B→φK*, h(‘)K decays and scalartensor 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
1
Polarization in B→VV
L,0 :Longitudinal,
∥: Parallel
⊥: Perpendicular
(fig. [Beneke, et.al, hep-ph/0612290])
Mar. 6, 2007
KEKPH07, Tsukuba, Japan
2
B→VV observables
Mar. 6, 2007
KEKPH07, Tsukuba, Japan
3
B→VV polarization puzzle
fL =
AL
AL
2
+ AP
2
2
+ A^
In SM(QCD), AL ≈
1.0
2
HFAG06Aug
Q A0 : AP : A^ = O (1) : O (m b- 1 ) : O (m b- 1 )
H 00 : H -
-
AP( ^ ) =
Mar. 6, 2007
: H + + = O (1) : O (m b- 1 ) : O (m b- 2 )
1
(H + + + (- )H - - ), A0 = H 00
2
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Possible Solutions
 NP contribution

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
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NP significance
[Das-Yang]
Mar. 6, 2007
KEKPH07, Tsukuba, Japan
6
b→sss
scalar-tensor operators
Scalar operators
Tensor operators
Fierz Transformation Relations:
Mar. 6, 2007
KEKPH07, Tsukuba, Japan
7
NP contribution
B→φK*
B→η(‘)K :
Here
Mar. 6, 2007
KEKPH07, Tsukuba, Japan
8
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
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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 WCs@mb∝WCs@mW:
(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
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Results(preliminary)-1/4
Best-fit parameters
•B→φK*: result of scenario
A is consistent with [DasYang]
•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
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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
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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
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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
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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
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Unused slides
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KEKPH07, Tsukuba, Japan
16
NP WC @ μ=mW
C11 C13
. mg
5
500, mq
10
600, 23dLL
15
20
1,
33dLR
25
1, 23dRR
1, 33dLRc
1 ;
30
-0.02
-0.04
mA 500
-0.06
-0.08
mA 300
-0.1
mA 150
-0.12
-0.14
Mar. 6, 2007
KEKPH07, Tsukuba, Japan
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(ir)relevance
Factorization:
B→MM
MM OO ¢ B =
å
M O 0 M O ¢ B + ...
B→PP
B→VV
B→PV(note)
(B→η（’）K)
(B→φK*)
(B→φK, B→K*φ)
Scalar OP ○(sensitive) ×
Tensor OP ×(insensitive ○
)
(note)
Mar. 6, 2007
f S, P 0 K S, P B
­» 0
×
×
f T 0 K T B
­» 0
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Scalar-Tensor OPs in MSSM
Mar. 6, 2007
KEKPH07, Tsukuba, Japan
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QCDF corrections-A
aip (M 1M 2 )
Vertex correction
Ci ± 1 ö
æ
÷
ç
= ççC i +
÷
÷N i (M 2 )
è
Nc ø
ù
Ci± 1 CF é
4p 2
ê
+
V i (M 2 ) +
H i (M 1M 2 ) ú+ Pi p (M 2 )
ú
N c 4p êë
Nc
û
Hard spectator scattering
(Charm loop and soft spec. scat.)
Penguin correction
Mar. 6, 2007
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QCDF corrections -B
Weak annihilation
Mar. 6, 2007
(Flavor singlet annihilation)
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A+B/B ratio
mA 1TeV
mA 500 GeV
mA 250 GeV
A B B
mA 125 GeV
2.5
2.25
2
1.75
1.5
1.25
tan
5
Mar. 6, 2007
10
15
20
25
30
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