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We study B^+/- --> J/psi pi^+/- and B^+/- --> J/psi K^+/- decays
in a sample of about 89 million BB~ pairs collected with the
BABAR detector at the PEP-II asymmetric B-factory at SLAC.
We observe a signal of 244 +/- 20 B^+/- --> J/psi pi^+/- events
and determine the ratio BF(B^+/- --> J/psi pi^+/-)/BF(B^+/- -->
J/psi K^+/-) to be
[5.37 +/- 0.45 (stat.) +/- 0.11 (syst)]%.
The charge asymmetries for the B^+/- --> J/psi pi^+/-
and B^+/- --> J/psi K^+/- decays are determined to be
A_pi = 0.123 +/- 0.085 (stat.) +/- 0.004 (syst.)
and A_K = 0.030 +/- 0.015 (stat.) +/- 0.006 (syst.),
respectively.
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