  Inspired by recent observation of the first doubly charmed tetraquark
$T_{cc}$, we apply linear Regge relation and mass scaling to study low-lying
mass spectra of the doubly heavy tetraquark in heavy-diquark-light-antidiquark
picture. The measured data and other compatible estimates of ground-state
masses of doubly heavy baryons are employed to evaluate masses of heavy diquark
$M_{QQ}$ ($Q=c,b$) and the $D/D_{s}$ meson masses are used in mass scaling to
determine the hyperfine mass splitting. Our mass computation indicates that all
low-lying states of doubly heavy tetraquarks are unstable against strong decays
to two heavy-light mesons, except for the ground states of nonstrange $bb$
tetraquarks.
