1. B→φK*, h(‘)K decays and scalar-tensor operators
H. Hatanaka(Chung-Yuan Christian University中原大學),
Based on the work with K. C. Yang(CYCU) (in progress)
Outline
B→VV polarization & puzzle
Scalar-Tensor operators
Numerical Analysis
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

2. Polarization in B→VV L,0 :Longitudinal, ∥: Parallel ⊥: Perpendicular
(fig. [Beneke, et.al, hep-ph/ ])
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

3. B→VV observables
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

4. B→VV polarization puzzle
HFAG06Aug
In SM(QCD), AL ≈ 1.0
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

5. Possible Solutions NP contribution SM
Right-handed current operator(Kagan (2004))
R-parity violating terms(Y.D.Yang et.al(2004))
non-universal Z’(C.H.Chen & HH, 2006)
Scalar-Tensor operators (P.K.Das&K.C.Yang(2004)) combined model analysis(K.C.Yang & HH, in progress) SM
Large Charm Penguin(Bauer et.al, 2003)
Changing form factors(H.N.Li, et.al, 2004)
Large Annihilation(Beneke et.al, 2006) …
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

6. NP significance
[Das-Yang]
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

7. b→sss scalar-tensor operators
Scalar operators
Tensor operators
Fierz Transformation Relations:
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

8. NP contribution B→φK* B→η(‘)K : Here Mar. 6, 2007
KEKPH07, Tsukuba, Japan

9. Scalar Tensor-OPs from MSSM
Induced by gluino box diagrams [Borzumati, et.al, PRD62:075005(2000)]
@ μ=mW [J.F.Cheng, et.al, NPB701-54(2004)]
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

10. Numerical analysis(preliminary)
Combined analysis of B→η(‘)K and B→φK*
# of Data = 7(ηK)+15(φK* )(preliminary:#independent observables=8-10)
# of parameters : 7
QCDF(Beneke, 2003) uncertainty in B→ηK: XA, XH(2 complex numbers)
We assume the form of (c19,21 are neglected ∵f.t.→（V±A）×（V∓A）-current(sub-leading))
Assume A<<B
Scenario A(a25=0⇔ξ’=0) , B(a23=0⇔ξ=0)
Sin2bb-ccs=0.674
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

11. Results(preliminary)-1/4
Best-fit parameters
B→φK*: result of scenario A is consistent with [Das-Yang]
B→η’K: 2nd best solution
(Scenario A)
weak phase is small
Strong phase～45deg
(scenario B)
Weak,strong phase are large ～165deg
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

12. Results(preliminary)-2/4
Best fit value for B→η(‘)K
Consistent with Exp
small(large)Br of B→η(‘)K
Large(small)ACP of B→η(‘)K
Sin2β is a little bigger than sin2bexp
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

13. Results (preliminary)-3/4
Best fit values for B→φK*
(common)
Λ00～0.5, Λ||||～0.8Λ⊥⊥
(scenario-A)
ACP (Σ⊥||,⊥⊥) ～0
(scenario-B)
ACP⊥、tot (Σ⊥||,⊥⊥) ≠0
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

14. Results(preliminary)-4
Predictions from the fit
(common)
Small Br of B→ηK0
(scenario-A)
Large ACP of B→ηK0
Large sin2beta of B→ηK0
|Δφ|～0
(scenario-B)
Small ACP of B→ηK0
Small sin2beta of B→ηK0
Large |Δφ|s
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

15. Summary(preliminary)
Relate the B→VV and B→PP by using Fierz transfs of b->sss Scalar-Tensor operators
Combined Numerical analysis of B→φK* and B→η(‘)K in MSSM
There are solutions of scalar-tensor NP parameters fitting B→η’K and B→φK* simultaneously.
Perspective --- More combinations (e.g., with B→f0K, B→KKK) will improve the information on New Physcs.
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

16. Unused slides
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

17. NP μ=mW
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

18. (ir)relevance B→MM B→PP B→VV B→PV(note) Scalar OP ○(sensitive) ×
Factorization:
B→MM
B→PP
(B→η（’）K)
B→VV
(B→φK*)
B→PV(note)
(B→φK, B→K*φ)
Scalar OP
○(sensitive) ×
Tensor OP
×(insensitive) ○
(note)
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

19. Scalar-Tensor OPs in MSSM
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

20. QCDF corrections-A Hard spectator scattering Vertex correction
(Charm loop and soft spec. scat.)
Penguin correction
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

21. QCDF corrections -B Weak annihilation (Flavor singlet annihilation)
Mar. 6, 2007
KEKPH07, Tsukuba, Japan

22. A+B/B ratio
Mar. 6, 2007
KEKPH07, Tsukuba, Japan