeV Upgrade A LR (ee ee) to ±2.5% Δsin 2 θ W (m Z ) MS =± ! Comparable to Z pole studies! A LR (ee) exp =A LR (ee) SM (1+7(m Z /m Zχ ) 2 + ) Explores m Zχ 1.5TeV Better than APV, S 0.1 etc. Future JLAB Flagship Experiment! Very Hard To Do Better! ep Collider Goal: ±0.2%

22 H PV =G µ / 2[(C 1u uγ ν u+c 1d dγ ν d) eγ ν γ 5 e+ (C 2u uγ ν γ 5 u+c 2d dγ ν γ 5 d )eγ ν e+ ] Q W (p)=2(2c 1u +C 1d ) Q W (Cs)=2(188C 1u +211C 1d ) Not renormalized by strong interactions at Q=0 What about the C 2q?

23 What About C 2u and C 2d? Renormalized at low Q 2 by Strong Interactions Measure in Deep-Inelastic Scattering (DIS), ed & ep A RL (ed ex) 2x10-4 GeV -2 Q 2 [(C 1u -C 1d /2)+f(y)(C 2u -C 2d /2)] f(y)=[1-(1-y) 2 ]/[1+(1-y) 2 ] Standard Model: C 1u = (1-8sin 2 θ W /3)/ C 1d =-(1-4sin 2 θ W /3)/ C 2u = (1-4sin 2 θ W )/ C 2d =-(1-4sin 2 θ W )/ C 2q sensitive to RC & New Physics eg Zχ (SO(10)) Measure A RL to ±1/2%? Measure C 2q to ±1-2%? Theory (loops)?

24 JLAB 6 GeV DIS ed ex Proceeding JLAB 12 GeV DIS ed Future Goals: Measure C 2q s, New Physics, Charge Sym. Violation Effective Luminosity (Fixed Target) cm -2 sec -1! What can ep and ed at e-ion contribute? Asymmetry F.O,M, A 2 N, A Q 2, N 1/Q 2 (acceptance?) High Q 2 Better (but Collider Luminosity?) K. Kumar Talk 100fb -1 (L cm -2 s -1 ) Needed Program can be started with lower luminosity Do DIS ep, ed, en at factor of 10 lower (Polarized p & Nuclei) Bjorken Sum Rule, Pol Structure Functions, Spin Distribution

25 Single and Double Polarization Asymmetries Polarized e: A e RL=(σ RR +σ RL -σ LL -σ LR )/(σ RR +σ RL +σ LL +σ LR ) P e Polarized p: A p RL=(σ RR +σ LR -σ RL -σ LL )/(σ RR +σ LR +σ RL +σ LL ) P p Polarized e&p A ep RRLL= (σ RR -σ LL )/(σ RR +σ LL ) P eff P eff =(P e -P p )/(1-P e P p ) opposite signs like relativistic velocities addition 1 eg P e =0.8±0.008, P p =-0.7±0.03 P eff =0.962±0.004 small uncertainty How to best utilize P eff? Measure: σ RR,σ LL,σ RL,σ LR Fit Polarization Dist.

26 Example: Polarized Protons or Deuterons (Unpolarized Electrons) C 1q C 2q (1-4sin 2 θ W ) Use to measure sin 2 θ W?

27 LDRD A RL GOALS Examine Machine and Detector Requirements For ±1% A RL Include EW Radiative Corrections to DIS Is 100fb -1 Sufficient? (Y. Li Δsin 2 θ W /sin 2 θ W =±0.2%) Utility of Proton Polarization? Stage 1 e-ion aim for ±4% Determine EW Structure Functions Study Nuclear Effects (EMC, CSV, Sum Rules) Important Secondary e-ion Goal? Improves Proposal?