NUCLEAR ELECTRIC DIPOLE MOMENTS OF FEW-NUCLEON SYSTEMS Young-Ho Song(RISP, Institute for Basic Science) Collaboration with Rimantas Lazauskas( IPHC, IN2P3-CNRS) Vladimir Gudkov( University of South Carolina) 8 th APCTP-BLTP JINR Joint Workshop Jeju, Korea

Outline Introduction T-reversal invariance violation Electric dipole moments(EDM) Current status of EDM search Formalism Nuclear EDM TVPV potential Numerical Results Discussion My work: Y.-H. Song, R. Lazauskas and V. Gudkov, Phys. Rev. C 87, (2013) Good Review: Jonathan Engel, Michael J. Ramsey-Musolf, and U. van Kolck, arXiv:

What is the origin of baryonic matter? Energy budget of Universe Dark Energy(75%) Dark matter (20%) Matter (5 %) Sakharov Criteria for Baryogenesis B violation C & CP violation Nonequilibrium dynamics Sakharov, 1967

CP and T Symmetry

Electric Dipole Moment

Any non-zero observation of Electric Dipole Moment of nucleon, lepton, nuclei or atom is a signal of beyond standard model(or QCD theta-term) ! CKM matrix prediction on the EDM are highly suppressed and beyond the accuracy of experiments in near future. BSM frontier : Low energy precision measurement complements High energy experiments. EDM can give important bounds on the BSM and excludes some of them.

Electric Dipole Moment Any non-zero observation of Electric Dipole Moment of nucleon, lepton, nuclei or atom is a signal of T-violation. However, it is not clear how to distinguish different scenario of CP violations from observation. QCD theta term Minimal left-right symmetric model Two Higgs doublet model Minimal Super-symmetric extension of the Standard Model Etc… EDM of Heavy nuclei suffers from large theoretical nuclear uncertainty. Similar to the situation of hadronic parity violation.

EDM of light nuclei EDM of light nuclei has less theoretical uncertainty. EDM of light nuclei (p, n, d, h3, he3) can be independent or have different sensitivity to CPV. Thus can be used to distinguish different scenarios of BSM physics. Measurement of the EDMs of charged particles with spin can be done in the storage ring. We computed the EDM of triton and helion (and deuteron) from TVPV potential. Matching between Nuclear EDM and effective TVPV Lagrangian at hadronic scale.

Effective Lagrangian of BSM Theoretical Challenge: How to connect EDM experiment with CP-violating parameters in the Lagrangian? Many steps between experiments and BSM Quark chromo-electric dipole moment, Quark EDM, Electron EDM, Three gluons, Four quarks….

Effective Lagrangian of BSM AT EW scale, the Effective CPV Lagrangian in terms of quarks and gluons QCD theta, quark EDM, quark chromo-EDM, chromo-EDM of gluon, four-quark operators..

Effective Lagrangian at hadronic level Quark chromo-electric dipole moment, Quark EDM, Three gluons, Four quarks…. Iso-scalar(vector) Nucleon EDM, TVPV pion-nucleon, TVPV Nucleon-Nucleon…. All details of BSM are hidden in the LECs of effective Lagrangian. The form is the same regardless the origin of CPV. Effective Lagrangian at Hadronic scale: Nucleons and pions

What it looks like: hadronic scale Iso-scalar(vector) Nucleon EDM, TVPV pion-nucleon, TVPV Nucleon-Nucleon…. All details of BSM are hidden in the LECs of effective Lagrangian. The form is the same regardless the origin of CPV. Different theory can have different magnitude of LECs. Effective Lagrangian at Hadronic scale: Nucleons and pions Nucleon EDM TVPV pi-N interaction TVPV NN contact interaction Can we distinguish QCD theta from other BSM effects? We need several clean observables

Our Approach(Hybrid Method) Traditional Approach to T-violating Hadronic interaction based on the meson exchange model Many old works are written in terms of meson exchange model Effective field theory with/without pion are popular nowadays. No(or less) model dependence Four nucleon contact interaction Pion-nucleon interaction. We use hybrid approach: Compute wave function from strong phenomenological potentials and TVPV potentials for EFT or meson exchange models. (Later full EFT calculation result is very similar)

TVPV NN potentials Most general static TVPV potential leading order in momentum expansion 5 operator structures Specific form of scalar function depends on the model Weak Coupling Strong Coupling π, ρ, ω TVPV

TVPV potentials Meson exchange model Weak Coupling Strong Coupling π, ρ, ω Many unknown coefficients One meson can affect different operators Yukawa function is fixed by meson mass

TVPV potentials Pionless EFT Pionful EFT: OPE+contact terms Same operator structures: only differences are in the form of scalar functions and LECs. TVPV Low Energy Constants are independent Freedom of scalar function: only require locality

TVPV potentials We have the same operator structures and the same scalar functions for all potential models only differences are Magnitude of LECs combination of matrix elements Meaning of mass scale in Yukawa function Thus, we compute matrix elements with TVPV potential for different mass scale factoring out unknown LECs

EDM of light nuclei We only consider leading order: no TVPV one-pion exchange currents no TVPV two-pion exchange potential (nucleon EDM+…) (polarization EDM)

Results: Deuteron EDM Nucleon EDM of deuteron: potential model independent Polarization EDM of deuteron: In Meson exchange model for AV18 potential (Only iso-vector operator contribute) Good agreement with other calculations

Results: Triton and Helion EDM Nucleon EDM: relatively small model dependence among local two-body potentials. Non-local potential, 3-body force effects

Results: Triton and Helion EDM Polarization EDM: result does not include LECs

Results: Triton and Helion EDM EDM of A=3 nuclei : one example (AV18UIX potential) Similar equation can be written for EFT potential: only pion exchange and contact terms for pionful EFT Consistent with recent full EFT calculation.

Model dependence: Deuteron EDM Model dependence : relative deviation from av18 In meson exchange model: Small model dependence In one pion exchange Larger model dependence In heavy meson exchange In EFT: Cutoff dependence should be Removed by renormalization

Model dependence: Triton and Helion EDM Polarization EDM: Model dependence Small model dependence among local potentials INOY potential shows large deviation from other potentials INOY is non-local, softest core and tensor interaction Note that the table and graph does not include LECs. Full prediction require to multiply LECs and also its cutoff dependence.

Results: Triton and Helion EDM Inconsistency(?) with no-core shell model results I. Stetcu et.al, Phys. Lett. B 665, 168(2008) Nucleon EDM are in good agreement: strong wave functions are equally good( Binding energy, charge radius…) Recently, the problem resolved by other group. (J. Bsaisou, Ulf-G. Meissner etc)

Summary and Discussion If we consider specific scenarios of CPV, almost all gives very small iso-tensor pion coupling. Pion exchange dominates for two-nucleon contribution. Theoretical calculations by other groups are consistent. ( discrepancy resolved ) Most recent summary : arXiv: by W.Dekens et.al.

Discussion Measurement of EDM might distinguish different effective BSM models Naive Dimensional Analysis: J.de Vries et.al., Phys. Rev. C 84, For example: all model predicts (proton EDM)~(neutron EDM) If (deuteron EDM)> (neutron EDM), it favors Chromo EDM or left-right symmetric models

Summary and Discussion Analysis in arXiv: by W.Dekens et.al. Combined measurement of Deuteron EDM, proton EDM and neutron EDM measurement can distinguish QCD theta term and other BSM scenarios considered. (d_D-d_n-d_p) Measurement of Triron and Helion EDM will provide further distinction between BSM models: larger two-body contributions Another direct T-violation measurement: T-violating asymmetry in n-d (or p-d scattering) cross section Neutron spin rotation in n-d scattering Complementary to EDM experiment: gives different combination Y.-H. Song, R. Lazauskas, V. Gudkov, Phys. Rev. C83, (2011)