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Polarizations in B ---> VV decays

Nov, 2004
26 pages
Published in:
  • Phys.Rev.D 71 (2005) 054025
e-Print:
DOI:
Report number:
  • TU-735
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Abstract:
We demonstrate that the polarization fractions of most tree-dominated B→VVB\to VV decays can be simply understood by means of kinematics in the heavy-quark or large-energy limit. For example, the longitudinal polarization fractions RLR_L of the B0→(Ds∗+,D∗+,ρ+)D∗−B^0\to (D_s^{*+}, D^{*+}, \rho^+)D^{*-} and B+→(Ds∗+,D∗+,ρ+)ρ0B^+\to (D_s^{*+}, D^{*+}, \rho^+)\rho^0 modes increase as the masses of the mesons Ds∗+,D∗+,ρ+D_s^{*+}, D^{*+}, \rho^+ emitted from the weak vertex decrease. The subleading finite-mass or finite-energy corrections modify these simple estimates only slightly. Our predictions for the B→D(s)∗D∗B\to D_{(s)}^* D^* polarization fractions derived in the perturbative QCD framework, especially RL∼1R_L\sim 1 for B0→Dˉ∗0D∗0B^0\to {\bar D}^{*0} D^{*0} governed by nonfactorizable WW-exchange amplitudes, can be confronted with future data. For penguin-dominated modes, such as B→ρ(ω)K∗B\to\rho(\omega) K^*, the polarization fractions can be understood by the annihilation effect from the (S−P)(S+P)(S-P)(S+P) operators, plus the interference with a small tree amplitude. At last, we comment on the various mechanism proposed in the literature to explain the abnormal B→ϕK∗B\to \phi K^* polarization data, none of which are satisfactory.
Note:
  • 26 pages, 4 figures: corrected typos, version to appear in Phys. Rev. D Report-no: TU-735
  • 12.38.Bx
  • 11.10.Hi
  • 13.25.Hw
  • B: hadronic decay
  • vector meson: pair production
  • polarization: longitudinal
  • polarization: transverse
  • quantum chromodynamics: perturbation theory
  • factorization
  • tree approximation
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