1. Electroweak Physics at an EIC: Theory Prospects M.J. Ramsey-Musolf Wisconsin-Madison http://www.physics.wisc.edu/groups/particle-theory/ NPAC Theoretical Nuclear, Particle, Astrophysics & Cosmology INT, October 2009

2. Questions What are the opportunities for probing the “new Standard Model” and novel aspects of nucleon structure with electroweak processes at an EIC? What EIC measurements are likely to be relevant after a decade of LHC operations and after completion of the Jefferson Lab electroweak program? How might a prospective EIC electroweak program complement or shed light on other key studies of neutrino properties and fundamental symmetries in nuclear physics?

3. Outline Lepton flavor violation: e - +A K  - + A Neutral Current Processes: PV DIS & PV Moller Charged Current Processes: e - +A K E T + j Disclaimer: some ideas worked out in detail; others need more research

4. Lepton Number & Flavor Violation LNV & Neutrino Mass  Mechanism Problem CLFV as a Probe  K e Conversion at EIC ? Uncovering the flavor structure of the new SM and its relationship with the origin of neutrino mass is an important task. The observation of charged lepton flavor violation would be a major discovery in its own right.

5.  -Decay: LNV? Mass Term? Dirac Majorana Theory Challenge: matrix elements+ mechanism

6.  -Decay: Mechanism Dirac Majorana Theory Challenge: matrix elements+ mechanism Mechanism: does light M exchange dominate ? How to calc effects reliably ? How to disentangle H & L ? O(1) for  ~ TeV

7.  -Decay: Interpretation  signal equivalent to degenerate hierarchy Loop contribution to m of inverted hierarchy scale

8. Sorting out the mechanism Models w/ Majorana masses (LNV) typically also contain CLFV interactions RPV SUSY, LRSM, GUTs (w/ LQ’s) If the LNV process of  arises from TeV scale particle exchange, one expects signatures in CLFV processes  K e Conversion at EIC could be one probe

9. CLFV, LNV & the Scale of New Physics MEG:   ~ 5 x 10 -14  2e: B  ->e ~ 5 x 10 -17 Also PRIME  !e  : M1  !e  : M1 ! R ~  R = B  ->e B  ->e  Comparison of results could provide diagnostic for scale of CLV High scale CLNV ! M1 transitions and R ~   Low scale CLNV ! Penguin operator for conversion and R ~ 1

10. Lepton Flavor & Number Violation MEG: B  ->e  ~ 5 x 10 -14  2e: B  ->e ~ 5 x 10 -17 Logarithmic enhancements of R Raidal, Santamaria; Cirigliano, Kurylov, R- M, Vogel 0  decay RPV SUSY LRSM Tree Level Low scale LFV: R ~ O(1) GUT scale LFV: R ~ O 

11.  Lepton Flavor & Number Violation Exp: B  ->e  ~ 1.1 x 10 -7 EIC:  ~ 10 3 | A 1  e | 2 fb Raidal, Santamaria; Cirigliano, Kurylov, R- M, Vogel Logarithmic enhancements of R |A 2  e | 2 < 10 -8 EIC:  ~ 10 -5 fb If |A 2  e | 2 ~ |A 1  e | 2 Log or tree-level enhancement: |A 1  e | 2 / |A 2  e | 2 ~ | ln m e / 1 TeV | 2 ~ 100 B  Ke   48    |A 2  e | 2 Need ~ 1000 fb M1 operator Penguin op Refined  analysis: Gonderinger & R-M

12.  CLFV & Other Probes Exp: B  ->e  ~ 1.1 x 10 -7 EIC:  ~ 10 3 | A 1  e | 2 fb h  e h ee + h  h  e + h  h  e  if RH; PV Moller if LH  Ke(   Doubly Charged Scalars  Ke(   h ee h e  + h e  h  + h e  h  All h ab $ m if part of see- saw LHC:     BRs (in pair prod) Possible for effects in  eCLFV are >> than in  eCLFV

13. LFV w/  leptons: HERA & Rare Decays Veelken (H1, Zeus) (2007) Leptoquark Exchange: Like RPV SUSY /w /  eqq eff op  lq | 2 < 10 -4 (M LQ / 100 GeV) 2 HW Assignment: Induce  Ke  at one loop? Consistent with B  Ke  ? HERA & rare decay limits look stronger Connection w/ m &  in GUTS ? Applicable to other (non-LQ) models that generate tree- level ops? Gonderinger, R-M in process

14. Direct probes of LNV e - + A(Z,N) !       + X Suppressed? L (q,e) = e.g. Like  with: e !  ’ 111 !    ’ 211, ’ 311 h ee !   h e  , h e   e - + A(Z,N) !       + W - + X LHC: qq ’ ! W +* !    

15. Neutral Current Probes: PV Effective eq PV couplings in SM & beyond New physics ? SUSY, Z’, LQ as illustration Probing QCD

16. C 1,2 and Radiative Corrections Tree Level Radiative Corrections sin 2 Flavor-independent Normalization Scale-dependent effective weak mixing Flavor-dependent Constrained by Z-pole precision observables Large logs in  Sum to all orders with running sin 2  W & RGE

17. Weak Mixing in the Standard Model Scale-dependence of Weak Mixing JLab Future SLAC Moller Parity-violating electron scattering Z 0 pole tension

18. PVES & New Physics …  1j1 Radiative Corrections RPV SUSYZ / BosonsLeptoquarks Doubly Charged Scalars  h ee Semi-leptonic only Moller only

19. PVES & APV Probes of SUSY  Q W P, SUSY / Q W P, SM RPV: No SUSY DM Majorana s SUSY Loops  Q W e, SUSY / Q W e, SM g  -2  12 GeV  6 GeV E158 Q-Weak (ep)Moller (ee)  Kurylov, RM, Su Hyrodgen APV or isotope ratios Global fit: M W, APV, CKM,  l 2,…

20. Comparing A d DIS and Q w p,e e p RPV Loops

21. Probing Z’ : LHC Discovery Petriello (CIPANP 09) Heterotic string motivated Z’

22. Probing Z’ : PVES & LHC Petriello (CIPANP 09) See also Chang, Ng, & Wu: 0901.0163 PV Couplings: q R e L Leptonic PV Couplings: e L,R Qweak: Break LHC Sign Degeneracy LHC: Cone in e L - e R plane Moller: Hyperbola

23. Probing Leptoquarks with PVES General classification: SU(3) C x SU(2) L x U(1) Y Q-Weak sensitivities: SU(5) GUT: m ,  prot LQ 2 15 H Dorsner & Fileviez Perez, NPB 723 (2005) 53 Fileviez Perez, Han, Li, R-M NPB 819 (2009) 139

24. Leptoquarks: PVES, m  & LHC PV Sensitivities Fileviez Perez, Han, Li, R-M NPB 819 (2009) 139 4% Q W p (M LQ =100 GeV) LHC Search = M  v 

25. PVES, New Physics, & the LHC …  1j1 Radiative Corrections RPV SUSYZ / BosonsLeptoquarks Doubly Charged Scalars < 1.5 TeV Masses ~ few 100 GeV & large tan   h ee Moller: ~ 2.5% on A PV PVDIS: ~ 0.5% on A PV Need L ~ 10 33 - 10 34 Glatzmaier, Mantry, & R-M in process Could a separate determination of the C 2q term in PV DIS provide a more powerful probe than Q-Weak? Theoretically cleaner at EIC energies compared to Jlab PVDIS: larger Q 2 & smaller HT uncertainties ?

26. Deep Inelastic PV: Beyond the Parton Model & SM e-e- N X e-e- Z*Z* ** d(x)/u(x): large x Electroweak test: e-q couplings & sin 2  W Higher Twist: qq and qqg correlations Charge sym in pdfs

27. PVDIS & QCD Low energy effective PV eq interaction PV DIS eD asymmetry: leading twist Higher Twist (J Lab) CSV (J Lab, EIC) d/u (J Lab, EIC) +

28. Bjorken & Wolfenstein ‘78 Isospin decomposition: V = isovector S = isoscalar y-independent term: C 1q Differences in VV and SS: C 1q terms are “contaminated” only by 4q, double handbag  = 4 effects Isolates 4q HT operator: PVDIS a unique probe  0.2 Possible extraction of C 1q term at EIC w/ y- dependence? Comparison with Jlab PVDIS to extract four- quark HT correction ? On-going theoretical work: QCD evolution of HT contributions Use of neutrino data for HT in C 2q term Belitsky, Glatzmaier, Mantry, Paz, R-M, Sacco

29. Summary Precision studies and symmetry tests are poised to discovery key ingredients of the new Standard Model during the next decade There may be a role for an EIC in the post-LHC era Promising: PV Moller & PV DIS for neutral currents Homework: Charged Current probes -- can they complement LHC & low-energy studies? Intriguing: LFV with eK  conversion: