Lecture VI: Paramagnetic & Diamagnetic Systems M.J. Ramsey-Musolf U Mass Amherst http://www.physics.umass.edu/acfi/ ACFI EDM School November 2016 � 1
Lecture VIII Outline I. General Considerations II. Schiff Theorem III. Paramagnetic Systems IV. Diamagnetic Atoms V. Semileptonic CPV 2
I. General Considerations 3
EDM Interpretation & Multiple Scales Collider Searches Baryon Asymmetry BSM CPV Particle spectrum; also Early universe CPV scalars for baryon asym SUSY, GUTs, Extra Dim… Energy Scale d= 6 Effective Operators: “ CPV Sources ” fermion EDM, quark chromo EDM, 3 gluon, 4 fermion QCD Matrix Elements Nuclear & atomic MEs d n , g π NN , … Schiff moment, other P- & T-odd moments, e-nucleus Expt CPV 4
Effective Field Theory BSM Scale Energy Scale +… Weak Scale Hadronic Scale 5
Leptonic CPV e − Electron γ EDM e − EDMs of atoms & molecules (Tl, ThO…)
Effective Field Theory BSM Scale Energy Scale +… Weak Scale Hadronic Scale Now consider this energy regime 7
TVPV Hadronic & Nuclear Interactions Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)
TVPV Hadronic & Nuclear Interactions Nucleon EDMs See V. Cirigliano, Lecture VII Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)
TVPV Hadronic & Nuclear Interactions I = 0, 1, 2 π − PVTV π N + ! γ p interaction π π π − n Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)
TVPV Hadronic & Nuclear Interactions PVTV 4N interaction Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)
What is an EDM ? Nuclear Moments P T P T P T P T E ✖ ✖ O C J EDM, Schiff… O ✖ ✖ E MQM…. T M J ✖ O E ✖ T E J Anapole…
What is an EDM ? Nuclear Moments P T P T P T P T E ✖ ✖ O C J EDM, Schiff… O ✖ ✖ E MQM…. T M J ✖ O E ✖ T E J Anapole… Sources of diamagnetic atom EDMS ( 199 Hg…)
What is an EDM ? Nuclear Moments P T P T P T P T Nuclear E ✖ ✖ O C J EDM, Schiff… Enhancements O ✖ ✖ E MQM…. T M J ✖ O E ✖ T E J Anapole…
Semileptonic CPV e − N e − N EDMs of atoms & molecules (Hg, ThO…)
II. Schiff Theorem 16
The Theorem Schiff Screening The EDM of a neutral system will vanish if: • Constituents are non- relativistic Classical picture: non- • Constituents are point-like acceleration of neutral non-rel system • Interactions are electrostatic
Schiff Screening: Corrections Schiff Screening The EDM of a neutral system will vanish if: • Constituents are non- relativistic Classical picture: non- • Constituents are point-like acceleration of neutral non-rel system • Interactions are electrostatic Paramagnetic systems w/ large Z: e - are highly relativistic
Schiff Screening: Corrections Schiff Screening The EDM of a neutral system will vanish if: • Constituents are non- relativistic Classical picture: non- • Constituents are point-like acceleration of neutral non-rel system • Interactions are electrostatic Diamagnetic atoms w/ large A: nuclei are large r ~ (1 fm) x A 1/3
Schiff Screening: Corrections Schiff Screening The EDM of a neutral system will vanish if: • Constituents are non- relativistic Classical picture: non- • Constituents are point-like acceleration of neutral non-rel system • Interactions are electrostatic St’d Model magnetic interactions, BSM e-q interactions,…
III. Paramagnetic Systems 21
Schiff Screening: Corrections Schiff Screening The EDM of a neutral system will vanish if: • Constituents are non- relativistic Classical picture: non- • Constituents are point-like acceleration of neutral non-rel system • Interactions are electrostatic Paramagnetic systems w/ large Z: e - are highly relativistic
Electron EDM Interactions External fields: 1 st order energy shift Internal (nuclear) fields: 2 nd order energy shift 23
Electron EDM: Schiff Screening Δ E = Δ E (1’) + Δ E (2’) 24
Electron EDM: Schiff Screening Δ E = Δ E (1’) + Δ E (2’) Connects upper & lower components of e - wavefunctions: vanishes in v e ! 0 limit 25
Electron EDM: Heavy Atoms d A = ρ A e d e +… 26
Electron EDM: Heavy Atoms d A = ρ A e d e +… Paramagnetic 27
Electron EDM: Heavy Atoms d A = ρ A e d e +… Paramagnetic Diamagnetic 28
Electron EDM: Polar Molecules E internal 29
Electron EDM: Polar Molecules E internal d e 30
Electron EDM: Polar Molecules E external E internal 31
Electron EDM: Polar Molecules E external E internal Electron experiences enhanced E int as due to much smaller E ext YbF 32
IV. Diamagnetic Atoms 33
Schiff Screening: Corrections Schiff Screening The EDM of a neutral system will vanish if: • Constituents are non- relativistic Classical picture: non- • Constituents are point-like acceleration of neutral non-rel system • Interactions are electrostatic Diamagnetic atoms w/ large A: nuclei are large r ~ (1 fm) x A 1/3
What is an EDM ? Nuclear Moments P T P T P T P T E ✖ ✖ O C J EDM, Schiff… O ✖ ✖ E MQM…. T M J ✖ O E ✖ T E J Anapole… Sources of diamagnetic atom EDMS ( 199 Hg…)
Nuclear Schiff Moment I Schiff Screening Nuclear Schiff Moment Nuclear EDM: Screened in atoms Atomic effect from nuclear finite size: Schiff moment + ! π EDMs of diamagnetic atoms ( 199 Hg )
Nuclear Schiff Moment II Schiff Screening Atomic effect from nuclear finite size: Schiff moment Screened EDM Schiff moment, MQM,… EDMs of diamagnetic atoms ( 199 Hg )
Nuclear Schiff Moment III Nuclear Enhancements Schiff moment, MQM,… Nuclear polarization: mixing of opposite parity states by H TVPV ~ 1 / Δ E EDMs of diamagnetic atoms ( 199 Hg )
Nuclear Schiff Moment IV Nuclear Enhancements: Octupole Deformation Opposite parity states mixed by H TVPV Nuclear polarization: mixing of opposite parity states by H TVPV ~ 1 / Δ E EDMs of diamagnetic atoms ( 199 Hg ) See J. Engel talk
Low Scale Observables Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)
Low Scale Observables Nucleon EDMs Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)
Low Scale Observables I = 0, 1, 2 π − PVTV π N + ! γ p interaction π π π − n Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)
Low Scale Observables PVTV 4N interaction Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)
Nuclear Schiff Moment + ! π 44
Nuclear Schiff Moment Nuclear many-body computations Non-perturbative hadronic computations 45
Nuclear Matrix Elements See J. Engle Lecture IX 46
V. Semileptonic Interactions 47
Schiff Screening: Corrections Schiff Screening The EDM of a neutral system will vanish if: • Constituents are non- relativistic Classical picture: non- • Constituents are point-like acceleration of neutral non-rel system • Interactions are electrostatic St’d Model magnetic interactions, BSM e-q interactions,…
Semileptonic CPV e − N EDMs of atoms & molecules (Hg, ThO…) e − N
Wilson Coefficients: Model Independent fermion EDM (3) δ f ~ quark CEDM (2) δ q ~ C G 3 gluon (1) C quqd non-leptonic (2) C lequ, ledq semi-leptonic (3) C ϕ ud induced 4f (1) light flavors only (e,u,d) 12 total + θ 50 50
Global Analysis: Input Chupp & R-M: 51 1407.1064
Paramagnetic Systems: Two Sources e − Electron γ EDM e − e − N γ (Scalar q) x (PS e - ) e − N Tl, YbF, ThO… 52
Paramagnetic Systems: Two Sources e − Chupp & R-M: Electron γ 1407.1064 EDM e − e − N γ (Scalar q) x (PS e - ) e − N Tl, YbF, ThO… 53
Paramagnetic Systems: Two Sources e − Chupp & R-M: Electron γ 1407.1064 EDM e − e − N γ (Scalar q) x (PS e - ) e − ∼ × N p Λ > ∼ (1 . 5 TeV) × sin φ CPV Electron EDM (global) ∼ p Λ > ∼ (1300 TeV) × sin φ CPV C S (global) Tl, YbF, ThO… 54
Paramagnetic Systems: Two Sources e − Chupp & R-M: Electron γ 1407.1064 EDM e − e − N γ (Scalar q) x (PS e - ) e − ∼ × N p Λ > ∼ (1 . 5 TeV) × sin φ CPV Electron EDM (global) ∼ p Λ > ∼ (1300 TeV) × sin φ CPV C S (global) Tl, YbF, ThO… LHC accessible? 55
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