  The commonly used Hamiltonian of the chromomagnetic hyperfine splitting is
inversely proportional to the product of the masses of two constituent quarks
composing the meson. So it is expected to have
$(M_{D^*}-M_{D})/(M_{D_s^*}-M_{D_s})$ $\simeq$
$(M_{B^*}-M_{B})/(M_{B_s^*}-M_{B_s})$ $\simeq$ $1.6$, when the constituent
quark masses $m_{u,d}=0.33$ GeV and $m_s=0.53$ GeV are used. However, the
experimental results show that the above ratios are very close to 1. We solve
this puzzle by employing the Hamiltonian recently proposed by Scora and Isgur.
