1. Lecture VI: Electric Dipole Moments Beyond the Standard Model
M.J. Ramsey-Musolf
U Mass Amherst
ACFI EDM School November 2016

2. Lecture IV Outline General Considerations BSM Motivation
Supersymmetry (Minimal Model)
Higgs Portal CPV: 2 Higgs Doublet Model
Extended Gauge Sector: Left-Right Symmetric Model

3. I. General Considerations

4. Recall: SM EDMs

5. EDMs & SM Physics
dn ~ (10-16 e cm) x qQCD + dnCKM

6. EDMs & SM Physics
dn ~ (10-16 e cm) x qQCD + dnCKM
Strong CP Problem

7. EDMs & SM Physics dn ~ (10-16 e cm) x qQCD + dnCKM
Suppression factors
( DS = 1 CPV ) x ( DS = 1 CPC )
s1 s2 s3 sd
Multi loop

8. EDMs & SM Physics dnCKM = (1 – 6) x 10-32 e cm
dn ~ (10-16 e cm) x qQCD + dnCKM
dnCKM = (1 – 6) x e cm
C. Seng arXiv:

9. EDMs & BSM Physics
d ~ (10-16 e cm) x (u / L)2 x sinf x yf F

10. EDMs & BSM Physics d ~ (10-16 e cm) x (u / L)2 x sinf x yf F
CPV Phase: large enough for baryogenesis ?

11. EDMs & BSM Physics d ~ (10-16 e cm) x (u / L)2 x sinf x yf F
BSM mass scale: TeV ? Much higher ?
u = 246 GeV Higgs vacuum expectation value
L > 246 GeV Mass scale of BSM physics

12. EDMs & BSM Physics d ~ (10-16 e cm) x (u / L)2 x sinf x yf F
BSM dynamics: perturbative? Strongly coupled?
yf Fermion f Yukawa coupling
F Function of the dynamics

13. EDMs & BSM Physics d ~ (10-16 e cm) x (u / L)2 x sinf x yf F
Need information from at least three “frontiers”

14. EDMs & BSM Physics d ~ (10-16 e cm) x (u / L)2 x sinf x yf F
Need information from at least three “frontiers”
Baryon asymmetry Cosmic Frontier
High energy collisions Energy Frontier
EDMs Intensity Frontier

15. EDM Interpretation & Multiple Scales
Collider Searches
Particle spectrum; also scalars for baryon asym
Baryon Asymmetry
Early universe CPV
BSM CPV
SUSY, GUTs, Extra Dim…
Energy Scale
d= 6 Effective Operators: “CPV Sources”
fermion EDM, quark chromo EDM, 3 gluon, 4 fermion
QCD Matrix Elements
dn , gNN , …
Nuclear & atomic MEs
Schiff moment, other P- & T-odd moments, e-nucleus CPV
Expt

16. Wilson Coefficients: Summary
f fermion EDM (3)
q quark CEDM (2)
CG 3 gluon (1)
Cquqd non-leptonic (2)
Clequ, ledq semi-leptonic (3)
Cud induced 4f (1) ~ ~
light flavors only (e,u,d)
12 total +  16

17. BSM Origins dL uL uR dR W+ EDM: ff CEDM: gff Weinberg ggg:RS
MSSM
LRSM dL uL uR dR W+ 
EDM: ff
CEDM: gff
Weinberg ggg:
Four fermion
udHH

18. II. BSM Motivation

19. The Origin of Matter
Cosmic Energy Budget
Dark Matter
Dark Energy
27 %
Baryons
Baryons
5 %
68 %
Explaining the origin, identity, and relative fractions of the cosmic energy budget is one of the most compelling motivations for physics beyond the Standard Model

20. Naturalness Problem

21. Scalar Fields in Particle Physics

22. Scalar Fields in Particle Physics
Scalar fields are a simple
Scalar fields are theoretically problematic
m2 ~ 2
Discovery of a (probably) fundamental 125 GeV scalar :
Is it telling us anything about  ? Naturalness?

23. Scalar Fields in Particle Physics
Scalar fields are a simple
Scalar fields are theoretically problematic
m2 ~ 2
Discovery of a (probably) fundamental 125 GeV scalar :
mh2 ~ l v2 & GF ~ 1/v2 : what keeps GF “large” ?

24. LHC Implications
Weak scale BSM physics (e.g., SUSY) is there but challenging for the hadronic collider
BSM physics is there but a bit heavy (some fine tuning)
We are thinking about the problem incorrectly (cosmological constant???)

25. Symmetries & Cosmic History
EW Symmetry Breaking: Higgs
New Forces ?
Standard Model Universe
QCD: q+g! n,p…
QCD: n+p! nuclei
Astro: stars, galaxies,..

26. Symmetries & Cosmic History
EW Symmetry Breaking: Higgs
New Forces ?
Standard Model Universe
SUSY ?
GUTS ?
Extra Dims ? WL ~ WR
WL*
Puzzles the Standard Model can’t solve
Origin of matter
Unification & gravity
Weak scale stability
Neutrinos

27. Symmetries & Cosmic History
EW Symmetry Breaking: Higgs
New Forces ?
Standard Model Universe
SUSY ?
GUTS ?Extra Dims ? WL ~ WR
WL*
Puzzles the Standard Model can’t solve
Origin of matter
Unification & gravity
Weak scale stability
Neutrinos

28. Symmetries & Cosmic History
EW Symmetry Breaking: Higgs ?
New Forces ?
Standard Model Universe
10 2
10 18
100 10
Unification
-1 
100 10
10 2
10 18
-1 
“Near miss” for grand unification
g = g()
Desert

29. Symmetries & Cosmic History
EW Symmetry Breaking: Higgs ?
New Forces ?
Standard Model Universe
100 10
10 2
10 18
-1
SUSY: Canceling quantum corrections protect GF
g = g()
Weak Int Rates:
Solar burning
Element abundances
Desert 

30. Symmetries & Cosmic History
EW Symmetry Breaking: Higgs ?
New Forces ?
Standard Model Universe
SUSY ?
GUTS ?
Extra Dims ? WL ~ WR
WL*
Puzzles the Standard Model can’t solve
Origin of matter
Unification & gravity
Weak scale stability
Neutrinos

31. Neutrinos & the Flavor Problem
EW Symmetry Breaking: Higgs ?
New Forces ?
Standard Model Universe
Seesaw R ? WL ~ WR NR
WL*
Observed light  s
Unobserved heavy  s
“Seesaw Mechanism”
~ 1014 GeV
Courtesy R. D. McKeown
New “Periodic Table”
Why so different ?
Not physical states

32. III. Supersymmetry

33. GF is Too Large
GF ~ 10-5/MP mWEAK ~ 250 GeV l

34. SUSY protects GF
=0 if SUSY is exact

35. SUSY: a candidate symmetry of the early Universe
Unify all forces
Protect GF from shrinking
Produce all the matter that exists
3 of 4
Yes
Maybe so
Maybe
Probably necessary
Account for neutrino properties
Give self-consistent quantum gravity

36. Minimal Supersymmetric Standard Model (MSSM)
No new coupling constants
Two Higgs vevs
Supersymmetric Higgs mass, 
Minimal Supersymmetric Standard Model (MSSM)
Supersymmetry
Charginos, neutralinos
Fermions
Bosons
sfermions
gauginos
Higgsinos

37. Minimal Supersymmetric Standard Model (MSSM)

38. SUSY and R Parity If nature conserves
vertices have even number of superpartners
Consequences
Lightest SUSY particle
is stable
viable dark matter candidate
Proton is stable
Superpartners appear only in loops

39. SUSY must be a broken symmetry
Superpartners have not been seen
Theoretical models of SUSY breaking
Visible World
Hidden World
Flavor-blind mediation
SUSY Breaking
How is SUSY broken?

40. MSSM SUSY Breaking One solution: af ~ Yf Gaugino mass
Superpartners have not been seen
Theoretical models of SUSY breaking
~ 100 new parameters
40 new CPV phases
Flavor mixing parameters
Gaugino mass
Triscalar interactions
Sfermion mass
O(1) CPV phases & flavor mixing ruled out by expt: “SUSY CP” & “SUSY flavor” problems
How is SUSY broken?

41. EDMs BSM: MSSM j = arg (Mjb*) A = arg (Af Mj ) One Loop: EDM, cEDM
Two Loop “Barr Zee”: EDM, cEDM

42. EDMs BSM: MSSM j = arg (Mjb*) A = arg (Af Mj )
Two Loop: Weinberg 3 Gluon

43. EDMs BSM: MSSM j = arg (Mjb*) A = arg (Af Mj ) One Loop: EDM, cEDM
Universality Assumption

Common A
A = arg (Af Mj )
One Loop: EDM, cEDM
Ritz CIPANP 09 +

44. EDMs BSM: MSSM j = arg (Mjb*) A = arg (Af Mj ) One Loop: EDM, cEDM
Two Loop “Barr Zee”: EDM, cEDM
Heavy squarks: electroweak Barr-Zee dominates

45. EDMs BSM: MSSM j = arg (Mjb*) A = arg (Af Mj )
mq ~ 200 GeV ~
mq ~ 500 GeV ~
mq ~ 1000 GeV ~
One & two Loop: EDM, cEDM

46. IV. Higgs Portal CPV

47. What is the CP Nature of the Higgs Boson ?
Interesting possibilities if part of an extended scalar sector

48. What is the CP Nature of the Higgs Boson ?
Interesting possibilities if part of an extended scalar sector
Two Higgs doublets ?
H ! H1 , H2

49. What is the CP Nature of the Higgs Boson ?
Interesting possibilities if part of an extended scalar sector
Two Higgs doublets ?
H ! H1 , H2
An example: MSSM but not most general due to restrictions of supersymmetry

50. What is the CP Nature of the Higgs Boson ?
Interesting possibilities if part of an extended scalar sector
Two Higgs doublets ?
New parameters:
H ! H1 , H2
tan b = <H1> / <H2>
sin ab
CPV !

51. Two Higgs Double Model: Features
Scalar Potential
Complex parameters: m122 & l5,6,7

52. Two Higgs Double Model: Features
Yukawa Interactions
Notation: hj Matrices in flavor space (denoted Yj elsewhere)
“Type III 2DHM” Both doublets couple to uR & dR

53. Two Higgs Double Model: Features
Yukawa Interactions
Avoid “Flavor Changing Neutral Currents” :
Place restrictions on the the Yukawa couplings !
“Type I & Type II 2DHM”

54. Two Higgs Double Model: Features
Yukawa Interactions
Avoid “Flavor Changing Neutral Currents” :
Place restrictions on the the Yukawa couplings !
“Type I & Type II 2DHM”

55. Two Higgs Double Model: Features
Scalar Potential : CPV w/ “Z2 Symmetry”
Complex parameters: m122 & l5
“Rephasing invariant”:

56. Higgs Portal CPV + loops w/ quarks & external gluons
Inoue, R-M, Zhang:
Higgs Portal CPV
CPV & 2HDM: Type I & II
l6,7 = 0 for simplicity
EWSB
+ loops w/ quarks & external gluons

57. EDM “Anatomy” Electron Inoue, R-M, Zhang: 1403.4257 Type II Type I
Note: absolute values plotted

58. EDM “Anatomy” Neutron Inoue, R-M, Zhang: 1403.4257 Type I Type II
Note: absolute values plotted

59. EDM “Anatomy” TVPV pNN Coupling (I=0) Inoue, R-M, Zhang: 1403.4257
Type I
Type II
Note: absolute values plotted

60. Future Reach: Higgs Portal CPV
CPV & 2HDM: Type II illustration
l6,7 = 0 for simplicity Hg
ThO n Ra
Present
Future:
dn x 0.1
dA(Hg) x 0.1
dThO x 0.1
dA(Ra)
Future:
dn x 0.01
dA(Hg) x 0.1
dThO x 0.1
dA(Ra)
sin ab : CPV scalar mixing
Inoue, R-M, Zhang: 68

61. Higgs Portal CPV: EDMs & LHC
CPV & 2HDM: Type II illustration
l6,7 = 0 for simplicity Hg
ThO n
LHC Current Ra
Dawson et al:
Mh2 = 400 GeV
Present
Future:
dn x 0.1
dA(Hg) x 0.1
dThO x 0.1
dA(Ra)
Future:
dn x 0.01
dA(Hg) x 0.1
dThO x 0.1
dA(Ra)
sin ab : CPV scalar mixing
Inoue, R-M, Zhang: 68

62. Higgs Portal CPV: EDMs & LHC
CPV & 2HDM: Type II illustration
l6,7 = 0 for simplicity Hg
ThO n
LHC Future ? Ra
Dawson et al:
Mh2 = 400 GeV
Present
Future:
dn x 0.1
dA(Hg) x 0.1
dThO x 0.1
dA(Ra)
Future:
dn x 0.01
dA(Hg) x 0.1
dThO x 0.1
dA(Ra)
sin ab : CPV scalar mixing
Inoue, R-M, Zhang: 68

63. Higgs Portal CPV: EDMs & LHC
CPV & 2HDM: Type II illustration
l6,7 = 0 for simplicity
Mh2 = 550 GeV
Chen, Li, RM preliminary
Run II
Current dn Hg
LHC 100 fb-1
LHC 300 fb-1
ThO n Ra
Present
Future:
dn x 0.1
dA(Hg) x 0.1
dThO x 0.1
dA(Ra) [10-27 e cm]
Future:
dn x 0.01
dA(Hg) x 0.1
dThO x 0.1
dA(Ra)
sin ab : CPV scalar mixing
Inoue, R-M, Zhang:

64. Low-Energy / High-Energy Interplay
Discovery
“Diagnostic” ?
Low energy
High energy

65. V. Left-Right Symmetric Model

66. BSM Physics: Where Does it Live ?
SUSY, LNV, extended Higgs sector… MW
Mass Scale
BSM ?
Sterile n’s, axions, dark U(1)…
Coupling

67. BSM Mass Scale Parity Breaking Scale ~ MWR ? Energy Scale
Weak Scale ~ MWL

68. Left-Right Symmetric Model
Parity Breaking Scale ~ MWR ?
Energy Scale
Weak Scale ~ MWL
SU(2)L x SU(2)R x U(1)B-L

69. Left-Right Symmetric Model
See-saw scale ?
Parity Breaking Scale ~ MWR ?
Energy Scale
Weak Scale ~ MWL
SU(2)L x SU(2)R x U(1)B-L

70. Left-Right Symmetric Model
Gauge boson mass eigenstates
CKM Matrices for LH & RH sectors

71. Left-Right Symmetric Model
Dimensionless EDM: d
LRSM: One loop

72. Left-Right Symmetric Model
Dimensionless EDM: d
LRSM: One loop
WL – WR mixing
VCKMR
VCKML

73. Left-Right Symmetric Model
Dimensionless EDM: d
LRSM: One loop
WL – WR mixing
VCKMR
VCKML

74. Left-Right Symmetric Model
Dimensionless EDM: d
LRSM: Neutron

75. Left-Right Symmetric Model
Four quark operator: dL uL uR dR W+ 

76. Left-Right Symmetric Model
Four quark operator: dL uL uR dR W+ 
Caveat: large nuclear theory uncertainty !

77. EDM Interpretation & Multiple Scales
Collider Searches
Particle spectrum; also scalars for baryon asym
Baryon Asymmetry
Early universe CPV
BSM CPV
SUSY, GUTs, Extra Dim…
Energy Scale
d= 6 Effective Operators: “CPV Sources”
fermion EDM, quark chromo EDM, 3 gluon, 4 fermion
QCD Matrix Elements
dn , gNN , …
Nuclear & atomic MEs
Schiff moment, other P- & T-odd moments, e-nucleus CPV
Expt

78. Wilson Coefficients: Summary
f fermion EDM (3)
q quark CEDM (2)
CG 3 gluon (1)
Cquqd non-leptonic (2)
Clequ, ledq semi-leptonic (3)
Cud induced 4f (1) ~ ~
light flavors only (e,u,d)
12 total +  78

79. BSM Origins dL uL uR dR W+ EDM: ff CEDM: gff Weinberg ggg:RS
MSSM
LRSM dL uL uR dR W+ 
EDM: ff
CEDM: gff
Weinberg ggg:
Four fermion
udHH

80. Back Up Slides

81. EDM Probes: EWB Implications
sinCP ~ 1 ! M > 5000 GeV
M < 500 GeV! sinCP < 10-2
Universal gaugino phases
Arg(Mib*) =
Arg(Mjb*)
Cirigliano, R-M, Tulin, Lee ‘06
Ritz CIPANP 09 +
Cirigliano, R-M, Tulin, Lee ‘06

82. EDMs BSM: MSSM
j = arg (Mjb*)
A = arg (Af Mj )
One Loop: EDM, cEDM

83. EDMs BSM: MSSM j = arg (Mjb*) A = arg (Af Mj ) Quark & Lepton EDMs
Universality Assumption

Common A
A = arg (Af Mj )
EW scale
Quark & Lepton EDMs
EWSB

84. MSSM: SUSY Breaking Models I
Visible Sector:
Hidden Sector: SUSY-breaking
MSSM
Flavor-blind mediation
Gravity-Mediated (mSUGRA)

85. MSSM: SUSY Breaking Models II
Visible Sector:
Hidden Sector: SUSY-breaking
MSSM
Flavor-blind mediation
Gauge-Mediated (GMSB)
messengers

86. MSSM: SUSY Breaking Models III
Visible Sector:
Hidden Sector: SUSY-breaking
MSSM
Flavor-blind mediation
Parameter evolution: mass
at the weak scale

87. GF & the “hierarchy problem”
SUSY Relation:
Quadratic divergence ~ UV2 cancels
After EWSB:

88. Gaugino-Higgsino Mixing
= N11B 0 + N12W 0 + N13Hd0 + N14Hu0
BINO
WINO
HIGGSINO
T << TEW
Chargino Mass Matrix
T << TEW : mixing of H,W to c+, c0 ~
T ~TEW : scattering of H,W from background field
CPV M2 m
MC =
Neutralino Mass Matrix M1 -m M2
-mZ cos b sin qW
mZ cos b cos qW
mZ sin b sin qW
-mZ sin b sin qW
MN =

89. Relic Abundance of SUSY DM
T << TEW : mixing of H,W to c+, c0 ~
Neutralino Mass Matrix M1 -m M2
-mZ cos b sin qW
mZ cos b cos qW
mZ sin b sin qW
-mZ sin b sin qW
MN =
= N11B 0 + N12W 0 + N13Hd0 + N14Hu0
BINO
WINO
HIGGSINO
+ res
+ coannihilation

90. Sfermion Mixing T ~TEW : scattering of fL, fR from background field
T << TEW : mixing of fL, fR to f1, f2 ~
T ~TEW : scattering of fL, fR from background field
Sfermion mass matrix
Qf < 0
Qf > 0