  Hyperfine splittings between the heavy vector (D*, B*) and pseudoscalar (D,
B) mesons have been calculated numerically in lattice QCD, where the pion mass
(which is related to the light quark mass) is much larger than its physical
value. Naive linear chiral extrapolations of the lattice data to the physical
mass of the pion lead to hyperfine splittings which are smaller than
experimental data. In order to extrapolate these lattice data to the physical
mass of the pion more reasonably, we apply the effective chiral perturbation
theory for heavy mesons, which is invariant under chiral symmetry when the
light quark masses go to zero and heavy quark symmetry when the heavy quark
masses go to infinity. This leads to a phenomenological functional form with
three parameters to extrapolate the lattice data. It is found that the
extrapolated hyperfine splittings are even smaller than those obtained using
linear extrapolation. We conclude that the source of the discrepancy between
lattice data for hyperfine splittings and experiment must lie in non-chiral
physics.
