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We study the F-wave c_bar s heavy meson doublets (2+,3+) and (3+,4+). Theyhave large orbital excitations L=3, and may be good challenges (tests) fortheoretical studies. To study them we use the method of QCD sum rule in theframework of heavy quark effective theory. Their masses are predicted to bem_{(2+,3+)} = (3.45 \pm 0.25, 3.50 \pm 0.26) GeV and m_{(3+,4+)} = (3.20 \pm0.22, 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 areprovisional.

F-wave heavy-light meson spectroscopy in QCD sum rules and heavy quark effective theory