Download APCTP-WCU APR 16 - Y.

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, 2013.04.14-2013.04.24
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, 015501(2013)
CP and T Symmetry
• Symmetry is the most fundamental concepts in physics.
Understanding symmetry and its violation leads to new
physics.
• Unsolved mysteries in the origin of universe
• Origin of Dark Energy
• Origin of Dark matter
• Origin of Matter: Tiny but the reason we can be here.
• Observed baryon asymmetry require additional CP
violating mechanism other than CKM matrix in SM.( CP
violation from CKM matrix is too small)
• CPT theorem: CP violation ↔ T violation
Electric Dipole Moment
• The EDM of any stable quantum system violates both T and P
symmetry. (Induced EDM does not)
• Permanent EDM 𝑑 ∝ 𝐽
• Interaction − 𝑑 ∙ 𝐸 ∝ 𝐽 ∙ 𝐸 violates both P and T
• Induced EDM: − 𝑑 ∙ 𝐸 ∝ 𝐸 ∙ 𝐸
• Prediction of EDM from CKM matrix is too small to detect in
near future.
• 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) !
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 nonrelativistic 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
Strong
Coupling
π, ρ, ω
Weak
Coupling
TVPV potentials
• Pionless EFT
TVPV
• 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.
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, 065501
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, 065503(2011)