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
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
• Flavour and CP Violation in the MSSM SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• Flavour and CP Violation in the MSSM 31 ⊕ 33 ⊕ 47 = 111 • Gaugino masses: 3 ⊕ 3 = 6 −L soft ⊃ 1 g + M 2 � W � W + M 1 � B � 2( M 3 � g � B + h . c . ) • Trilinear couplings: a f ij ≡ h f ij · A f ij : 3 × (3 ⊕ 6 ⊕ 9) = 54 R a u � QH u − � R a d � R a e � u ∗ d ∗ e ∗ −L soft ⊃ ( � QH d − � LH d + h . c . ) • Sfermion masses: 5 × (3 ⊕ 3 ⊕ 3) = 45 Q † M 2 L † M 2 −L soft ⊃ � Q � Q + � L � u R + � d � u ∗ R M 2 d ∗ R M 2 e ∗ R M 2 L + � u � d R + � e � e R e e e e e • Higgs masses: 3 ⊕ 1 = 4 , and the µ - term : 1 ⊕ 1 = 2 H d H † −L soft ⊃ M 2 H u H † u H u + M 2 d H d + ( BµH u H d + h . c . ) SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• Flavour and CP Violation in the MSSM 31 ⊕ 33 ⊕ 45 = 109 ! • Gaugino masses: 3 ⊕ 3 = 6 −L soft ⊃ 1 g + M 2 � W � W + M 1 � B � 2( M 3 � g � B + h . c . ) • Trilinear couplings: a f ij ≡ h f ij · A f ij : 3 × (3 ⊕ 6 ⊕ 9) = 54 R a u � QH u − � R a d � R a e � u ∗ d ∗ e ∗ −L soft ⊃ ( � QH d − � LH d + h . c . ) • Sfermion masses: 5 × (3 ⊕ 3 ⊕ 3) = 45 Q † M 2 L † M 2 −L soft ⊃ � Q � Q + � L � u R + � d � u ∗ R M 2 d ∗ R M 2 e ∗ R M 2 L + � u � d R + � e � e R e e e e e • Higgs masses: 3 ⊕ 1 = 4 , and the µ - term : 1 ⊕ 1 = 2 H d H † −L soft ⊃ M 2 H u H † u H u + M 2 d H d + ( BµH u H d + h . c . ) SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• Minimal Flavour Violating Approach to Flavour and CP • The MFV: m 0 ( M MFV ) , m 1 / 2 ( M MFV ) , A ( M MFV ) ; tan β ( m t ) , M Z up to sign( µ ) with real and positive m 0 , m 1 / 2 , and A SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• Minimal Flavour Violating Approach to Flavour and CP • The MFV: m 0 ( M MFV ) , m 1 / 2 ( M MFV ) , A ( M MFV ) ; tan β ( m t ) , M Z up to sign( µ ) with real and positive m 0 , m 1 / 2 , and A • Next to MFV: m 0 ( M MFV ) , m 1 / 2 ( M MFV ) , A ( M MFV ) ; tan β ( m t ) , M Z with complex m 1 / 2 and A SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• Minimal Flavour Violating Approach to Flavour and CP • The MFV: m 0 ( M MFV ) , m 1 / 2 ( M MFV ) , A ( M MFV ) ; tan β ( m t ) , M Z up to sign( µ ) with real and positive m 0 , m 1 / 2 , and A • Next to MFV: m 0 ( M MFV ) , m 1 / 2 ( M MFV ) , A ( M MFV ) ; tan β ( m t ) , M Z with complex m 1 / 2 and A • What is the maximal extension to MFV? SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• 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.] U † → U † → h u,d U,D h u,d U Q , h e E h e U L , � U † Q,L,U,D,E � M 2 M 2 → Q,L,U,D,E U Q,L,U,D,E , Q,L,U,D,E U † → U † a u,d → U,D a u,d U Q , a e E a e U L . SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• 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.] U † → U † → h u,d U,D h u,d U Q , h e E h e U L , � U † Q,L,U,D,E � M 2 M 2 → Q,L,U,D,E U Q,L,U,D,E , Q,L,U,D,E U † → U † a u,d → U,D a u,d U Q , a e E a e U L . • Maximal CP and Minimal Flavour Violation (MCPMFV) [e.g. J. Ellis, J. S. Lee, A. P., PRD76 (2007) 115011.] � Q,L,U,D,E = � M 2 M 2 M 2 M 1 , 2 , 3 , H u,d , Q,L,U,D,E 1 3 , A u,d,e = A u,d,e 1 3 3 ⊕ 3 3 ⊕ 3 2 5 13 ⊕ 6 = 19 Parameters ! SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• Electric Dipole Moments T Violation ⇐ ⇒ CP Violation (under CPT) Experimental limits: | d Tl | < 9 × 10 − 25 e · cm | d e | < 1 . 7 × 10 − 27 e · cm → [B. C. Regan, E. D. Commins, C. J. Schmidt, D. DeMille, PRL88 (2002) 071805] | d n | < 3 × 10 − 26 e · cm [C. A. Baker et al. , PRL97 (2006) 131801.] | d Hg | < 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.] | d D | < (1 – 3) × 10 − 27 e · cm 10 − 29 e · cm → SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• EDMs in the MSSM ˜ f ′ ˜ ˜ ˜ ˜ L f L f R f L f R × × with f = e, u, d × × × f L f R g ˜ W − ˜ 2 , ˜ W 3 , � � � h − h − B 1 � � 2 � � d f � 1 − loop � ∼ (10 − 25 cm) ×{ Im m λ , Im A f } 1 TeV m f e max( M ˜ f , m λ ) max( M ˜ f , m λ ) 10 MeV SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• EDMs in the MSSM ˜ f ′ ˜ ˜ ˜ ˜ L f L f R f L f R × × with f = e, u, d × × × f L f R g ˜ W − ˜ 2 , ˜ W 3 , � � � h − h − B 1 � � 2 � � d f � 1 − loop � ∼ (10 − 25 cm) ×{ Im m λ , Im A f } 1 TeV m f e max( M ˜ f , m λ ) max( M ˜ f , m λ ) 10 MeV Schemes for resolving the 1-loop CP crisis: SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• EDMs in the MSSM ˜ f ′ ˜ ˜ ˜ ˜ L f L f R f L f R × × with f = e, u, d × × × f L f R g ˜ W − ˜ 2 , ˜ W 3 , � � � h − h − B 1 � � 2 � � d f � 1 − loop � ∼ (10 − 25 cm) ×{ Im m λ , Im A f } 1 TeV m f e max( M ˜ f , m λ ) max( M ˜ f , m λ ) 10 MeV Schemes for resolving the 1-loop CP crisis: ∼ 10 − 3 ; M ˜ • Im m λ / | m λ | , Im A f / | A f | < f , m λ ∼ 200 GeV SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• EDMs in the MSSM ˜ f ′ ˜ ˜ ˜ ˜ L f L f R f L f R × × with f = e, u, d × × × f L f R g ˜ W − ˜ 2 , ˜ W 3 , � � � h − h − B 1 � � 2 � � d f � 1 − loop � ∼ (10 − 25 cm) ×{ Im m λ , Im A f } 1 TeV m f e max( M ˜ f , m λ ) max( M ˜ f , m λ ) 10 MeV Schemes for resolving the 1-loop CP crisis: ∼ 10 − 3 ; M ˜ • Im m λ / | m λ | , Im A f / | A f | < f , m λ ∼ 200 GeV ∼ 5 –10 TeV, for ˜ u, ˜ > • CP phases ∼ 1 , but M ˜ f = ˜ d, ˜ e, ˜ ν L f SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
• EDMs in the MSSM ˜ f ′ ˜ ˜ ˜ ˜ L f L f R f L f R × × with f = e, u, d × × × f L f R g ˜ W − ˜ 2 , ˜ W 3 , � � � h − h − B 1 � � 2 � � d f � 1 − loop � ∼ (10 − 25 cm) ×{ Im m λ , Im A f } 1 TeV m f e max( M ˜ f , m λ ) max( M ˜ f , m λ ) 10 MeV Schemes for resolving the 1-loop CP crisis: ∼ 10 − 3 ; M ˜ • Im m λ / | m λ | , Im A f / | A f | < f , m λ ∼ 200 GeV ∼ 5 –10 TeV, for ˜ u, ˜ > • CP phases ∼ 1 , but M ˜ f = ˜ d, ˜ e, ˜ ν L f • Cancellations between the different EDM terms SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
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 d Hg : 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 3 g -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
Weinberg’s three-gluon operator g ν t L g R ˜ ˜ g µ t L 3! d 3 g f abc � L 3 g = − 1 G a µ G b ν λ G c λ × × × ν µ ˜ t R g L ˜ t R g λ SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
Weinberg’s three-gluon operator g ν g R ˜ t L g µ ˜ t L 3! d 3 g f abc � L 3 g = − 1 G a µ G b ν λ G c λ × × × ν µ ˜ t R g L ˜ t R g λ Estimate based on naive dimensional analysis: t Im ( A t − µ ∗ cot β ) d 3 g ∼ g 3 3 α 2 g m 2 m ˜ s s m 4 g M 2 16 π 2 4 π ˜ ˜ t � d n � � 0 . 5 TeV � 2 m 2 t Im ( A t − µ ∗ cot β ) 3 g ∼ (10 − 26 cm) × ⇒ = M 2 e m ˜ t m ˜ g g ˜ > EDM constraint: m ˜ ∼ 400 GeV. g SUSY ’11 , Fermilab, 1 September 2011 A. Pilaftsis
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