Measurement of branching fractions of B decays to K1(1270)pi and K1(1400)pi and determination of the CKM angle alpha from B0 --> a1(1260)+/- pi-/+

We report measurements of the branching fractions of neutral and charged B meson decays to final states containing a K_1(1270) or K_1(1400) meson and a charged pion. The data, collected with the BaBar detector at the SLAC National Accelerator Laboratory, correspond to 454 million B Bbar pairs produced in e^+ e^- annihilation. We measure the branching fractions BF(B^0 --> K_1(1270)^+ \pi^- + K_1(1400)^+ \pi^-) = 3.1^{+0.8}_{-0.7} x10^{-5} and BF(B^+ --> K_1(1270)^0 \pi^+ + K_1(1400)^0 \pi^+) = 2.9^{+2.9}_{-1.7} x10^{-5} (<8.2 x10^{-5} at 90% confidence level), where the errors are statistical and systematic combined. The B^0 decay mode is observed with a significance of 7.5\sigma, while a significance of 3.2\sigma is obtained for the B^+ decay mode. Based on these results, we estimate the weak phase \alpha = (79 +/- 7 +/- 11)^{\circ} from the time dependent CP asymmetries in B^0 --> a_1(1260)^{+/-} \pi^{-/+} decays.