  The form factors of $B_{(s)}$ decays into P-wave excited charmed mesons
(including $D^*_0(2300)$, $D_1(2430)$, $D_1(2420)$, $D^*_2(2460)$ and their
strange counterparts, denoted generically as $D^{**}_{(s)}$) are systematically
calculated via the QCD sum rules in the framework of heavy quark effective
field theory (HQEFT). We consider contributions up to the next leading order of
heavy quark expansion and give all the relevant form factors, including the
scalar and tensor ones only relevant for possible new physics effects. The
expressions for the form factors in terms of several universal wave functions
are derived via heavy quark expansion. These universal functions can be
evaluated through QCD sum rules. Then, the numerical results of the form
factors are presented. With the form factors given here, a model independent
analysis of relevant semileptonic decays $B_{(s)} \rightarrow D^{**}_{(s)} l
\bar{\nu}_l$ is performed, including the contributions from possible new
physics effects. Our predictions for the differential decay widths, branching
fractions and ratios of branching fractions $R(D^{**}_{(s)})$ may be tested in
more precise experiments in the future.
