Charmless B{yields}K{sub h{eta}}{sup (')} decays with K{sub h}=K, K{sup *}, K{sub 0}{sup *}(1430), K{sub 2}{sup *}(1430)

Journal Article · Sun Aug 01 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.034014· OSTI ID:21432854

Cheng, Hai-Yang ^[1]; Chua, Chun-Khiang ^[2]

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1. Institute of Physics, Academia Sinica, Taipei, Taiwan 115 (China)
2. Department of Physics, Chung Yuan Christian University, Chung-Li, Taiwan 320 (China)

We study the charmless decays B{yields}K{sub h{eta}} and B{yields}K{sub h{eta}}{sup '} within the framework of QCD factorization (QCDF) for K{sub h}=K, K{sup *}, K{sub 0}{sup *}(1430) and naive factorization for K{sub h}=K{sub 2}{sup *}(1430). There are three distinct types of penguin contributions: (i) b{yields}sqq{yields}s{eta}{sub q}, (ii) b{yields}sss{yields}s{eta}{sub s}, and (iii) b{yields}sqq{yields}qK{sub h}, where {eta}{sub q}=(uu+dd)/{radical}(2) and {eta}{sub s}=ss. B{yields}K{sup (*){eta}(')} decays are dominated by type-II and type-III penguin contributions. The interference, constructive for K{eta}{sup '} and K{sup *{eta}} and destructive for K{eta} and K{sup *{eta}'}, between type-II and type-III diagrams explains the pattern of {Gamma}(B{yields}K{eta}{sup '})>>{Gamma}(B{yields}K{eta}) and {Gamma}(B{yields}K{sup *{eta}'})<<{Gamma}(B{yields}K{sup *{eta}}). Within QCDF, the observed large rate of the K{eta}{sup '} mode can be naturally explained without invoking flavor-singlet contributions or something exotic. The decay pattern for B{yields}K{sub 0}{sup *}(1430){eta}{sup (')} decays depends on whether the scalar meson K{sub 0}{sup *}(1430) is an excited state of {kappa} or a lowest-lying P-wave qq state. Hence, the experimental measurements of B{yields}K{sub 0}{sup *}(1430){eta}{sup (')} can be used to explore the quark structure of K{sub 0}{sup *}(1430). If K{sub 0}{sup *}(1430) is a low-lying qq bound state, we find that K{sub 0}{sup *{eta}} has a rate slightly larger than K{sub 0}{sup *{eta}'} owing to the fact that the {eta}-{eta}{sup '} mixing angle in the {eta}{sub q}, {eta}{sub s} flavor basis is less than 45 degree sign , in agreement with experiment. The type-III penguin diagram does not contribute to B{yields}K{sub 2}{sup *{eta}(')} under the factorization hypothesis and the type-II diagram dominates. The ratio {Gamma}(B{yields}K{sub 2}{sup *{eta}'})/{Gamma}(B{yields}K{sub 2}{sup *{eta}}) is expected to be of order 2.5 as a consequence of (i) |f{sub {eta}}{sup 's}|>|f{sub {eta}}{sup s}| and (ii) a destructive (constructive) interference between type-I and type-II penguin diagrams for K{sub 2}{sup *{eta}} (K{sub 2}{sup *{eta}'}). However, the predicted rates of B{yields}K{sub 2}{sup *{eta}(')} in naive factorization are too small by 1 order of magnitude and this issue remains to be resolved. There are two K{sup (*){eta}(')} modes in which direct CP asymmetries have been measured with significance around 4{sigma}: A{sub CP}(K{sup -}{eta})=-0.37{+-}0.09 and A{sub CP}(K{sup *0}{eta})=0.19{+-}0.05. In QCDF, power corrections from penguin annihilation which are needed to resolve CP puzzles in K{sup -}{pi}{sup +} and {pi}{sup +}{pi}{sup -} modes will flip A{sub CP}(K{sup -}{eta}) into a wrong sign. We show that soft corrections to the color-suppressed tree amplitude a{sub 2} in conjunction with the charm content of the {eta} will finally lead to A{sub CP}(K{sup -}{eta})=-0.15{sub -0.28}{sup +0.19}. Likewise, this power correction is needed to improve the prediction for A{sub CP}(K{sup *0{eta}}).

• OSTI ID: 21432854
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevD.82.034014; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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ANNIHILATION
ASYMMETRY
B MESONS
BOUND STATE
CORRECTIONS
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P WAVES
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