B → φK*, h (‘) K decays and scalar-tensor operators

B→φK*, h(‘)Kdecays 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 KEKPH07, Tsukuba, Japan

Polarization in B→VV L,0 :Longitudinal, ∥: Parallel ⊥: Perpendicular (fig. [Beneke, et.al, hep-ph/0612290]) KEKPH07, Tsukuba, Japan

B→VV observables KEKPH07, Tsukuba, Japan

B→VV polarization puzzle HFAG06Aug In SM(QCD), AL ≈ 1.0 KEKPH07, Tsukuba, Japan

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) • … KEKPH07, Tsukuba, Japan

NP significance [Das-Yang] KEKPH07, Tsukuba, Japan

　 b→sss scalar-tensor operators Scalar operators Tensor operators Fierz Transformation Relations: KEKPH07, Tsukuba, Japan

NP contribution B→φK* B→η(‘)K : Here KEKPH07, Tsukuba, Japan

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)] KEKPH07, Tsukuba, Japan

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 KEKPH07, Tsukuba, Japan

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 KEKPH07, Tsukuba, Japan

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

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 KEKPH07, Tsukuba, Japan

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 KEKPH07, Tsukuba, Japan

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. KEKPH07, Tsukuba, Japan

Unused slides KEKPH07, Tsukuba, Japan

NP WC @ μ=mW KEKPH07, Tsukuba, Japan

(ir)relevance Factorization: (note) KEKPH07, Tsukuba, Japan

Scalar-Tensor OPs in MSSM KEKPH07, Tsukuba, Japan

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

QCDF corrections -B Weak annihilation (Flavor singlet annihilation) KEKPH07, Tsukuba, Japan

A+B/B ratio KEKPH07, Tsukuba, Japan

B → φK*, h (‘) K decays and scalar-tensor operators