Supersymmetry and Electric Dipole Moments Apostolos Pilaftsis - - PowerPoint PPT Presentation

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Supersymmetry and Electric Dipole Moments Apostolos Pilaftsis School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom & Department of Theoretical Physics and IFIC, University of Valencia, E-46100,

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SLIDE 1

Supersymmetry and Electric Dipole Moments

Apostolos Pilaftsis

School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom & Department of Theoretical Physics and IFIC, University of Valencia, E-46100, Valencia, Spain

SUSY 2011, 1 September 2011, Fermilab, USA

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SLIDE 2

Plan of the talk

  • Flavour and CP Violation in the MSSM
  • Electric Dipole Moments
  • Geometric Approach for Optimizing CP Violation
  • Nuclei with Enhanced Schiff Moments
  • Summary

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
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SLIDE 3
  • Flavour and CP Violation in the MSSM

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-4
SLIDE 4
  • Flavour and CP Violation in the MSSM

31 ⊕ 33 ⊕ 47 = 111

  • Gaugino masses: 3 ⊕ 3 = 6

−Lsoft ⊃ 1 2(M3 g g + M2 W W + M1 B B + h.c.)

  • Trilinear couplings: afij ≡ hfij · Afij: 3 × (3 ⊕ 6 ⊕ 9) = 54

−Lsoft ⊃ ( u∗

R au

QHu − d∗

R ad

QHd − e∗

R ae

LHd + h.c.)

  • Sfermion masses: 5 × (3 ⊕ 3 ⊕ 3) = 45

−Lsoft ⊃ Q† M2

e Q

Q + L† M2

e L

L + u∗

R M2 e u

uR + d∗

R M2 e d

dR + e∗

R M2 e e

eR

  • Higgs masses: 3 ⊕ 1 = 4, and the µ-term: 1 ⊕ 1 = 2

−Lsoft ⊃ M 2

HuH† uHu + M 2 HdH† dHd + (BµHuHd + h.c.) SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-5
SLIDE 5
  • Flavour and CP Violation in the MSSM

31 ⊕ 33 ⊕ 45 = 109 !

  • Gaugino masses: 3 ⊕ 3 = 6

−Lsoft ⊃ 1 2(M3 g g + M2 W W + M1 B B + h.c.)

  • Trilinear couplings: afij ≡ hfij · Afij: 3 × (3 ⊕ 6 ⊕ 9) = 54

−Lsoft ⊃ ( u∗

R au

QHu − d∗

R ad

QHd − e∗

R ae

LHd + h.c.)

  • Sfermion masses: 5 × (3 ⊕ 3 ⊕ 3) = 45

−Lsoft ⊃ Q† M2

e Q

Q + L† M2

e L

L + u∗

R M2 e u

uR + d∗

R M2 e d

dR + e∗

R M2 e e

eR

  • Higgs masses: 3 ⊕ 1 = 4, and the µ-term: 1 ⊕ 1 = 2

−Lsoft ⊃ M 2

HuH† uHu + M 2 HdH† dHd + (BµHuHd + h.c.) SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
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SLIDE 6
  • Minimal Flavour Violating Approach to Flavour and CP
  • The MFV:

m0(MMFV) , m1/2(MMFV) , A(MMFV) ; tan β(mt) , MZ up to sign(µ) with real and positive m0, m1/2, and A

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-7
SLIDE 7
  • Minimal Flavour Violating Approach to Flavour and CP
  • The MFV:

m0(MMFV) , m1/2(MMFV) , A(MMFV) ; tan β(mt) , MZ up to sign(µ) with real and positive m0, m1/2, and A

  • Next to MFV:

m0(MMFV) , m1/2(MMFV) , A(MMFV) ; tan β(mt) , MZ with complex m1/2 and A

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-8
SLIDE 8
  • Minimal Flavour Violating Approach to Flavour and CP
  • The MFV:

m0(MMFV) , m1/2(MMFV) , A(MMFV) ; tan β(mt) , MZ up to sign(µ) with real and positive m0, m1/2, and A

  • Next to MFV:

m0(MMFV) , m1/2(MMFV) , A(MMFV) ; tan β(mt) , MZ with complex m1/2 and A

  • What is the maximal extension to MFV?

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
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SLIDE 9
  • Breaking of the [SU(3) ⊗ U(1)]5 flavour symmetries in the MSSM:

[R. S. Chivukula and H. Georgi, PLB188 (1987) 99;

  • G. D’Ambrosio, G. F. Giudice, G. Isidori, A. Strumia, NPB645 (2002) 155;

Generalization of GIM mechanism: S.L. Glashow, J. Iliopoulos, L. Maiani, PRD2 (1970) 1285.]

hu,d → U†

U,D hu,d UQ ,

he → U†

E he UL ,

  • M2

Q,L,U,D,E

→ U†

Q,L,U,D,E

M2

Q,L,U,D,E UQ,L,U,D,E ,

au,d → U†

U,D au,d UQ ,

ae → U†

E ae UL . SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
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SLIDE 10
  • Breaking of the [SU(3) ⊗ U(1)]5 flavour symmetries in the MSSM:

[R. S. Chivukula and H. Georgi, PLB188 (1987) 99;

  • G. D’Ambrosio, G. F. Giudice, G. Isidori, A. Strumia, NPB645 (2002) 155;

Generalization of GIM mechanism: S.L. Glashow, J. Iliopoulos, L. Maiani, PRD2 (1970) 1285.]

hu,d → U†

U,D hu,d UQ ,

he → U†

E he UL ,

  • M2

Q,L,U,D,E

→ U†

Q,L,U,D,E

M2

Q,L,U,D,E UQ,L,U,D,E ,

au,d → U†

U,D au,d UQ ,

ae → U†

E ae UL .

  • Maximal CP and Minimal Flavour Violation (MCPMFV)

[e.g. J. Ellis, J. S. Lee, A. P., PRD76 (2007) 115011.]

M1,2,3 , M 2

Hu,d ,

  • M2

Q,L,U,D,E =

M 2

Q,L,U,D,E 13 ,

Au,d,e = Au,d,e 13 3 ⊕ 3 2 5 3 ⊕ 3 13 ⊕ 6 = 19 Parameters !

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-11
SLIDE 11
  • Electric Dipole Moments

T Violation ⇐ ⇒ CP Violation (under CPT) Experimental limits: |dTl| < 9 × 10−25 e · cm → |de| < 1.7 × 10−27 e · cm

[B. C. Regan, E. D. Commins, C. J. Schmidt, D. DeMille, PRL88 (2002) 071805]

|dn| < 3 × 10−26 e · cm

[C. A. Baker et al., PRL97 (2006) 131801.]

|dHg| < 3.1 × 10−29 e · cm

[W. C. Griffith et al, PRL102 (2009) 101601.]

Future Deuteron EDM:

[Y. K. Semertzidis et al. [EDM Collaboration], AIP Conf. Proc. 698 (2004) 200;

  • Y. F. Orlov, W. M. Morse, Y. K. Semertzidis, PRL96 (2006) 214802.]

|dD| < (1–3) × 10−27 e · cm → 10−29 e · cm

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-12
SLIDE 12
  • EDMs in the MSSM

× × fL fR ˜ g ˜ fL ˜ fR × ×

  • W3,

B ˜ fL ˜ fR × ˜ f ′

L

  • W −˜

h−

2 , ˜

h−

1

with f = e, u, d df e 1−loop ∼ (10−25 cm)×{Im mλ, Im Af} max(M ˜

f, mλ)

  • 1 TeV

max(M ˜

f, mλ)

2 mf 10 MeV

  • SUSY ’11, Fermilab, 1 September 2011
  • A. Pilaftsis
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SLIDE 13
  • EDMs in the MSSM

× × fL fR ˜ g ˜ fL ˜ fR × ×

  • W3,

B ˜ fL ˜ fR × ˜ f ′

L

  • W −˜

h−

2 , ˜

h−

1

with f = e, u, d df e 1−loop ∼ (10−25 cm)×{Im mλ, Im Af} max(M ˜

f, mλ)

  • 1 TeV

max(M ˜

f, mλ)

2 mf 10 MeV

  • Schemes for resolving the 1-loop CP crisis:

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-14
SLIDE 14
  • EDMs in the MSSM

× × fL fR ˜ g ˜ fL ˜ fR × ×

  • W3,

B ˜ fL ˜ fR × ˜ f ′

L

  • W −˜

h−

2 , ˜

h−

1

with f = e, u, d df e 1−loop ∼ (10−25 cm)×{Im mλ, Im Af} max(M ˜

f, mλ)

  • 1 TeV

max(M ˜

f, mλ)

2 mf 10 MeV

  • Schemes for resolving the 1-loop CP crisis:
  • Im mλ/|mλ|, Im Af/|Af| <

∼ 10−3; M ˜ f, mλ ∼ 200 GeV SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
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SLIDE 15
  • EDMs in the MSSM

× × fL fR ˜ g ˜ fL ˜ fR × ×

  • W3,

B ˜ fL ˜ fR × ˜ f ′

L

  • W −˜

h−

2 , ˜

h−

1

with f = e, u, d df e 1−loop ∼ (10−25 cm)×{Im mλ, Im Af} max(M ˜

f, mλ)

  • 1 TeV

max(M ˜

f, mλ)

2 mf 10 MeV

  • Schemes for resolving the 1-loop CP crisis:
  • Im mλ/|mλ|, Im Af/|Af| <

∼ 10−3; M ˜ f, mλ ∼ 200 GeV

  • CP phases ∼ 1, but M ˜

f > ∼ 5–10 TeV, for ˜

f = ˜ u, ˜ d, ˜ e, ˜ νL

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-16
SLIDE 16
  • EDMs in the MSSM

× × fL fR ˜ g ˜ fL ˜ fR × ×

  • W3,

B ˜ fL ˜ fR × ˜ f ′

L

  • W −˜

h−

2 , ˜

h−

1

with f = e, u, d df e 1−loop ∼ (10−25 cm)×{Im mλ, Im Af} max(M ˜

f, mλ)

  • 1 TeV

max(M ˜

f, mλ)

2 mf 10 MeV

  • Schemes for resolving the 1-loop CP crisis:
  • Im mλ/|mλ|, Im Af/|Af| <

∼ 10−3; M ˜ f, mλ ∼ 200 GeV

  • CP phases ∼ 1, but M ˜

f > ∼ 5–10 TeV, for ˜

f = ˜ u, ˜ d, ˜ e, ˜ νL

  • Cancellations between the different EDM terms

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
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SLIDE 17

An incomplete list of studies of EDMs:

  • 1-loop EDMs:
  • J. Ellis, S. Ferrara and D.V. Nanopoulos, PLB114 (1982) 231;
  • W. Buchm¨

uller and D. Wyler, PLB121 (1983) 321;

  • J. Polchinski and M. Wise, PLB125 (1983) 393; . . .
  • Heavy squark/gaugino decoupling:
  • P. Nath, PRL66 (1991) 2565;
  • Y. Kizukuri and N. Oshimo, PRD46 (1992) 3025
  • Cancellation mechanism:
  • T. Ibrahim and P. Nath, PLB418 (1998) 98;
  • M. Brhlik, L. Everett, G.L. Kane and J. Lykken, PRL83 (1999) 2124.
  • Constraints from dHg:
  • T. Falk, K.A. Olive, M. Pospelov and R. Roiban, NPB600 (1999)3;
  • S. Abel, S. Khalil and O. Lebedev, NPB606 (2001) 151.
  • EDMs induced by the 3g-Weinberg operator:
  • J. Dai, H. Dykstra, R.G. Leigh, S. Paban and D. Dicus, PLB237 (1990) 216.
  • Higgs-Mediated 2-Loop EDMs:
  • D. Chang, W.-Y. Keung and A.P., PRL82 (1999) 900;

A.P., NPB644 (2002) 263.

  • Reviews:
  • M. Pospelov, A. Ritz, Annals Phys. 318 (2005) 119;
  • J. R. Ellis, J. S. Lee, A. P., JHEP0810 (2008) 049.

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-18
SLIDE 18

Weinberg’s three-gluon operator × × × gµ gν gλ ˜ gR ˜ gL tL tR ˜ tL ˜ tR L3g = − 1

3! d3g f abc

Ga µ

ν

Gb ν

λ Gc λ µ SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-19
SLIDE 19

Weinberg’s three-gluon operator × × × gµ gν gλ ˜ gR ˜ gL tL tR ˜ tL ˜ tR L3g = − 1

3! d3g f abc

Ga µ

ν

Gb ν

λ Gc λ µ

Estimate based on naive dimensional analysis: d3g ∼ g3

s

4π 3α2

s

16π2 m˜

g m2 t Im (At − µ∗ cot β)

m4

˜ g M 2 ˜ t

= ⇒ dn e

  • 3g

∼ (10−26 cm) × 0.5 TeV m˜

g

  • 2 m2

t Im (At − µ∗ cot β)

M 2

˜ t m˜ g

EDM constraint: m˜

g > ∼ 400 GeV. SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-20
SLIDE 20

The proper Weinberg three-gluon operator in the MSSM

[S. Weinberg, PRL63 (1989) 2333;

  • D. A. Dicus, PRD41 (1990) 999;
  • J. R. Ellis, J. S. Lee, A. P., JHEP0810 (2008) 049]

t, b ˜ t,˜ b ˜ g t, b Hi

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-21
SLIDE 21

Higgs-Mediated 2-Loop EDMs

[ D. Chang, W.-Y. Keung, A.P., PRL82 (1999) 900; A.P., NPB644 (2002) 263; SUSY extension of the mechanism by S.M. Barr, A. Zee, PRL65 (1990) 21.] f a, φ1,2 γ, (g) f f γ, (g) ˜ t, ˜ t∗, ˜ b, ˜ b∗ (a) f a, φ1,2 γ, (g) γ, (g) f f ˜ t, ˜ t∗, ˜ b, ˜ b∗ (b) f a, φ1,2 γ, (g) f f γ, (g) t, tC, b, bC (c) f a, φ1,2 γ f f γ χ± (d)

df ∝ arg(µAt, µm˜

g, µmf W) , tan β ,

1 Ma

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-22
SLIDE 22

Other Higgs-mediated contributions

[ A.P., NPB644 (2002) 263;

  • D. A. Demir, O. Lebedev, K. A. Olive, M. Pospelov and A. Ritz, NPB680 (2004) 339;

initially studied in the 2HDM by S. Barr, PRL68 (1992) 1822.] tβ t2

β

a φ1,2, a e− e− g g b, bC, t, tC (a) a φ1,2, a e− e− g g ˜ t, ˜ t∗, ˜ b, ˜ b∗ + a φ1,2, a e− e− g g ˜ t, ˜ t∗, ˜ b, ˜ b∗ (b)

C(b,bC)

S

∝ arg(µAt, µm˜

g) , tan3 β ,

1 M 3

a SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-23
SLIDE 23

And . . . more EDM contributions:

  • FCNC effects on EDMs

[J. Hisano, M. Nagai, P. Paradisi, PRD78 (2008) 075019.]

  • Higgsino-mediated 2-loop EDMs

[A.P., PRD62 (2000) 016007.]

  • Other subdominant 2-loop EDMs

[A.P., PLB471 (1999) 174;

  • Y. Li, S. Profumo, M. Ramsey-Musolf, PLB673 (2009) 95.]

Most EDM contributions now included in CPsuperH2.2

[J.S. Lee, M. Carena, J. Ellis, A.P., C. Wagner, CPC180 (2009) 312.] SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-24
SLIDE 24
  • Geometric Approach for Optimizing CP Violation

Simple 3D Example:

  • Φ2
  • Φ3
  • Φ1

E ≡ ∇E O ≡ ∇O Φ∗ CP-violating observable: O(Φ1,2,3) ≈ Φ · O, with O = ∇O. EDM constraint: E(Φ1,2,3) ≈ Φ · E = 0, with E = ∇E. Optimal CP-odd direction: Φ∗ = E ×

  • O × E
  • .

Maximum allowed value: O = φ∗ Φ∗ · O = ± φ∗

  • |O|2 − (O ·

E)2 .

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-25
SLIDE 25
  • Generalization to N Dimensions

[J. Ellis, J. S. Lee, A.P., JHEP10 (2010) 049.]

A 6D Example: the MCPMFV model with 3 EDM constraints Ea,b,c = 0 E = ⇒ Aαβγ = Ea

[α Eb β Ec γ] :

Triple exterior product. O × E = ⇒ Bµν = εµνλρστ Oλ Ea

ρ Eb σ Ec τ :

Hodge-dual product 6D Optimal direction for the CP-odd observable O: Φ∗

α = N εαβγδµν Aβγδ Bµν = N εαβγδµν εµνλρστ Ea β Eb γ Ec δ Oλ Ea ρ Eb σ Ec τ

Maximum allowed value for the observable O: O = φ∗ Φ∗

κ Oκ

= ± N

  • εµναβγδ εµνλρστ Oα Oλ Ea

β Eb γ Ec δ Ea ρ Eb σ Ec τ

  • ,

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-26
SLIDE 26

Maximazing dD, dµ and ACP

[J. Ellis, J. S. Lee, A.P., JHEP10 (2010) 049.]

tanβ | Φ

∧ * ⋅ O [ dD / dD EXP

] | φ

∼ α = 0o

 : dD dir. − − : dµ dir. ⋅ ⋅ ⋅ ⋅ : ACP dir.  : ∆Φ1,Ae=0 dir.  : ∆Φ2,3=0 dir. tanβ | Φ

∧ * ⋅ O [ dµ / dµ EXP

] |

φ

∼ α = 0o

tanβ | Φ

∧ * ⋅ O [ ACP ( % ) ] |

φ

∼ α = 0o

tanβ | Φ

∧ * ⋅ O [ dD / dD EXP

] |

φ

∼ α = 180o

tanβ | Φ

∧ * ⋅ O [ dµ / dµ EXP

] |

φ

∼ α = 180o

tanβ | Φ

∧ * ⋅ O [ ACP ( % ) ] |

φ

∼ α = 180o

10

  • 2

10

  • 1

1 20 40 10

  • 5

10

  • 4

10

  • 3

20 40 10

  • 4

10

  • 3

10

  • 2

20 40 10

  • 2

10

  • 1

1 20 40 10

  • 5

10

  • 4

10

  • 3

20 40 10

  • 4

10

  • 3

10

  • 2

20 40

M 2

Hu = M 2 Hd = f

M 2

Q = f

M 2

U = f

M 2

D = f

M 2

L = f

M 2

E = (100 GeV)2 ,

|M1,2,3| = 250 GeV , |Au| = |Ad| = |Ae| = 100 GeV , tan β = 40

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-27
SLIDE 27

EDM constraints on the length φ∗ = |Φ∗(MGUT)|

[J. Ellis, J. S. Lee, A.P., JHEP10 (2010) 049.]

φ* dTl / dTl

EXP

φ

∼ α = 0o

 : dD dir. − − : dµ dir. ⋅⋅⋅⋅⋅ : ACP dir.  : ∆Φ1,Ae=0 dir.  : ∆Φ2,3=0 dir. φ* dn

(QCD) / dn EXP

φ

∼ α = 0o

φ* dHg / dHg

EXP

φ

∼ α = 0o

φ* dTl / dTl

EXP

φ

∼ α = 180o

φ* dn

(QCD) / dn EXP

φ

∼ α = 180o

φ* dHg / dHg

EXP

φ

∼ α = 180o

  • 4
  • 3
  • 2
  • 1

1 2 3 4

  • 100

100

  • 1
  • 0.75
  • 0.5
  • 0.25

0.25 0.5 0.75 1

  • 100

100

  • 5
  • 4
  • 3
  • 2
  • 1

1 2 3 4 5

  • 100

100

  • 4
  • 3
  • 2
  • 1

1 2 3 4

  • 100

100

  • 1.5
  • 1
  • 0.5

0.5 1 1.5

  • 100

100

  • 8
  • 6
  • 4
  • 2

2 4 6 8

  • 100

100

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-28
SLIDE 28

EDM constraints on CP-odd phases at MSUSY, for tan β = 10

[J. Ellis, J. S. Lee, A.P., JHEP10 (2010) 049.]

φ* Φ1 [

  • ]

 : dD dir. − − : dµ dir. ⋅⋅⋅⋅ : ACP dir.  : ∆Φ1,Ae=0 dir.  : ∆Φ2,3=0 dir.

φ* Φ2 [

  • ]

φ* Φ3 [

  • ]

φ* ΦAu [

  • ]

φ* ΦAd [

  • ]

φ* ΦAe [

  • ]

φ* ΦAt ( MSUSY )[

  • ]

φ* ΦAb ( MSUSY )[

  • ]

φ* ΦAτ ( MSUSY )[

  • ]
  • 4
  • 2

2 4

  • 100

100

  • 1
  • 0.5

0.5 1

  • 100

100

  • 2

2

  • 100

100

  • 50

50

  • 100

100

  • 50

50

  • 100

100

  • 50

50

  • 100

100 176 178 180 182 184

  • 100

100 170 180 190

  • 100

100 140 160 180 200 220

  • 100

100

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-29
SLIDE 29

Maximal allowed values for dD, dµ and ACP

[J. Ellis, J. S. Lee, A.P., JHEP10 (2010) 049.]

φ* dD / dD

EXP

 : dD dir. − − : dµ dir. ⋅⋅⋅⋅ : ACP dir.  : ∆Φ1,Ae=0 dir.  : ∆Φ2,3=0 dir.

φ

~ α = 0o

φ* dµ / dµ

EXP

φ

~ α = 0o

φ* ACP [ % ] φ

~ α = 0o

φ* dD / dD

EXP

φ

~ α = 180o

φ* dµ / dµ

EXP

φ

~ α = 180o

φ* ACP [ % ] φ

~ α = 180o

  • 10
  • 8
  • 6
  • 4
  • 2

2 4 6 8 10

  • 100

100

  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4

  • 100

100

  • 3
  • 2
  • 1

1 2 3

  • 100

100

  • 10
  • 8
  • 6
  • 4
  • 2

2 4 6 8 10

  • 100

100

  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4

  • 100

100

  • 0.04
  • 0.03
  • 0.02
  • 0.01

0.01 0.02 0.03 0.04

  • 100

100

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-30
SLIDE 30

Interplay between EDMs and Observables

[J. Ellis, J. S. Lee, A.P., JHEP10 (2010) 049.]

tanβ Cos ( O [ dD ] ⋅ E

a ; φ ∼ α

= 0

  • )

dTl dn dHg tanβ Cos ( O [ dµ ] ⋅ E

a ; φ ∼ α

= 0

  • )

tanβ Cos ( O [ ACP ] ⋅ E

a ; φ ∼ α

= 0

  • )

tanβ Cos ( O [ dD ] ⋅ E

a ; φ ∼ α

= 180

  • )

tanβ Cos ( O [ dµ ] ⋅ E

a ; φ ∼ α

= 180

  • )

tanβ Cos ( O [ ACP ] ⋅ E

a ; φ ∼ α

= 180

  • )
  • 1
  • 0.75
  • 0.5
  • 0.25

0.25 0.5 0.75 1 20 40

  • 1
  • 0.75
  • 0.5
  • 0.25

0.25 0.5 0.75 1 20 40

  • 1
  • 0.75
  • 0.5
  • 0.25

0.25 0.5 0.75 1 20 40

  • 1
  • 0.75
  • 0.5
  • 0.25

0.25 0.5 0.75 1 20 40

  • 1
  • 0.75
  • 0.5
  • 0.25

0.25 0.5 0.75 1 20 40

  • 1
  • 0.75
  • 0.5
  • 0.25

0.25 0.5 0.75 1 20 40

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-31
SLIDE 31

7D Extension: including θQCD (tan β = 10)

[J. Ellis, J. S. Lee, A.P., JHEP10 (2010) 049.]

φ* dTl / dTl

EXP

φ

∼ α = 0o

 : dD dir. − − : dµ dir. ⋅⋅⋅⋅⋅ : ACP dir.  : ∆Φ1,Ae=θ

∧=0 dir.

 : ∆Φ2,3=θ

∧=0 dir.

φ* dn

(QCD) / dn EXP

φ

∼ α = 0o

φ* dHg / dHg

EXP

φ

∼ α = 0o

φ* dD / dD

EXP

φ

~ α = 0o

φ* dµ / dµ

EXP

φ

~ α = 0o

φ* ACP [ % ]

φ

~ α = 0o

  • 10
  • 8
  • 6
  • 4
  • 2

2 4 6 8 10

  • 50

50

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4 0.5

  • 50

50

  • 4
  • 3
  • 2
  • 1

1 2 3 4

  • 50

50

  • 100
  • 80
  • 60
  • 40
  • 20

20 40 60 80 100

  • 50

50

  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4

  • 50

50

  • 0.08
  • 0.06
  • 0.04
  • 0.02

0.02 0.04 0.06 0.08

  • 50

50

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-32
SLIDE 32
  • Nuclei with Enhanced Schiff Moments

[L. I. Schiff, Phys. Rev. 132 (1963) 2194;

  • I. B. Khriplovich, R. A. Korkin, Nucl. Phys. A665 (2000) 365.]

T/CP-odd πNN interactions: LT

/ πNN = ¯

g(0)

πNNNτ aNπa + ¯

g(1)

πNNNNπ0 + ¯

g(2)

πNN

  • Nτ aNπa − 3Nτ 3Nπ0

Schiff moment: S = (a0 + b) gπNN¯ g(0)

πNN + a1 gπNN¯

g(1)

πNN + (a2 − b) gπNN¯

g(2)

πNN ,

gπNN: CP/T-even strong coupling constant, gπNN = 13.45. a0,1,2: dependence of the Schiff moment on T-odd interactions. b: dependence on the nucleon dipole moment. ¯ g(0),(1)

πNN

receive contributions predominantly from CEDMs dC

u and dC d , with

¯ g(0)

πNN

¯ g(1)

πNN

= 0.2 × dC

u + dC d

dC

u − dC d [M. Pospelov, PLB530 (2002) 123.] SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-33
SLIDE 33
  • EDMs of 199Hg and 225Ra due to enhanced Schiff moments:

[J. Ellis, J. S. Lee, A.P., JHEP02 (2011) 045, for references] 199Hg EDM:

dHg[S] = 10−17 CS

Hg e · cm ×

  • S

e·fm3

  • .

Both CS

Hg(= −2.8) and S are model-dependent:

d I

Hg[S]

≃ 1.8 × 10−3 e ¯ g(1)

πNN /GeV ,

d II

Hg[S]

≃ 7.6 × 10−6 e ¯ g(0)

πNN /GeV + 1.0 × 10−3 e ¯

g(1)

πNN /GeV ,

d III

Hg[S]

≃ 1.3 × 10−4 e ¯ g(0)

πNN /GeV + 1.4 × 10−3 e ¯

g(1)

πNN /GeV ,

d IV

Hg[S]

≃ 3.1 × 10−4 e ¯ g(0)

πNN /GeV + 9.5 × 10−5 e ¯

g(1)

πNN /GeV . 225Ra EDM to the 10−27 e · cm level (HIE-ISOLDE project): [L. Willman, K. Jungmann, H.W. Wilshut, CERN-INTC-2010-049;

  • J. Pakarinen et al, CERN-INTC-2010-022.]

dRa[S] ≃ −8.7 × 10−2 e ¯ g(0)

πNN /GeV + 3.5 × 10−1 e ¯

g(1)

πNN /GeV .

Typical enhancement factor: dRa[S]/dHg[S] ∼ 200

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-34
SLIDE 34

Interplay of 199Hg and 225Ra EDMs

[J. Ellis, J. S. Lee, A.P., JHEP02 (2011) 045.]

tanβ Cos ( O [ dRa ] ⋅ E

a )

dTl dn d

Hg I

d

Hg II

d

Hg III

d

Hg IV

  • 1
  • 0.75
  • 0.5
  • 0.25

0.25 0.5 0.75 1 5 10 15 20 25 30 35 40

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-35
SLIDE 35

Maximal 225Ra EDM for tan β = 40

[J. Ellis, J. S. Lee, A.P., JHEP02 (2011) 045.]

φ* dRa / 10

  • 27 e cm

d

Hg I

 : dRa dir. − − − − : Φ1,Ae=0 dir. ⋅⋅⋅⋅⋅⋅⋅⋅⋅ : Φ2,3=0 dir.

φ* dRa / 10

  • 27 e cm

d

Hg II

φ* dRa / 10

  • 27 e cm

d

Hg III

φ* dRa / 10

  • 27 e cm

d

Hg IV

  • 15
  • 10
  • 5

5 10 15

  • 100
  • 50

50 100

  • 15
  • 10
  • 5

5 10 15

  • 100
  • 50

50 100

  • 15
  • 10
  • 5

5 10 15

  • 100
  • 50

50 100

  • 100
  • 80
  • 60
  • 40
  • 20

20 40 60 80 100

  • 100
  • 50

50 100

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-36
SLIDE 36
  • SUMMARY
  • The MSSM with MFV extended to MCPMFV is an interesting

framework for studying New Physics. It contains 19 parameters = 13 CP-even ⊕ 6 CP-odd.

  • Non-observation of Thallium, neutron and Mercury EDMs give

strict constraints on 3 combinations of the 6 soft CP-odd phases

  • f MFV-type scenarios.
  • Geometric approach introduced for maximazing CP observables in

the small phase approximation.

  • Interplay of future EDM observables (Deuteron and Radium) will

further constrain soft CP violation in SUSY, including θQCD. = ⇒ Pushing the limit to θQCD <

∼ 10−12 SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis
slide-37
SLIDE 37
  • EDMs constrain:

– Radiative Higgs-sector CP violation at Tevatron and LHC.

[A.P., PLB435 (1998) 88; A.P., C. Wagner, NPB553 (1999) 3; S.Y. Choi, M. Drees, J.S. Lee, PLB481 (2000) 57;

  • M. Carena et al, NPB586 (2000) 92; NPB659 (2003) 145.]

– Resonant CP Violation at LHC, ILC (e+e−) and γγ colliders.

[ A.P., NPB504 (1997) 61;

  • J. Ellis, J.S. Lee, A.P., PRD70 (2004) 075010; PRD72 (2005) 095006; NPB718 (2005) 247.]

– FCNC observables: ∆MK,B, ǫK, ǫ′/ǫ, B(Bd,s → ℓ+ℓ−), ACP(Bd,s → ℓ+

L(R)ℓ− L(R)),

B(B → Xsγ), . . .

[For review, see, T. Ibrahim and P. Nath, RMP80 (2008) 577; talk by M. Neubert]

– Electroweak Baryogenesis in the MSSM

[M. Carena, M. Quiros, M. Seco, C. Wagner, NPB650 (2003) 24;

  • T. Konstandin, T. Prokopec, M. G. Schmidt, M. Seco, NPB738 (2006) 1;
  • D. J. H. Chung, B. Garbrecht, M. J. Ramsey-Musolf and S. Tulin, PRL102 (2009) 061301.]

SUSY ’11, Fermilab, 1 September 2011

  • A. Pilaftsis