  Spectrum of the doubly heavy tetraquarks is studied in a constituent quark
model including one-pion exchange (OPE) potential. Central and tensor forces
induced by OPE between two light quarks are considered. Our results show that
$I(J^P)=0(1^+)$ compact bound states are shifted up because of the repulsive
central force between $\bar{q}\bar{q}$. This effect possibly leads to the small
binding energy in $T_{cc}$. In addition, a $I(J^P)=1(1^+)$ resonant state is
reported with $ E=10641 \ \rm{MeV},\Gamma=15 \ \rm{MeV}$ and $ E=10640 \
\rm{MeV},\Gamma=15 \ \rm{MeV}$, without and with including OPE potential,
respectively. The repulsive central force and attractive tensor force almost
cancel with each other and leave a small energy difference when OPE potential
is included.
