Abstract:
We calculate the branching ratio of B three-body decay to
\rmf_0(500,\;980,\;1\;500,\;1\;790) resonance in perturbative QCD factorization approach with the two-hadron distribution amplitude input parameter. The Flatté and the Breit-Wigner models are adopted to parameterize the time-like scalar form factors. The Sudakov form factors suppress the soft dynamics effectively, and make the perturbative calculation possible. We get the results
6.41 \times 10^ - 9 ,
1.25 \times 10^ - 7 ,
1.92 \times 10^ - 8 ,
5.66 \times 10^ - 9 respectively. For the decay
Br(\rmB^ + \to \textπ^ + f_0(980)\textπ^ + \textπ^ - ) , the pQCD prediction agrees very well with currently available experimental upper limits,
1.5 \times 10^ - 6 . Compared with the experimental data, we can see that the calculation including vertex corrections and
\rms\bar s component contribution are more accurate and reliable than the results before, and the main changes come from the
\rms\bar s component contribution.