  We study the F-wave c_bar s heavy meson doublets (2+,3+) and (3+,4+). They
have large orbital excitations L=3, and may be good challenges (tests) for
theoretical studies. To study them we use the method of QCD sum rule in the
framework of heavy quark effective theory. Their masses are predicted to be
m_{(2+,3+)} = (3.45 \pm 0.25, 3.50 \pm 0.26) GeV and m_{(3+,4+)} = (3.20 \pm
0.22, 3.26 \pm 0.23) GeV, with mass splittings Delta m_{(2+,3+)} = m_{3+} -
m_{2+} = 0.046 \pm 0.030 GeV and Delta m_{(3+,4+)} = 0.053 \pm 0.044 GeV,
respectively. We note that this is a pioneering work and these results are
provisional.
