1. Mitglied der Helmholtz-Gemeinschaft Electric dipole moments of light nuclei from dimension-six operators Jordy de Vries, Institute for Advances Simulation, Institut für Kernphysik, and Jülich center for hadron physics In collaboration with: E. Mereghetti (LBL), U. van Kolck (University of Arizona), R. Timmermans (KVI), W. Dekens (KVI), C.-P. Liu(NDHU,Taiwan)

2. Mitglied der Helmholtz-Gemeinschaft 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. Mitglied der Helmholtz-Gemeinschaft EDM’s in the Standard Model Electroweak CP-violation Nobel prize for predicting third generation Highly Suppressed Pospelov, Ritz (2005)

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

5. Mitglied der Helmholtz-Gemeinschaft 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 Size of θ is unknown (in QED ~ )

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

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

8. Mitglied der Helmholtz-Gemeinschaft Baker et al PRL ’06 (ILL) New neutron EDM experiments at ILL, SNS, PSI, TRIUMF current proposed Experiments on hadronic EDMs

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

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

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

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

13. Mitglied der Helmholtz-Gemeinschaft Finding the Source

14. Mitglied der Helmholtz-Gemeinschaft Can we pinpoint the microscopic source of P+T- violation from light-nuclear EDM measurements? Finding the Source

15. Mitglied der Helmholtz-Gemeinschaft Standard Model as an EFT 1 TeV ? SUSY? 100 GeV Standard Model Energy Effectively becomes

16. Mitglied der Helmholtz-Gemeinschaft 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. Mitglied der Helmholtz-Gemeinschaft 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. Mitglied der Helmholtz-Gemeinschaft Running through the scales Energy New Physics SUSY? Integrate out heavy New Physics 100 GeV 1 GeV ? TeV Dekens & JdV, JHEP, ‘13

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

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

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

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

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

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

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

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

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

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

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

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

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

32. Mitglied der Helmholtz-Gemeinschaft 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. Mitglied der Helmholtz-Gemeinschaft Hierarchy among the sources π π 0 ±,0 Each source transforms differently under chiral and isospin symmetry

34. Mitglied der Helmholtz-Gemeinschaft Hierarchy among the sources because is isospin-breaking Each source transforms differently under chiral and isospin symmetry  θ-term breaks chiral symmetry but conserves isospin symmetry

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

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

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

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

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

40. Mitglied der Helmholtz-Gemeinschaft Hierarchy among the sources Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM+4Q 111 Mereghetti, Hockings, van Kolck, Ann. of. Phys. (2010), JdV et al, Ann. of. Phys. (2013) Each source transforms differently under chiral and isospin symmetry

41. Mitglied der Helmholtz-Gemeinschaft Hierarchy among the sources Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM+4Q 111 1 Mereghetti, Hockings, van Kolck, Ann. of. Phys. (2010), JdV et al, Ann. of. Phys. (2013) Each source transforms differently under chiral and isospin symmetry

42. Mitglied der Helmholtz-Gemeinschaft Six important interactions EDMs of light nuclei at LO depend on six low-energy constant (LECs) γ π 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. Mitglied der Helmholtz-Gemeinschaft 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. Mitglied der Helmholtz-Gemeinschaft 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. Mitglied der Helmholtz-Gemeinschaft Nucleon EDM + The Nucleon Electric Dipole Moment Calculated for each source from the PT-odd chiral Lagrangian θ-term + quark chromo-EDM (FQLR)

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

47. Mitglied der Helmholtz-Gemeinschaft Nucleon EDM The Nucleon Electric Dipole Moment Calculated for each source from the PT-odd chiral Lagrangian quark EDM + gluon chromo-EDM + 4Q (loops are suppressed)

48. Mitglied der Helmholtz-Gemeinschaft Calculated for each source from the PT-odd chiral Lagrangian quark EDM + gluon chromo-EDM + 4Q (loops are suppressed) Nucleon EDM The Nucleon Electric Dipole Moment

49. Mitglied der Helmholtz-Gemeinschaft 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) The Nucleon Electric Dipole Moment Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM + 4Q Proton EDM/ Neutron EDM O(1)

50. Mitglied der Helmholtz-Gemeinschaft Current limit: Baker et al, PRL (2006) JdV, Mereghetti, Timmermans, van Kolck, PLB. (2011) The Nucleon Electric Dipole Moment Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM + 4Q Proton EDM/ Neutron EDM O(1)

51. Mitglied der Helmholtz-Gemeinschaft Baker et al, PRL (2006) Certain SUSY-models, if natural Pospelov, Ritz (2005) JdV, Mereghetti, Timmermans, van Kolck, PLB. (2011) The Nucleon Electric Dipole Moment Current limit: Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM + 4Q Proton EDM/ Neutron EDM O(1)

52. Mitglied der Helmholtz-Gemeinschaft Baker et al, PRL (2006) Certain SUSY-models, if Pospelov, Ritz (2005) JdV, Mereghetti, Timmermans, van Kolck, PLB. (2011) The Nucleon Electric Dipole Moment Current limit: Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM + 4Q Proton EDM/ Neutron EDM O(1)

53. Mitglied der Helmholtz-Gemeinschaft F Q2Q2 d EDM Schiff Moment The Nucleon Schiff Moment

54. Mitglied der Helmholtz-Gemeinschaft The Nucleon Schiff Moment Calculated for each source from the PT-odd chiral Lagrangian θ-term + quark chromo-EDM (FQLR) Schiff Moment Ottnad et al, PLB ’10 Mereghetti et al, PLB ‘11

55. Mitglied der Helmholtz-Gemeinschaft The Nucleon Schiff Moment Calculated for each source from the PT-odd chiral Lagrangian quark EDM + gluon chromo-EDM + 4Q (loops are suppressed) Schiff Moment are very small JdV et al, PLB ’11

56. Mitglied der Helmholtz-Gemeinschaft Theta termQuark CEDMQuark EDMGluon CEDM Proton EDM/ Neutron EDM O(1) Schiff Moments could separate (theta & qCEDM) from (qEDM & gCEDM) Can they be measured? JdV, Mereghetti, Timmermans, van Kolck, PLB. (2011) The Nucleon Schiff Moment

57. Mitglied der Helmholtz-Gemeinschaft EDMs of light nuclei Measurement of neutron and proton EDM not enough for disentangling the source Need more observables Light nuclei can be described within same framework as the nucleon using chiral effective field theory Only nucleons is not enough!

58. Mitglied der Helmholtz-Gemeinschaft Storage rings experiments Anomalous magnetic moment Electric dipole moment Farley et al PRL ’04 Proton at brookhaven/Fer milab? All-purpose ring (proton, deuteron, helion) at COSY?

59. Mitglied der Helmholtz-Gemeinschaft EDM of a general light nucleus EDM of a nucleus with A nucleons can be separated in 2 contributions

60. Mitglied der Helmholtz-Gemeinschaft EDM of a general light nucleus EDM of a nucleus with A nucleons can be separated in 2 contributions PT-odd admixtured wave-function

61. Mitglied der Helmholtz-Gemeinschaft EDM of a general light nucleus EDM of a nucleus with A nucleons can be separated in 2 contributions PT-odd admixtured wave-function = P+T violating NN potential

62. Mitglied der Helmholtz-Gemeinschaft EDM of a general light nucleus EDM of a nucleus with A nucleons can be separated in 2 contributions Phenomenological Potentials Argonne 18, Nijmegen II, Reid93 Should be replaced by chiral potentials

63. Mitglied der Helmholtz-Gemeinschaft EDM of a general light nucleus EDM of a nucleus with A nucleons can be separated in 2 contributions Different for every source!

64. Mitglied der Helmholtz-Gemeinschaft EDM of a general light nucleus The most important ingredients are the PT-odd Potential + Currents They are derived from the PT-odd Lagrangian (unique for each source) = theta-term = quark colour-EDM + FQLR or = gluon color-EDM + 4Q + Maekawa, Mereghetti, JdV, van Kolck, NPA (2011) PT-potential

65. Mitglied der Helmholtz-Gemeinschaft EDM of a general light nucleus The most important ingredients are the PT-odd Potential + Currents They are derived from the PT-odd Lagrangian (unique for each source) = theta-term PT-potential Maekawa, Mereghetti, JdV, van Kolck, NPA (2011) Isospin breaking and relativistic corrections NNLO LO

66. Mitglied der Helmholtz-Gemeinschaft The deuteron EDM Deuteron EDM at LO in principle 3 contributions π One-body: T-violating pion-exchange T-violating NN interactions

67. Mitglied der Helmholtz-Gemeinschaft Must be Isovector! The deuteron EDM Deuteron is a special case due to N=Z

68. Mitglied der Helmholtz-Gemeinschaft Deuteron is a special case due to N=Z Must be Isovector! The deuteron EDM

69. Mitglied der Helmholtz-Gemeinschaft The deuteron EDM We recycle the work of Liu+Timmermans PRC ‘04 Obtain deuteron wave function from phenomenological potentials (Argonne 18, Nijmegen II, Reid93) Results differ within 5% for different potentials Afnan, Gibson PRC ‘10 π 0

70. Mitglied der Helmholtz-Gemeinschaft The deuteron EDM We recycle the work of Liu+Timmermans PRC ‘04 Obtain deuteron wave function from phenomenological potentials (Argonne 18, Nijmegen II, Reid93) Results differ within 5% for different potentials Afnan, Gibson PRC ‘10 π 0 Khriplovich+Korkin NPA ’00 Liu+Timmermans PRC ’04 JdV et al PRC ’11 Bsaisou et al ‘12

71. Mitglied der Helmholtz-Gemeinschaft The deuteron EDM Which effect dominates depends on the ratio of the LECs π 0

72. Mitglied der Helmholtz-Gemeinschaft The deuteron EDM Which effect dominates depends on the ratio of the LECs This depends on the fundamental source! Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM + 4Q 1 π 0

73. Mitglied der Helmholtz-Gemeinschaft The deuteron EDM Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM + 4Q Deuteron EDM/ (neutron+proton EDM) 111 For 3 out of 4 sources is approximately For qCEDM/FQLR JdV, Mereghetti, Timmermans, van Kolck, PRL ‘11

74. Mitglied der Helmholtz-Gemeinschaft The deuteron EDM Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM + 4Q Deuteron EDM/ (neutron+proton EDM) 111 For 3 out of 4 sources is approximately For qCEDM/FQLR For qCEDM/FQLR significantly larger than O(20%) JdV, Mereghetti, Timmermans, van Kolck, PRL ‘11

75. Mitglied der Helmholtz-Gemeinschaft The deuteron EDM Theta term Quark CEDM+FQLR Quark EDM Gluon CEDM + 4Q Deuteron EDM/ (neutron+proton EDM) 111 For 3 out of 4 sources is approximately For qCEDM/FQLR For qCEDM/FQLR significantly larger than Exact value of can be used to identify strong CP-violation JdV, Mereghetti, Timmermans, van Kolck, PRL ‘11 O(20%) Bsaisou et al, EJPA ‘13

76. Mitglied der Helmholtz-Gemeinschaft Helion (3He) and Triton (3H) EDMs The same strategy as for the deuteron EDM has been employed to calculate the EDMs of 3He and 3H Stetcu et al, PLB ’08 JdV et al PRC ’ 11 Song et al PRC ‘13 Bsaisou, Wirzba et al, in prep

77. Mitglied der Helmholtz-Gemeinschaft Helion (3He) and Triton (3H) EDMs The same strategy as for the deuteron EDM has been employed to calculate the EDMs of 3He and 3H Additional difficulties due to short-range interactions (but appear to be small) Stetcu et al, PLB ’08 JdV et al PRC ’ 11 Song et al PRC ‘13 Bsaisou, Wirzba et al, in prep += + Gluon chromo-EDM + 4Q

78. Mitglied der Helmholtz-Gemeinschaft Helion (3He) and Triton (3H) EDMs The same strategy as for the deuteron EDM has been employed to calculate the EDMs of 3He and 3H Also new features in 3-body system for certain four-quark operators Unique chiral properties induce a PT-odd three-body force at LO Stetcu et al, PLB ’08 JdV et al PRC ’ 11 Song et al PRC ‘13 Bsaisou, Wirzba et al, in prep FQLR Disclaimer: no quantitative calculations yet JdV et al AOP ’ 13

79. Mitglied der Helmholtz-Gemeinschaft We can now combine the predictions for different sources Assume one source is dominant Separating the sources

80. Mitglied der Helmholtz-Gemeinschaft If also helion (triton) EDM deviate significantly from neutron (proton) EDM Point towards Standard Model (theta term) We can now combine the predictions for different sources Assume one source is dominant Separating the sources If deuteron EDM is approx. neutron + proton EDM Rule out quark chromo-EDM and certain four-quark operators Further quantitave tests

81. Mitglied der Helmholtz-Gemeinschaft We can now combine the predictions for different sources Assume one source is dominant Separating the sources If deuteron EDM much larger than neutron + proton EDM New physics in form of quark chromo-EDM or four-quark operators Further tests Predict other EDMs or higher moments (i.e. Schiff or magnetic quadrupole)

82. Mitglied der Helmholtz-Gemeinschaft Measurements on nucleon and light nuclear EDMs can shed light on the mechanism of T-violation So!

83. Mitglied der Helmholtz-Gemeinschaft A single hadronic EDM measurement can be fitted by theta (Standard Model) or by new physics At low energies the effects of new physics can be captured by effective interactions of dimension-six Standard techniques used to build the chiral T-odd Lagrangian Different sources Different chiral Lagrangians We have built a consistent framework for quantitative calculations of T-odd observables in A=1,2,3,..? nuclear systems The framework allows the disentanglement of the various T-odd sources Conclusions/Summary