moment of electrons Key words : CP violation, electron dipole moment - - PowerPoint PPT Presentation

Searching for electric dipole moment of electrons

Key words : CP violation, electron dipole moment (EDM), ACME collaboration 2018.11.21 KAIST Department of Physics Geun-Hee Lee

1 KAIST Physics/November 21st, 2018

Contents

• Introduction
• CP violation and electric dipole moment (EDM)
• Theory
• CP violation in standard model (SM) and possibility of new CP symmetry breaking

channels in beyond standard model (BSM)

• Experiment
• Effort for finding electron EDM : ACME collaboration
• Summary

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Introduction : CP violation and electric dipole moment (EDM)

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Symmetries and CP violation

• Symmetry : Operation that leaves physical situation

invariant.

• Broken symmetry (or violation) means symmetric
• peration is no longer symmetric.
• Two kinds of symmetries : continuous or discrete
• CPT theorem : successive operation of charge

conjugation, parity and time reversal is symmetry, under the Lorentz invariant theory & Lorentz invariant vacuum.

• One implication : CP violation iff T symmetry is broken.

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Symmetry Action Explanation P Ԧ 𝑠 → −Ԧ 𝑠 Inversion of spatial coordinate T 𝑢 → −𝑢 Inversion of time coordinate C 𝑟 → −𝑟 Inversion of internal quantum number Kinds of discrete symmetries

Symmetries and EDM

• By the virtue of Wigner-Eckart theorem, EDM of spin ½

particles should be collinear with their spin direction.

• EDM exists only if both P and T symmetries are broken.
• P-violation : 𝛾-decay of 60𝐷𝑝
• CP-violation (= T-violation) : Neutral Kaon mixing
• So possibility of finding EDM of fundamental particles! (New

source of CP violation)

• But electron EDM has not been measured yet.
• Related topics : Strong CP problem & baryogenesis

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P and T violation in the presence of EDM (Wikipedia, neutron electric dipole moment)

60𝐷𝑝 − 𝛾 𝑒𝑓𝑑𝑏𝑧

(https://galileospendulum.org/tag/symmetry/)

CP-violating QCD Hamiltonian

Theory : CP violation in and beyond Standard Model (SM)

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EDM in SM

7 KAIST Physics/November 21st, 2018 Yukawa interaction in SM CKM matrix with conventional notation Three loop diagram generating electron EDM

• In standard model, the only observed CP violating

mechanism is quark mixing: From complex Yukawa interaction

• Cabbibo-Kobayashi-Maskawa (CKM) quark mixing matrix

involves CP-violating phase.(𝜀𝐿𝑁)

• However, it is hard to make electron EDM only using this

mechanism: Loop should involve quarks, All effects from three-loop diagrams are vanished.

• Order estimation of electron EDM yields 𝑒𝑓 < 10−37 𝑓 ⋅ 𝑑𝑛.
• Note : Possibility of lepton mixing, and CP-violation during
• that. Resultant EDM is negligible, even if comparing with

quark mixing.

EDM in BSM

• Feynman diagram should involve quark loop to generate EDM:

Small electron EDM

• BSMs introduce new particles which can make CP-violation in
• ne-loop diagram.
• Supersymmetric(SUSY) model : Complex superpotential,

spontaneous SUSY breaking

• Left-Right symmetric model : Complex vacuum expectation value
• f Higgs multiplet and their contribution on mass of weak bosons.
• Etc..
• If we found relatively large electron EDM, then we reasonably

consider another channels of CP violation. (Suggested by models other than SM)

• Generous assumptions yield 𝑒𝑓 ≈ 10−27𝑓 ⋅ 𝑑𝑛

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Generic one-loop diagram generating EDM, F and B refer fermions and bosons

One loop contributions to EDM of neutralinos, charginos, and RH neutrinos

Experiment : ACME collaboration

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General experiment scheme

• How can we measure electron EDM?
• Effective Hamiltonian for spin is

𝐼 = − 𝑒𝑓𝐹 + 𝑒𝑛𝐼 ⋅ Ԧ 𝜏

where

• 𝑒𝑓, 𝑒𝑛 are electric and magnetic dipole moment,
• 𝐹, 𝐼, Ԧ

𝜏 are electric, magnetic and spin, respectively.

• Hence the coupling between electric field and electron

EDM appears in terms of spin precession: initial state preparation and control of magnetic field are very important.

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http://www.electronedm.org/

en.wikipedia.org/wiki/Electron_electric_dipole_momnet

ACME collaboration

• Advanced Cold Molecule Electron EDM (ACME)

collaboration is experiment group to find electron EDM using cold molecules.

• They have used thorium monoxides
• Relatively high intramolecular electric field :

𝐹𝑓𝑔𝑔~84𝐻𝑊/𝑑𝑛

• Cold molecules (single quantum state) with high flux

(intensive signal)

• Metastable H state (long coherence time 𝜐𝑑~2𝑛𝑡)
• Direction of intra-molecular field is controlled by

external electric field.

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H-state of ThO : Red dot = magnetic field coupling, Green dot = electric field coupling

Spin precession described by wave function

ACME collaboration

Ultrafast Spin Dynamics Lab.

12 KAIST Physics/November 21st, 2018 Thermalization of 𝑈ℎ𝑃 J-cooling & M-remixing (designed to make larger J=1 population)

ACME collaboration

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ACME collaboration

• Systematic errors (caused by stray field, B-

gradient, spin orbit coupling, etc.) and statistical errors are comparable to measured value:

• Authors have limited energy scale of new CP-

violating physics using simple order estimation.

• Λ ≈ 3~30 TeV scale, Λ is rest-mass energy of new

particle mediating CP-violation

• Another experiments are currently designing.
• e.g. John Doyle (Harvard Univ, ACME collaborator)

proposed experiments on YbOH molecular trap, and expected PeV scale energy regime.

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Experiment 𝒆𝒇 values with error 90% confidence level ACME 1 𝑒𝑓 = −2.1 ± 3.7𝑡𝑢𝑏𝑢 ± 2.5𝑡𝑧𝑡𝑢 × 10−29 𝑓 ⋅ 𝑑𝑛 𝑒𝑓 < 8.7 × 10−29 𝑓 ⋅ 𝑑𝑛 ACME 2 𝑒𝑓 = 4.3 ± 3.1𝑡𝑢𝑏𝑢 ± 2.6𝑡𝑧𝑡𝑢 × 10−30 𝑓 ⋅ 𝑑𝑛 𝑒𝑓 < 1.1 × 10−29 𝑓 ⋅ 𝑑𝑛

Result of ACME experiments

Summary

• CP-violation (equivalent to T-violation under CPT theorem) with P-violation makes EDM of

fundamental particles.

• In SM, the only known source of CP-violation is quark mixing, and SM expects that it

would generate very small electron EDM (Order of 10−38𝑓 ⋅ 𝑑𝑛)

• Hence, discovery of large electron EDM opens the way of CP-symmetry breaking with

new channels through new particles.

• Experimentally, physicists found 𝑒𝑓 < 1.1 × 10−29𝑓 ⋅ 𝑑𝑛 using polar molecule ThO. This

implies there could be no particle mediating CP-violation up to tens of TeV level.

• They currently design new experiments searching PeV CP-violation regime.

Ultrafast Spin Dynamics Lab.

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