  Using a sample of 9.7 million B meson pairs collected with the CLEO detector,
we study B decays to the chi_c1 and chi_c2 charmonia states, which are
reconstructed via their radiative decays to J/psi. We first measure the
branching fraction for inclusive chi_c1 production in B decays to be
Br(B->chi_c1 X)=(4.14+-0.31+-0.40)*10^-3, where the first uncertainty is
statistical and the second one is systematic. We derive the branching fractions
for direct chi_c1 and chi_c2 production in B decays by subtracting the known
contribution of the decay chain B->psi(2S)X with psi(2S)->chi_c1,2 gamma. We
obtain Br[B->chi_c1(direct) X]=(3.83+-0.31+-0.40)*10^-3. No statistically
significant signal for chi_c2 production is observed in either case. Using the
Feldman-Cousins approach, we determine the 95% confidence intervals to be [0.2,
2.0]*10^-3 for Br(B->chi_c2 X), [0.0,1.7]*10^-3 for Br[B->chi_c2(direct) X],
and [0.00,0.44] for the ratio Br[B->chi_c2(direct) X]/Br[B->chi_c1(direct) X].
We also measure the branching ratio Br[B->chi_c2(direct)
X_s]/Br[B->chi_c1(direct) X_s] for different X_s configurations by
reconstructing B decays into exclusive final states with J/psi, a photon, a
kaon, and up to four pions. For all the X_s configurations we observe a strong
chi_c1 signal yet no statistically significant chi_c2 signal. We discuss how
our results compare with theoretical predictions in different models of
charmonium production.
