Final-state rescattering and SU(3) symmetry breaking in $B\rightarrow DK$ and $B\rightarrow DK^*$ decays

Z.-Z. Xing

doi:doi:10.1140/epjc/s2003-01162-0

EPJ

a
b
c
d
e
ap
st
h
plus
ds
pv
ti
qt
am
n

2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C 28, 63-69 (2003)
DOI: 10.1140/epjc/s2003-01162-0

Final-state rescattering and SU(3) symmetry breaking in $B\rightarrow DK$ and $B\rightarrow DK^*$ decays

Z.-Z. Xing^{1, 2}

¹ CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, P.R. China
² Institute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918 (4), Beijing 100039, P.R. China (Mailing address)

(Received: 26 January 2003 / Revised version: 31 January 2003 / Published online: 7 March 2003 )

Abstract
The first observation of the $\bar{B}^0_d\rightarrow D^0\bar{K}^0$ and $\bar{B}^0_d\rightarrow D^0\bar{K}^{*0}$ transitions by the Belle Collaboration allows us to do a complete isospin analysis of the $B\rightarrow DK^{(*)}$ decay modes. We find that their respective isospin phase shifts are very likely to lie in the ranges $37^\circ \leq (\phi_1 -\phi_0)_{DK} \leq 63^\circ$ (or around $50^\circ$ ) and $25^\circ \leq (\phi_1 -\phi_0)_{DK^*} \leq 50^\circ$ (or around $35^\circ$ ), although the possibility $(\phi_1 -\phi_0)_{DK} = (\phi_1 -\phi_0)_{DK^*} = 0^\circ$ cannot be ruled out at present. Thus significant final-state rescattering effects possibly exist in such exclusive $\vert\Delta B\vert = \vert\Delta C\vert = \vert\Delta S\vert =1$ processes. We determine the spectator and color-suppressed spectator quark-diagram amplitudes of the $B\rightarrow DK$ and $B\rightarrow DK^*$ decays, and compare them with the corresponding quark-diagram amplitudes of the $B\rightarrow D\pi$ and $B\rightarrow D\rho$ decays. The effects of SU(3) flavor symmetry breaking are in most cases understandable in the factorization approximation, which works for the individual isospin amplitudes. Very instructive predictions are also obtained for the branching fractions of rare $\bar{B}^0_d \rightarrow \bar{D}^0 \bar{K}^{(*)0}$ , $B^-_u \rightarrow \bar{D}^0 K^{(*)-}$ and $B^-_u \rightarrow D^- \bar{K}^{(*)0}$ transitions.