Electric dipole moments of light nuclei from dimension-six operators

1. Electric dipole moments of light nuclei from dimension-six operators Jordy de Vries, Institute forAdvances Simulation, Institut für Kernphysik, and Jülich centerforhadronphysics In collaborationwith: E. Mereghetti (LBL), U. van Kolck (University of Arizona), R. Timmermans (KVI), W. Dekens (KVI), C.-P. Liu(NDHU ,Taiwan)

2. Outline of this talk • Part I: Different sources of Time-Reversal Violation • Part II:Chiral techniques • Part III: Observables • IIIa: Nucleon EDM • IIIb: Light-Nuclear EDMs

3. EDM’s in the Standard Model • Electroweak CP-violation • Nobel prize for predicting third generation • Pospelov, Ritz (2005) Highly Suppressed

4. Upperbound nEDM 10^ [e cm] Electroweak CP-violation 5 to 6 orders below upper bound Out of reach!

5. EDM’s in the Standard Model • Second source: QCD theta-term • Due to complicated vacuum structure of QCD • Causes a ‘new’ CP-violating interaction with coupling constant θ (in QED ~ ) • Size of θ is unknown

6. Upperbound nEDM 10^ [e cm] Theta Term Predictions If θ ~ 1 • Crewther et al. (1979) Sets θ upper bound: θ < 10-10

7. Supersymmetry predictions Electric Dipole Moments = “the poor man’s high-energy physics” (S. Lamoreaux)

8. Experiments on hadronicEDMs • New neutron EDM experiments at ILL, SNS, PSI, TRIUMF Baker et al PRL ’06 (ILL) current proposed

9. Experiments on hadronicEDMs • New neutron EDM experiments at ILL, SNS, PSI, TRIUMF Baker et al PRL ’06 (ILL) current proposed • Proton EDM inferred from diamagnetic atoms Griffith et al PRL ’09 (UW) current Dmitriev + Sen’kov PRL ’03 Ongoing experiments on Ra, Rn, Xe….

10. Experiments on hadronicEDMs • New kid on the block: Charged particle in storage ring Farley et al PRL ’04 Electric dipole moment Anomalous magnetic moment Bennett et al (BNL g-2) PRL ‘09 • Limit on muon EDM

11. Experiments on hadronicEDMs • New kid on the block: Charged particle in storage ring Farley et al PRL ’04 Electric dipole moment Anomalous magnetic moment Bennett et al (BNL g-2) PRL ‘09 • Limit on muon EDM COSY @ Jülich Brookhaven/Fermilab • Proposals to measure EDMs • of proton and deuteron at level • Other light nuclei? 3He or 3H?

12. Current Situation Measurement of a hadronic EDM ? New sources of CP-violation Standard Model: θ-term

13. Finding the Source

14. Finding the Source Can we pinpoint the microscopic source of P+T-violation from light-nuclearEDM measurements?

15. Standard Model as an EFT SUSY? 1 TeV ? Effectively becomes Standard Model 100 GeV Energy

16. Effective Field Theories • Start the analysis right below: >> 100 GeV • Degrees of freedom: Full SM field content • Symmetries: Lorentz, SU(3)xSU(2)xU(1) gauge symmetries

17. Effective Field Theories • Start the analysis right below: >> 100 GeV • Degrees of freedom: Full SM field content • Symmetries: Lorentz, SU(3)xSU(2)xU(1) gauge symmetries

18. Running through the scales Dekens & JdV, JHEP, ‘13 New Physics SUSY? Energy Integrate out heavy New Physics ? TeV 100 GeV 1 GeV

19. Running through the scales Dekens & JdV, JHEP, ‘13 New Physics SUSY? Energy Integrate out heavy New Physics ? TeV QCD running Integrate out heavy SM fields 100 GeV 1 GeV

20. Running through the scales Dekens & JdV, JHEP, ‘13 New Physics SUSY? Energy Integrate out heavy New Physics ? TeV QCD running Integrate out heavy SM fields 100 GeV QCD running 1 GeV Non-perturbative QCD Hadronic/nuclear EDMs Lattice or Chiral Perturbation Theory

21. Dimension-six sources • Add to the SM all possible T+P-odd contact interactions • They start at dimension six Buchmuller & Wyler NPB ‘86 Gradzkowski et al JHEP ’10 B W 100 GeV + + H H H Few GeV Energy

22. Dimension-six sources • Add to the SM all possible T+P-odd contact interactions • They start at dimension six Buchmuller & Wyler NPB ‘86 Gradzkowski et al JHEP ’10 B W 100 GeV + + H H H Quark chromo-EDM Quark EDM γ + + Few GeV Energy

23. Dimension-six sources • Add to the SM all possible T+P-odd contact interactions • They start at dimension six Weinberg PRL ‘89 100 GeV Few GeV Energy

24. Dimension-six sources • Add to the SM all possible T+P-odd contact interactions • They start at dimension six Weinberg PRL ‘89 100 GeV Gluon chromo-EDM Braaten et al PRL ‘90 Quark (C)EDM mixing + Few GeV Energy

25. Four-quark operators Ramsey-Musolf & Su Phys. Rep. ‘08 Maekawa et al NPA ’11 Only two gauge-invariant four-quark interactions (u, d quarks only) Energy Don’t insist on SU(2) gauge symmetry -> you find 10 interactions! q q q q

26. Four-quark operators Ramsey-Musolf & Su Phys. Rep. ‘08 Maekawa et al NPA ’11 Only two gauge-invariant four-quark interactions (u, d quarks only) Energy Hisano et al ’12 Dekens, JdV ‘13 Quite strong QCD enhancement: q q q q q q q q

27. Dimension-six sources • Add to the SM all possible T+P-odd contact interactions • They start at dimension six Ng & Tulin PRD ’12 Finally: One quark-Higgs-Higgs interaction 100 GeV Few GeV Energy

28. Dimension-six sources • Add to the SM all possible T+P-odd contact interactions • They start at dimension six Ng & Tulin PRD ’12 Finally: One quark-Higgs-Higgs interaction 100 GeV An additional unsuppressed 4q term Few GeV Energy

29. Dimension-four and -six sources γ Few GeV + + + QCD (θ-term) + Quark chromo-EDM Quark EDM Gluon chromo-EDM 3*4quark operators Different models predict different operator(s)!!! q q Energy q q

30. Dimension-four and -six sources γ Few GeV + + + QCD (θ-term) Quark chromo-EDM Quark EDM Gluon chromo-EDM four-quark left-right term (FQLR) 2 Chiral-invariant four-q terms q q Energy q q

31. Dimension-four and -six sources γ Few GeV + + + QCD (θ-term) Quark chromo-EDM Quark EDM Gluon chromo-EDM π π Chiral Perturbation Theory 100 MeV …….. + π γ Energy …….. +

32. Outline of this talk • Part I: Different sources of Time-Reversal Violation • Part II:Chiral techniques • Part III: Observables • IIIa: Nucleon EDM • IIIb: Light-Nuclear EDMs

33. Hierarchy among the sources Each source transforms differently under chiral and isospin symmetry ±,0 π 0 π

34. Hierarchy among the sources Each source transforms differently under chiral and isospin symmetry • θ-term breaks chiralsymmetry but conserves isospinsymmetry • because is isospin-breaking

35. Hierarchy among the sources Each source transforms differently under chiral and isospin symmetry • θ-term breaks chiralsymmetry but conserves isospinsymmetry • because is isospin-breaking Here NDA, for QCD sum rules: Pospelov+Ritz ‘05

36. Hierarchy among the sources Each source transforms differently under chiral and isospin symmetry • θ-term breaks chiralsymmetry but conserves isospinsymmetry • because is isospin-breaking Here NDA, for QCD sum rules: Pospelov+Ritz ‘05 New estimate: Bsaisou et al ‘12

37. Hierarchy among the sources Each source transforms differently under chiral and isospin symmetry • θ-term breaks chiralsymmetry but conserves isospinsymmetry • Quark chromo-EDM (+ FQLR) breaks chiral and isospinsymmetry • because is isospin-breaking Here NDA, for QCD sum rules: Pospelov+Ritz ‘05

38. Hierarchy among the sources Each source transforms differently under chiral and isospin symmetry • Gluon chromo-EDM + 4Q conserve chiral and isospinsymmetry • Both and break chiral symmetry. • Suppressed by and • Chiral symmetric nucleon-nucleon interactions become important

39. Hierarchy among the sources Each source transforms differently under chiral and isospin symmetry • Gluon chromo-EDM + 4Q conserve chiral and isospinsymmetry • Both and break chiral symmetry. • Suppressed by and q q • For quark EDM and -interactions are suppressed by q q

40. Hierarchy among the sources Each source transforms differently under chiral and isospin symmetry Mereghetti, Hockings, van Kolck, Ann. of. Phys. (2010), JdV et al, Ann. of. Phys. (2013)

41. Hierarchy among the sources Each source transforms differently under chiral and isospin symmetry Mereghetti, Hockings, van Kolck, Ann. of. Phys. (2010), JdV et al, Ann. of. Phys. (2013)

42. Six important interactions • EDMs of light nuclei at LO depend on six low-energy constant (LECs) π γ • Which of the six are important depends on the PT-odd source • and the nucleus under consideration! JdV, Higa, Liu, Mereghetti, Stetcu, Timmermans, van Kolck, PRC ‘11

43. Outline of this talk • Part I: Different sources of Time-Reversal Violation • Part II:Chiral techniques • Part III: Observables • IIIa: Nucleon EDM • IIIb: Light-Nuclear EDMs

44. The Nucleon Electric Dipole Moment • In principle calculate on lattice • Results available for theta term • Unfortunately: No results for dimension-six sources yet Talks by Ulf-G. Meiβner & G. Schierholz Shintani et al. PRD ’05, ‘07 ‘08 Berruto et al. PRD ’06 Horsley et al. ‘08 Guo & Meiβner JHEP ‘12

45. The Nucleon Electric Dipole Moment • Calculated for each source from the PT-odd chiralLagrangian • θ-term + quark chromo-EDM (FQLR) Nucleon EDM +

46. The Nucleon Electric Dipole Moment • Calculated for each source from the PT-odd chiralLagrangian • θ-term + quark chromo-EDM (FQLR) Nucleon EDM + Crewther et al., PLB ‘79 Pich, Rafael, NPB ‘91 Hockings, van Kolck, PLB ’05 Ottnad et al, PLB ‘10

47. The Nucleon Electric Dipole Moment • Calculated for each source from the PT-odd chiralLagrangian • quark EDM + gluon chromo-EDM + 4Q (loops are suppressed) Nucleon EDM

48. The Nucleon Electric Dipole Moment • Calculated for each source from the PT-odd chiralLagrangian • quark EDM + gluon chromo-EDM + 4Q (loops are suppressed) Nucleon EDM Loops appear at next-to-next-to-leading order

49. The Nucleon Electric Dipole Moment • Measurement of neutron or proton EDM can be fitted by any source • For each source proton EDM is of same order as neutron EDM JdV, Mereghetti, Timmermans, van Kolck, PLB. (2011)

50. The Nucleon Electric Dipole Moment • Current limit: Baker et al, PRL (2006) JdV, Mereghetti, Timmermans, van Kolck, PLB. (2011)