Electroweak Physics At The EIC (Electron-Ion Collider) William J. Marciano (May 17, 2010) 1. WEAK NC PARITY VIOLATION i) APV vs Pol Electron Scattering ii) QWEAK, Moller, DIS (eD&ep) 2. Preliminary Collider Requirements For Competitive A RL Program ~100fb -1 (K. Kumar et al.) 2009 Talk *3. Utility of Both Beams Polarized

EIC Physics Case Must be primarily a Nuclear/QCD Facility Structure functions (polarized), small x gluons… Properties of quarks in nuclei (EMC effects)… Sum rules (Bj),  (Q 2 ) QCD … HERA(ep): L~10 31 cm -2 s -1  10 33,34,35 cm -2 s -1 polarized e,p,D, 3 He; Heavy Ions What about Electroweak Physics? Second Detector? Complementary Program!

BNL/LDRD Proposal 2009 Electroweak Physics with an Electron-Ion Collider (Deshpande, Kumar, Marciano, Vogelsang) DIS & Nuclear Structure Functions ( ,Z,W) (Beyond HERA) Bjorken Sum Rule, Polarized EMC… A RL, sin 2  W (Q 2 ), Radiative Corrections, “New Physics” Lepton Flavor Violation: eg ep  X (1000fb -1 !) Various Issues That Need Thorough Study What are the Machine and Detector Requirements? Inclusion of Electroweak Radiative Corrections (Important?) High Precision & Polarization(  0.5%?,  0.25%?) Proton, D, 3 HE Polarization (Spin Content-Other?)

1) PV Weak Neutral Currents (Past, Present and Future) Ancient History: By 1975 the SU(2) L xU(1) Y Weinberg-Salam Model was nearly established. Predicted Weak Neutral Currents seen in neutrino scattering at CERN! But did the NC have the right coupling? g 2 /cos  W Z  f   (T 3f -2Q f sin 2  W -T 3f  5 )f A New Form of Parity Violation! Non Maximal but Distinctive  -Z Interference  Parity Violation Everywhere!

Atomic Parity Violation (APV) Q W (Z,N) =Z(1-4sin 2  W )-N Weak Charge  W =Weak Mixing Angle Q W (p)=1-4sin 2  W =0.07 Q W ( 209 Bi 83 ) = sin 2  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  -Z Interference A RL =  R -  L /  R +  L  2x10 -4 Q 2 GeV -2 (1-2.5sin 2  W )~10 -4 Expected Exp. Gave A RL exp =1.5x10 -4  sin 2  W =0.21(2)

Confirmed SU(2) L xU(1) Y SM! ±10% Determination of sin 2  W Precision! Seemed to agree with GUTS (SU(5), SO(10)…) sin 2   W =3/8 at unification  =m X  2x10 14 GeV sin 2  W (m Z ) MS =3/8[1-109  /18  ln(m X /m Z )+…]  0.21! (Great Desert?) But later, minimal SU(5) ruled out by proton decay exps  (p  e +   )>10 33 yr  m X >3x10 15 GeV SUSY GUT Unification (m susy ~1TeV)  m X  GeV  p  yr sin 2  W (m Z ) MS =0.233 (Good Current Agreement!)

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

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

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

 -1 = , G  = x10 -5 Gev -2, m Z = GeV + m W =80.398(25)GeV  sin 2  W (m Z ) = (15) Implications: 114GeV<m Higgs <150GeV. New Physics Constraints From: m W, sin 2  W, ,& G  S=N D /6  (N D =# of heavy new doublets, eg 4th generation  N D =4) m W* = Kaluza-Klein Mass (Extra Dimensions) G   G  ( S+O(1)(m W /m W* ) 2 +…) sin 2  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  W (m Z ) MS !

What about low energy measurements? DIS Scattering: R  (  N   X)/  (  N  X) loops  m t heavy, sin 2  W (m Z ) MS =0.233  SUSY GUTS NuTeV sin 2  W (m Z ) MS =0.236(2) High? Rad. Corr.? Nuclear-Charge Symmetry Violation? Atomic Parity Violation Strikes Back 1990 Q W (Cs) exp =-71.04(1.38)(0.88) C. Wieman et al. Electroweak RC  Q W (Cs) SM =  PV (  PV (0)sin 2  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  W (m Z ) MS =0.2290(22) 2009 Q W (Cs) exp =-73.16(28)(20)  sin 2  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 Z  ) 2 +…) eg S=0.0  0.4 m Z  >1.2TeV, leptoquarks, …

Radiative Corrections to APV Q W (Z,N)=  PV (-N+Z(1-4  PV sin 2  W (m Z ) MS )  PV =1-  /2  (1/s 2 +4(1-4s 2 )(ln(m Z /M) 2 +3/2)+….)  0.99  PV (0)=1-  /2  s 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 f 2 )ln(m Z /m f ) 2 +…)  s 2  sin 2  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

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  (1-4sin 2  W ) EW Radiative Corretions  -50%! (Czarnecki &WJM) Measured to  12%  sin 2  W to  0.6%  sin 2  W (m Z ) MS =0.2329(13) slightly high Best Low Q 2 Determination of sin 2  W A LR (ee) exp =A LR (ee) SM (1+0.13T-0.20S+7(m Z /m Z  ) 2 …) Constrains “New Physics” eq m Z  >0.6TeV, H --,S, Anapole Moment, … Together APV(Cs) & E158  sin 2  W (Q 2 ) running sin 2  W (m Z ) MS =0.232(1)

Goals of Future Experiments High Precision:  sin 2  W  or better Low Q 2 Sensitivity to “New Physics” m Z’ >1TeV,  S  < , SUSY Loops, Extra Dim., 4th Generation….

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

Future Efforts QWEAK exp at JLAB Will measure forward A LR (ep  ep)  (1-4sin 2  W )=Q W (p) E=1.1GeV, Q 2  0.03GeV 2, Pol=0.80  1%  A RL (ep)  3x10 -7 small A RL requires long running Goal  sin 2  W (m Z ) MS = via  4% measurement of A LR Will be best low energy measurement of sin 2  W A LR (ep) exp =A LR (ep) SM (1+4(m Z /m Z  ) 2 +…) eg m z  ~0.9TeV Sensitivity (Not as good as APV) The Gorchtein - Horowitz Nightmare (PRL)  Z box diagrams: O(2  E e /  m p )  6% of Q W (p)! Recently Confirmed (Improved): Sibirtev et al.; Gorchtein et al. Proposed Qweak Theory Uncertainty < 2% JLAB Flagship Experiment

Longer Future Efforts: Polarized Moller at JLAB After 12GeV Upgrade A LR (ee  ee) to  2.5%  sin 2  W (m Z ) MS =  ! Comparable to Z pole studies! A LR (ee) exp =A LR (ee) SM (1+7(m Z /m Z  ) 2 +…) Explores m Z   1.5TeV Better than APV, S  0.1 etc. Future JLAB Flagship Experiment!

H PV =G  /  2[(C 1u  u  u+C 1d  d  d)  e   5 e+ (C 2u  u   5 u+C 2d  d   5 d  )e  e+…] Q W (p)=2(2C 1u +C 1d ) Q W (Cs)=2(188C 1u +211C 1d ) What about the C 2q ?

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  W /3)/2  0.20 C 1d =-(1-4sin 2  W /3)/2  C 2u = (1-4sin 2  W )/2  0.04 C 2d =-(1-4sin 2  W )/2  C 2q sensitive to RC & “New Physics” eg Z  (SO(10)) Measure A RL to  1/2%? Measure C 2q to  1-2%? Theory (loops)?

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…

Single and Double Polarization Asymmetries Polarized e: A e RL =(  RR +  RL -  LL -  LR )/(  RR +  RL +  LL +  LR )  P e Polarized p: A p RL =(  RR +  LR -  RL -  LL )/(  RR +  LR +  RL +  LL )  P p Polarized e&p A ep RRLL = (  RR -  LL )/(  RR +  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  small uncertainty How to best utilize P eff ? Measure:  RR,  LL,  RL,  LR Fit  Polarization Dist.

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

LDRD A RL GOALS Examine Machine and Detector Requirements For  1% Include EW Radiative Corrections to DIS Is 100fb -1 Sufficient? Utility of Proton Polarization? Stage 1 e-Ion aim for  4% Study Nuclear Effects (EMC, CSV, Sum Rules) Important Secondary e-Ion Goal? Improves Proposal?