J.Hisano, Y.S, hep-ph/ PLB)

Transcription

1 B φk s versus Electric Dipole Moment of 199 Hg Atom in Supersymmetric Models with Right-handed Squark Mixing J.Hisano, Y.S, hep-ph/ PLB) Yasuhiro Shimizu (To appear in Tohoku University super B 2004/1/21 p.1/21

2 Introduction CP violation in B φk S S φk = sin(2φ 1 ) = ± (SM) = 0.96 ± (BELLE) = 0.45 ± 0.43 ± 0.07 (BABAR) Combined: S φk = 0.15± σ deviation Can SUSY explain B φk S anomaly? Charmonium Modes φk 0 S η, K 0 S KKK 0 S OPAL ± 0.5 ALEPH ± 0.16 CDF BABAR ± ± Belle ± ± Average (charmonium) ± BABAR ± 0.43 ± 0.07 Belle ± BABAR ± 0.34 ± 0.03 Belle ± 0.27 ± 0.05 Belle ± Average (s penguin) 0.24 ± 0.15 Average (All) ± H F A G Summer sin(2β (eff) ) super B 2004/1/21 p.2/21

3 SUSY contribution to B φk S Y.Grossman, M.Worah, Phys. Lett. B 395, 241 (1997). T. Moroi, Phys. Lett. B 493, 366 (2000). R. Harnik, D. T. Larson, H. Murayama and A. Pierce, arxiv:hep-ph/ J. Hisano and Y. Shimizu, arxiv:hep-ph/ , E. Lunghi and D. Wyler, Phys. Lett. B 521, 320 (2001) A. Datta, Phys. Rev. D 66, (2002) B. Dutta, C. S. Kim and S. Oh, Phys. Rev. Lett. 90, (2003) S. Khalil and E. Kou, Phys. Rev. D 67, (2003) arxiv:hep-ph/ G. L. Kane, P. Ko, H. Wang, C. Kolda, J. Park and L. T. Wang, arxiv:hep-ph/ , Phys. Rev. Lett. 90, (2003) M. Ciuchini, E. Franco, A. Masiero and L. Silvestrini, Phys. Rev. D 67, (2003) S. Baek, arxiv:hep-ph/ A. Kundu and T. Mitra, arxiv:hep-ph/ K. Agashe and C. D. Carone, arxiv:hep-ph/ T.Goto, Y.Okada, Y.S, T.Shindou, M.Tanaka; hep-ph/ S.Mishima, A.I.Sanda, hepph/ super B 2004/1/21 p.3/21

4 SU(5) SUSY GUT with right-handed neutrinos d Ri and L i are unified in 5 d R1 d R2 d R3 ν e s R1 s R2 s R3 ν µ b R1 b R2 b R3 ν τ, e L µ L τ L Atmospheric neutrino oscillation: large ν µ ν τ Atmospheric neutrino makes large s R - b R mixing in SUSY SU(5) GUT ( 00, Moroi) super B 2004/1/21 p.4/21

5 Squark mixings in SUSY SU(5) GUT with right-handed neutrinos Right-handed mixing: neutrino mixing (m 2 dr ) 23 2 (4π) 2 e i(ϕ d 2 ϕ d3 ) U 32 U33 m ντ M N H f 2 (3m2 0 + A 2 0) log M P M GUT U: MNS matrix, ϕ di : GUT phases Left-handed mixing: CKM mixing (m 2 Q) 23 2 (4π) 2 V 32V 33 f 2 t (3m A 2 0)(3 log M G M GUT + log M GUT M SUSY ), V : CKM matrix super B 2004/1/21 p.5/21

6 gluino contribution to B d φk S Large s R - b R mixing contributes B d φk S s g g s b R g s s R s br b L bl br s R s R s R g s super B 2004/1/21 p.6/21

7 B φk S The contribution from the penguin diagram is dominant. H = C R 8 g s 8π 2 m bs R σ µν T A b L G A µν Mass insertion approximation C R 8 = πα s m 2 q m g m b (δ (d) RR ) 23(δ (d) LR ) 33( 1 3 M 1(x) + 3M 2 (x)) where (δ (d) LL ) 23 = (m 2 dl ) 23 /m 2 q, (δ (d) RR ) 32 = (δ (d) LL ) 33 = m b (A b µ tanβ)/m 2 q, (m 2 dr ) /m 2 q, 32 Double mass insertion LR + RR is dominant super B 2004/1/21 p.7/21

8 Hadronic uncertainty of B φk S The matrix element of C 8 in B φk S. Phenomenological calculation: R.Barbieri, A.Strumia, NPB508(1997)3. φk S g s 8π 2 m b( s i σ µν T a ijp R b j )G a µν B d =κ 4α s 9π (ɛ φp B )f φ m 2 φf + (m 2 φ) κ = 1.1: heavy-quark effective theory large theoretical uncertainty super B 2004/1/21 p.8/21

9 quark CEDM The chromo-electric dipole moment (CEDM) for u, d, s H = d C q i 2 g sqσ µν T A γ 5 qg A µν Feynman diagram is similar to that of B φk S g g s L s L bl br s R s R super B 2004/1/21 p.9/21

10 CP violating N-N-Meson coupling CEDMs CP violating N-N-meson coupling. ( 88 Khatsimovsky et al) From the current algebra, ḡ πpp = d u + d d 4f π ( p ūgs (Gσ)u dg s (Gσ)d p ) + d u d d 4f π ( p ūgs (Gσ)u + dg s (Gσ)d p m 2 p ūu + dd p ) ḡ ηpp = d s 3fπ ( p sgs (Gσ)s p m 2 p ss p ) where Gσ = G a µνt a σ µν and m 2 = 0 g q(gσ)q 0 0 qq 0 0.8GeV 2. We need to evaluate the matrix elements. super B 2004/1/21 p.10/21

11 QCD sum rule Using the QCD sum rule, ( 97 Zhitnitsky) where p qg s (Gσ)q p 5 3 m2 p qq p. p ūu p 4.8; p dd p 4.1; p ss p 2.8 for m u = 4.5 MeV, m d = 9.5 MeV and m s = 175 MeV. The CP violating N-N-Meson coupling NN N iγ 5 N N N N N η 0 π 0 N N N N super B 2004/1/21 p.11/21

12 Hg EDM 199 Hg atom: closed electronic shell (J=0) nucleus spin (I=1/2) Hg EDM is sensitive to the nucleus EDM.( NN N iγ 5 N ) d Hg = S fm 2 S: Schiff moment (V eff = es(i )δ(r)) S = G 1 F 3g πpp m 2 0 f π m 2 π ( d d d u d s )e fm 3. 99: Falk et al The experimental bound on Hg EDM e d C d d C u 0.012d C s < ecm e d C s < ecm super B 2004/1/21 p.12/21

13 Strange CEDM Mass insertion approximation d C s = c α s 4π m g m 2 q ( ) 1 [ ] 3 N 1(x) + 3N 2 (x) Im (δ (d) LL ) 23 (δ (d) LR ) 33 (δ (d) RR ) 32 = sinθ e cm ) ( ) ( ) ( 1 m q ((δ (d) LL ) 23 (δ (d) RR ) ) 32 µ tanβ 500GeV GeV θ = arg[(δ (d) LL ) 23 (δ (d) LR ) 33 (δ (d) RR ) 32] Naively, the strange CEDM becomes too large. super B 2004/1/21 p.13/21

14 Hg EDM vs S φks There is strong correlation between d C s and C R 8 d C s = m b 4π Im [ (δ (d) LL ) 23C R 8 ] (m g = m q ) g g g g b L bl br s R s R s L s L bl br s R s R super B 2004/1/21 p.14/21

15 Hg EDM vs S φks (II) κ= κ= 2 d C s [cm] S φks super B 2004/1/21 p.15/21

16 Constraints from B X s γ Gluino contribution to B X s γ. Br(B X s γ) = ( µ tanβ 5000GeV ) 2 ( m q 500GeV ) 4 ( (δ (d) RR ) ) 2 From the experimental value, Br(B X s γ) = (3.3 ± 0.4) 10 4, (δ (d) RR ) 23 < 0.27 ( µ tanβ 5000GeV ) 1 ( m q 500GeV ) 2, This constraint is weaker than the one from Hg EDM. super B 2004/1/21 p.16/21

17 1-loop correction to m s If 1-loop correction to m s is large, the quark mass matrix must be re-diagonalized. The rotation of the right-handed strange quark can remove the contributions to S φks. δm s 3 MeV ( ) ( (δ (d) LL ) ) ( ) (tan (δ (d) RR ) ) 32 µm g β ( mb ) 0.04 m 2 d 50 5 GeV g The one-loop correction to m s is small due to the Br(B X s γ) constraint. s L s L bl br s R s R super B 2004/1/21 p.17/21

18 Constraints on the GUT phases s R - b R mixing phase induce Hg EDM. (m 2 dr ) 32 2 (4π) 2 ei(ϕ d 2 ϕ d3 ) U 33 U23 m ντ M ντ H 2 2 (3m2 0 + A 2 0) log M G M GUT Hg EDM puts strong constraint on the GUT phases (δ (d) RR ) e i(ϕ d 2 ϕ d3 ) ( ) ( m ντ Mντ ev GeV )( U33 U 23 1/2 ) ( 3m A 2 0 3m 2 q ) super B 2004/1/21 p.18/21

19 Loopholes (δ (d) LL ) 23 < 10 4 s L is very heavy while other SUSY particles are O(100) GeV strong cancellation among d C q : d Hg d C d dc u 0.012d C s Large hadronic uncertainty in d Hg and B φk S (κ) strong cancellation among various SUSY contributions (chargino, neutralino, higgs, gluino diagram) super B 2004/1/21 p.19/21

20 Hg EDM Cancellation between d C d and d C s. hep-ph/ v2 (T.Goto, Y.Okada, Y.S, T.Shindou, M.Tanaka) A mix ( B d φ K S ) CP SU(5) ν R tan β = 30 non-degenerate d Hg [ e cm ] super B 2004/1/21 p.20/21

21 Summary Atmospheric neutrino makes large s R - b R mixing in SUSY SU(5) GUT. Large s R - b R can contribute various B decays, B φk s,b X s γ. When s L - b L mixing exists, large strange CEDM is induced. strange CEDM is strongly constrained by Hg EDM. S φks and Hg EDM have a strong correlation. Hg EDM should be suppressed by O(10 2 ) in order to get negative S φks. There is sizable theoretical uncertainty of Hg EDM. Lattice calculations can help reduce the uncertainty. super B 2004/1/21 p.21/21