Lecture VI: Paramagnetic & Diamagnetic Systems M.J. - - PowerPoint PPT Presentation

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Lecture VI: Paramagnetic & Diamagnetic Systems

ACFI EDM School November 2016

M.J. Ramsey-Musolf

U Mass Amherst

http://www.physics.umass.edu/acfi/

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Lecture VIII Outline

I. General Considerations II. Schiff Theorem III. Paramagnetic Systems IV. Diamagnetic Atoms V. Semileptonic CPV

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• I. General Considerations

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BSM CPV

SUSY, GUTs, Extra Dim…

Expt EDM Interpretation & Multiple Scales

Baryon Asymmetry

Early universe CPV

Collider Searches

Particle spectrum; also scalars for baryon asym

QCD Matrix Elements

dn , gπNN , …

Nuclear & atomic MEs

Schiff moment, other P- & T-odd moments, e-nucleus CPV

Energy Scale

d= 6 Effective Operators: “CPV Sources”

fermion EDM, quark chromo EDM, 3 gluon, 4 fermion

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Effective Field Theory

+…

Energy Scale BSM Scale Weak Scale Hadronic Scale

Leptonic CPV

EDMs of atoms & molecules (Tl, ThO…) e− e− γ

Electron EDM

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Effective Field Theory

+…

Energy Scale BSM Scale Weak Scale Hadronic Scale Now consider this energy regime

TVPV Hadronic & Nuclear Interactions

Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)

TVPV Hadronic & Nuclear Interactions

Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs) Nucleon EDMs

See V. Cirigliano, Lecture VII

TVPV Hadronic & Nuclear Interactions

Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs) PVTV πN interaction

π

I = 0, 1, 2

π

+!

γ

n p π − π −

TVPV Hadronic & Nuclear Interactions

Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs) PVTV 4N interaction

What is an EDM ?

CJ TM

J

TE

J

P T P T P T P T

E ✖ ✖ O O ✖ ✖ E ✖ O E ✖

Nuclear Moments

EDM, Schiff… MQM…. Anapole…

What is an EDM ?

CJ TM

J

TE

J

P T P T P T P T

E ✖ ✖ O O ✖ ✖ E ✖ O E ✖

Nuclear Moments

EDM, Schiff… MQM…. Anapole…

Sources of diamagnetic atom EDMS (199Hg…)

What is an EDM ?

CJ TM

J

TE

J

P T P T P T P T

E ✖ ✖ O O ✖ ✖ E ✖ O E ✖

Nuclear Moments

Nuclear Enhancements EDM, Schiff… MQM…. Anapole…

Semileptonic CPV

N

e−

N

e− EDMs of atoms & molecules (Hg, ThO…)

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• II. Schiff Theorem

The Theorem

Schiff Screening Classical picture: non- acceleration of neutral non-rel system

The EDM of a neutral system will vanish if:

• Constituents are non-

relativistic

• Constituents are point-like
• Interactions are electrostatic

Schiff Screening: Corrections

Schiff Screening Classical picture: non- acceleration of neutral non-rel system

The EDM of a neutral system will vanish if:

• Constituents are non-

relativistic

• Constituents are point-like
• Interactions are electrostatic

Paramagnetic systems w/ large Z: e- are highly relativistic

Schiff Screening: Corrections

Schiff Screening Classical picture: non- acceleration of neutral non-rel system

The EDM of a neutral system will vanish if:

• Constituents are non-

relativistic

• Constituents are point-like
• Interactions are electrostatic

Diamagnetic atoms w/ large A: nuclei are large r ~ (1 fm) x A1/3

Schiff Screening: Corrections

Schiff Screening Classical picture: non- acceleration of neutral non-rel system

The EDM of a neutral system will vanish if:

• Constituents are non-

relativistic

• Constituents are point-like
• Interactions are electrostatic

St’d Model magnetic interactions, BSM e-q interactions,…

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• III. Paramagnetic Systems

Schiff Screening: Corrections

Schiff Screening Classical picture: non- acceleration of neutral non-rel system

The EDM of a neutral system will vanish if:

• Constituents are non-

relativistic

• Constituents are point-like
• Interactions are electrostatic

Paramagnetic systems w/ large Z: e- are highly relativistic

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Electron EDM Interactions

External fields: 1st order energy shift Internal (nuclear) fields: 2nd order energy shift

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Electron EDM: Schiff Screening

ΔE = ΔE(1’) + ΔE(2’)

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Electron EDM: Schiff Screening

ΔE = ΔE(1’) + ΔE(2’)

Connects upper & lower components of e- wavefunctions: vanishes in ve ! 0 limit

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Electron EDM: Heavy Atoms

dA = ρA

e de +…

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Electron EDM: Heavy Atoms

dA = ρA

e de +…

Paramagnetic

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Electron EDM: Heavy Atoms

dA = ρA

e de +…

Paramagnetic Diamagnetic

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Electron EDM: Polar Molecules

Einternal

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Electron EDM: Polar Molecules

Einternal

de

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Electron EDM: Polar Molecules

Einternal

Eexternal

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Electron EDM: Polar Molecules

Einternal

Eexternal Electron experiences enhanced Eint as due to much smaller Eext

YbF

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• IV. Diamagnetic Atoms

Schiff Screening: Corrections

Schiff Screening Classical picture: non- acceleration of neutral non-rel system

The EDM of a neutral system will vanish if:

• Constituents are non-

relativistic

• Constituents are point-like
• Interactions are electrostatic

Diamagnetic atoms w/ large A: nuclei are large r ~ (1 fm) x A1/3

What is an EDM ?

CJ TM

J

TE

J

P T P T P T P T

E ✖ ✖ O O ✖ ✖ E ✖ O E ✖

Nuclear Moments

EDM, Schiff… MQM…. Anapole…

Sources of diamagnetic atom EDMS (199Hg…)

Nuclear Schiff Moment I

Schiff Screening Atomic effect from nuclear finite size: Schiff moment Nuclear Schiff Moment Nuclear EDM: Screened in atoms

EDMs of diamagnetic atoms ( 199Hg )

π

+!

Nuclear Schiff Moment II

Schiff Screening Atomic effect from nuclear finite size: Schiff moment

EDMs of diamagnetic atoms ( 199Hg )

Screened EDM Schiff moment, MQM,…

Nuclear Schiff Moment III

EDMs of diamagnetic atoms ( 199Hg )

Schiff moment, MQM,…

Nuclear Enhancements Nuclear polarization: mixing of opposite parity states by HTVPV ~ 1 / ΔE

Nuclear Schiff Moment IV

EDMs of diamagnetic atoms ( 199Hg ) Nuclear Enhancements: Octupole Deformation Nuclear polarization: mixing of opposite parity states by HTVPV ~ 1 / ΔE

Opposite parity states mixed by HTVPV See J. Engel talk

Low Scale Observables

Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)

Low Scale Observables

Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs) Nucleon EDMs

Low Scale Observables

Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs) PVTV πN interaction

π

I = 0, 1, 2

π

+!

γ

n p π − π −

Low Scale Observables

Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs) PVTV 4N interaction

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Nuclear Schiff Moment

π

+!

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Nuclear Schiff Moment

Nuclear many-body computations Non-perturbative hadronic computations

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Nuclear Matrix Elements

See J. Engle Lecture IX

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• V. Semileptonic Interactions

Schiff Screening: Corrections

Schiff Screening Classical picture: non- acceleration of neutral non-rel system

The EDM of a neutral system will vanish if:

• Constituents are non-

relativistic

• Constituents are point-like
• Interactions are electrostatic

St’d Model magnetic interactions, BSM e-q interactions,…

Semileptonic CPV

N

e−

N

e− EDMs of atoms & molecules (Hg, ThO…)

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Wilson Coefficients: Model Independent

δf fermion EDM (3) δq

quark CEDM

(2) CG

3 gluon

(1) Cquqd

non-leptonic

(2) Clequ, ledq

semi-leptonic

(3) Cϕud

induced 4f

(1) ~ ~ 12 total + θ light flavors only (e,u,d)

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Global Analysis: Input

Chupp & R-M: 1407.1064

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Paramagnetic Systems: Two Sources

e− e− γ

N

e−

N

e− γ Tl, YbF, ThO…

Electron EDM (Scalar q) x (PS e-)

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Paramagnetic Systems: Two Sources

e− e− γ

N

e−

N

e− γ Tl, YbF, ThO…

Electron EDM (Scalar q) x (PS e-)

Chupp & R-M: 1407.1064

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Paramagnetic Systems: Two Sources

e− e− γ

N

e−

N

e− γ Tl, YbF, ThO…

Electron EDM (Scalar q) x (PS e-)

∼ × Λ >

∼ (1.5 TeV) ×

p sin φCPV Electron EDM (global)

∼ Λ >

∼ (1300 TeV) ×

p sin φCPV CS (global)

Chupp & R-M: 1407.1064

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Paramagnetic Systems: Two Sources

e− e− γ

N

e−

N

e− γ Tl, YbF, ThO…

Electron EDM (Scalar q) x (PS e-)

∼ × Λ >

∼ (1.5 TeV) ×

p sin φCPV Electron EDM (global)

∼ Λ >

∼ (1300 TeV) ×

p sin φCPV CS (global)

Chupp & R-M: 1407.1064

LHC accessible?