Next-to-leading-order corrections to meson masses in the heavy quark effective theory

We use the QCD sum rule approach to calculate the splitting between vector and pseudoscalar mesons containing one light and one heavy quark and the kinetic energy of the heavy quark. Our result for the splitting induced by the chromomagnetic interaction agrees with the experimental data on charm and $b$-flavored mesons. For the matrix element of the kinetic energy operator, we obtain the value $K=-(0.60\mathrm{}\pm 0.10)$ Ge${\mathrm{V}}^2$.