1. Electric Dipole Moment Goals and “New Physics” William J. Marciano 12/7/09 d p with 10 -29 e-cm sensitivity! Why is it important?

2. d p not “just” complementary to d n Outstanding Discovery Potential!  Baryogenesis! (why do we exist?) Potential sensitivity an order of magnitude better than d n ! Probes New Physics(NP) at (1TeV/  NP ) 2 tan  NP  10 -7 ! or for  NP ~O(1)   NP ~3000TeV! (well beyond LHC) Paves the way for a new generation of storage ring experiments d p  d D, d( 3 He), d(radioactive nuclei), d 

3. Baryogenesis 1928 The Dirac Equation QM+Special Rel.+Spin+EM Gauge Invariance i(   - ieA µ (x))    (x) = m e  (x) First Order Mag. Moment:  =g e Qe/2m e s g e =2! Great Success-Cornerstone of Modern Physics Later realized  AntiMatter  positron! Why is the Universe Matter-Antimatter Asymmetric? (1964-CP Violation Discovered-Not Strong Enough) “New Physics” Source of CP Violation Needed!

4. Baryogenesis & New Physics CP Violation Examples of New Physics Models with potentially large CP Violation: Supersymmetry, Multi-Higgs, L-R Models, 4th Generation, Extra Dimensions… Generic Manifestation - Electric Dipole Moments What is the “New Physics”? Look for EDMs! No Standard Model Background (too small)

5. 1947 Small Anomalous Atomic Fine Structure Effects We could add extra terms to the Dirac Equation e/4m e a e F  (x)    (x) + i/2d e   F  (x)    (x) Anomalous Mag. Mom. Electric Dipole Mom. g e =2(1+a e ) (Violates P&T(CP) Electron g e =2.002 Not Observed Proton g p =5.59 |d e |<2x10 -27 e-cm But It Must Exist! 1948 Schwinger Calculates: a e =  /2  ≈0.00116 Agreed with measurement of Kusch & Foley! Great Success of QED -Quantum Field Theory

6. General Formalism (Spin1/2 Form Factors) =  u f (p’)   u f (p)   =F 1 (q 2 )   +iF 2 (q 2 )   q -F 3 (q 2 )     q … F 1 (0)=Q f e electric charge F 2 (0)=a f Q f e/2m f anom. mag. mom. F 3 (0)=d f Q f el. dipole mom.

7. Effective Dim. 5 Dipole Operators H dipole =-1/2[F 2  f(x)   f(x)+iF 3  f(x)     f(x)]F  (x) F 2 &F 3 Real, Finite & Calculable in Ren. QFT Complex Formalism: F D =F 2 +iF 3 H dipole =-1/2[F D  f L   f R +F D *  f R   f L ]F  F D =|F D |e i  (Relative to m f ) |F D |=(F 2 2 +F 3 2 ) 1/2, tan  =F 3 /F 2 tan  = Relative Degree of CP Violation egs. |tan  e | SM  10 -24 |tan  n | SM  10 -20

8. Anomalous Magnetic Dipole Moments fermion a f exp |d f (e/2m f ) exp | e 0.00115965218073(28) <1x10 -16  0.00116592089(63) <3x10 -6 p 1.792158142(28) <3x10 -12 (new d Hg ) n -1.9130427(5) <1x10 -13 “New Physics” expected to scale as (m f /  ) 2 (m  /m e ) 2  43000 Muon only a f sensitive to high  ~2TeV! All d f sensitive to “New Physics” if tan  NP not too small Nucleon edms Isovector or isoscalar? Mixed? Both d n and d p need to be measured!

9. “New Physics” Effects SUSY 1 loop a  Corrections (Most Likely Scenario)

10. SUSY Loops are like EW, but depend on: 2 spin 1/2  - (charginos) 4 spin 1/2  0 (neutralinos) including dark matter! spin 0 sneutrinos and sleptons with mixing Enhancement tan  =  2  /  1  ~3-40! Potentially large CP Violating Phases

11.  a  =a  exp -a  SM =255(63)(49)x10 -11 (3.2  !) New Physics? Nearly 2xStandard Model EW! Most Natural Explanation: SUSY Loops Generic 1 loop SUSY Conribution: a  SUSY = (sgn  )130x10 -11 (100GeV/m susy ) 2 tan  tan  3-40, m susy  100-500GeV Natural Explanation Other Explanations: Hadronic?      +isospin data (  a  =~157(63)(52)x10 -11 (2  )) Other New Physics ≤ 2TeV eg Extra Dimensions

12. If SUSY is responsible for g  -2 Happy Days Implications: sgn  0 (dark matter searches easier) SUSY at LHC very likely edms,  e , … Good Bets All chiral changing amplitudes L  R Enhanced by tan  ~ 3-40 factor But, why haven’t we seen edms if susy is correct?

13. Electric Dipole Moments: d e,d n,d p, d , d Hg (new) Many d n searches, starting with pioneering exp. Purcell & Ramsey Recent improvement in Atomic edn exps. Griffith, Swallows, Loftus, Romalis, Heckel & Fortson PRL102, 101601 (2009) Some Implications of  d Hg  <3.1x10 -29 e-cm d p (e-cm)<7.9x10 -25 Best d n (e-cm)<5.8x10 -26 ( Direct d n <2.9x10 -26 Best) d e (e-cm)<3x10 -27 (Tl: d e <1.6x10 -27 Best) Further factor 3-5 Improvement Expected!

14. Future Expectations d n  10 -27 -10 -28 e-cm Spallation Neutron Sources d p  10 -28 -10 -29 e-cm Storage Ring Proposal (BNL) d D  10 -29 e-cm Storage Ring Proposal d e  10 -30 e-cm or better d   10 -24 e-cm Storage Ring Proposal If SUSY is responsible for  a  deviation, then a susy loop induced observable edm may be right around the corner! Source of CP Violation in Baryogenesis?

15. If the same “New Physics” (  NP =100-1000GeV) responsible for  a  is also giving edms, we expect (scaling with m f ): |d  NP | ~ 3x10 -22 tan   NP e-cm |d e NP | ~ 2x10 -24 tan  e NP e-cm |d n NP | ~ 10 -22 tan  n NP e-cm |d p NP | ~ 10 -22 tan  p NP e-cm Future Experiments will have sensitivity:   NP ~10 -2 -10 -3  e NP ~  n NP ~10 -6  p NP ~10 -7 !

16. d p & d n Relationship Constituent Quark Model: d n =4/3d d -1/3d u d p =4/3d u -1/3d d Roughly 1/4<|d p /d n |<4 Similar Magnitudes Isovector (d p -d n )/2 or Isoscalar (d p +d n )/2? Need both d n & d p  d d & d u (Relationship?)  QCD leading effect isovector (  PT) d n =-d p ~3.6x10 -16  QCD e-cm

17. Currently: d n  QCD <10 -10 ! Future: 10 -12 d p at 10 -29 e-cm explores  QCD <10 -13 If a non-zero d n is discovered, the first thing we want to do is know d p Opposite sign? Isovector,  QCD Interpretation Same Sign?  QCD Unlikely More Likely: strangeness, gluonic, susy… Both d n & d p needed!

18. Physics Reach of d p ~10 -29 e-cm d p  0.01(m p /  NP ) 2 tan  NP e/2m p  10 -22 (1TeV/  NP ) 2 tan  NP e-cm If  NP is of O(1),  NP ~3000TeV Probed! If  NP ~O(1TeV),  NP ~10 -7 Probed! Unique Capabilities!

19. Conclusion 1. Measurements of d n & d p with similar sensitivity essential to unfold underlying physics. Explain Baryogenesis 2. d p has potential to do (10x) better than d n 3. d p at 10 -29 e-cm must do exp. if possible. Explores physics up to scales O(3000TeV) for  NP ~O(1) i.e. beyond LHC or  NP  10 -7 at LHC discovery scales! 4. Sets stage for d D =d n +d p +d(2 body), d( 3 He)…