ELECTRIC DIPOLE MOMENTS OF A=3 NUCLEI Young-Ho Song(Institute of Basic Science) Collaboration with Rimantas Lazauskas( IPHC, IN2P3-CNRS) Vladimir Gudkov( University of South Carolina) APCTP-WCU Focus Program, Pohang,

Outline Introduction T-reversal invariance breaking Electric dipole moments(EDM) Formalism Nuclear EDM TVPV potential Numerical Results Discussion Reference: Y.-H. Song, R. Lazauskas and V. Gudkov, Phys. Rev. C 87, (2013)

CP and T Symmetry

Electric Dipole Moment

Current status: C.-P. Liu’s presentation(2007)

Effective Lagrangian of BSM Possible sources of CP(or T) violation Standard Model: CKM matrix, QCD theta term Beyond standard Model(BSM): SUSY, GUTs, Extra Dimensions…. We can use effective Lagrangian at low energy scale: Details of the BSM models appears as coefficients in the effective Lagrangian at dimension 6: Quark chromo-electric dipole moment, Quark EDM Electron EDM, Three gluons, Four quarks…..

Effective Lagrangian at hadronic scale However, the degrees of freedom are still quarks, gluons, leptons… We need to scale down to hadronic degrees of freedom: nucleons, pions… Effective Lagrangian at the Hadronic scale Details of the effective BSM Lagrangian are hidden in the low energy constants(LECs) in the hadronic Lagrangian Require non-perturbative matching

EDM of atomic system It is difficult to measure EDM of charged nuclei. Experimental focus : neutron EDM or neutral Atomic EDM

EDM of atomic system However, there is electron shielding in atom. Schiff theorem: In the system of point-like nucleus and non- relativistic electrons with only Coulomb interaction, there is complete shielding of nuclear or electron EDM. Residual EDM of atom Schiff Moments from (1) finite size effect => Heavy atom (2) relativistic effects (3) non-Coulomb interaction Large theoretical uncertainty

EDM of light nuclei Light nuclei is easier to interpret the experimental results Less theoretical uncertainty No shielding of electron for ionized nuclei Recent interests in charged particle EDM in storage ring. proposal of proton EDM at BNL. Maybe Deuteron EDM To fix unknown constants in the effective Lagrangian: EDM of proton, neutron, deuteron, triton, helion have different sensitivity to the constants. We computed the EDM of triton and helion from TVPV potential. Matching between Nuclear EDM and effective TVPV Lagrangian at hadronic scale.

Our Approach(Hybrid Method) Traditional Approach to T-violating Hadronic interaction based on the meson exchange model Effective field theory with/without pion are popular nowadays. No(or less) model dependence Pion-nucleon interaction. Four nucleon contact interaction We use hybrid approach which can be interpreted in the same way to the meson exchange and EFT approach.

EDM of light nuclei Source of EDM in light nuclei: (1) TVPV EDM operator( currents operator) (2) TVPV NN potential( wave function) We will consider only nucleon EDM for TVPV EDM operators (no TVPV pion exchange currents) Thus, nuclear EDM=(nucleon EDMs)+(polarization EDMs)

Three body Wave functions Three body wave functions are obtained by solving Faddeev equation Assume pertubative TVPV potential Various phenomenological strong potential models

TVPV potentials Most general static TVPV potential leading order in momentum expansion 5 operator structures Specific form of scalar function depends on the model

TVPV potentials Meson exchange model Weak Coupling Strong Coupling π, ρ, ω

TVPV potentials Pionless EFT Choose Yukawa function as regulated delta function Pionful EFT: OPE+contact terms Same operator structures: only differences are in the form of scalar functions and LECs. TVPV

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

Results: Deuteron EDM Model dependence 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

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:

Results: 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

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…) Large cutoff mass scale dependence for contact term

Summary and Discussion EDM of A=3 nuclei : AV18UIX potential Further study is necessary to resolve the inconsistency with no-core shell model calculation.

Discussion Measurement of EDM might distinguish different effective BSM models Naive Dimensional Analysis: J.de Vries et.al., Phys. Rev. C 84,

Discussion Another direct T-violation experiment: T-violating asymmetry in n-d (or p-d scattering) Neutron spin rotation in n-d scattering Y.-H. Song, R. Lazauskas, V. Gudkov, Phys. Rev. C83, (2011)