A comprehensive study of the
S-wave heavy tetraquark states with identical
quarks and antiquarks, specifically
QQQˉ′Qˉ′ (
Q,Q′=c,b), $QQ\bar
s\bar s
/\bar Q\bar Q ss
,andQQ\bar q\bar q
/\bar Q\bar Q qq
(q=u,d$),
are studied in a unified constituent quark model. This model contains the
one-gluon exchange and confinement potentials. The latter is modeled as the sum
of all two-body linear potentials. We employ the Gaussian expansion method to
solve the full four-body Schr\"{o}dinger equations, and search bound and
resonant states using the complex-scaling method. We then identify
3 bound
and
62 resonant states. The bound states are all
QQqˉqˉ states with
the isospin and spin-parity quantum numbers
I(JP)=0(1+): two bound
bbqˉqˉ states with the binding energies, 153 MeV and 4 MeV below
the
BB∗ threshold, and a shallow
ccqˉqˉ state at
−15 MeV from
the
DD∗ threshold. The deeper
bbqˉqˉ bound state aligns with the
lattice QCD predictions, while
ccqˉqˉ bound state, still has a much
larger binding energy than the recently observed
Tcc+ by LHCb
collaboration. No bound states are identified for the
QQQˉ′Qˉ′,
QQsˉsˉ and
QQqˉqˉ with
I=1. Our analysis shows that the
bound
QQQˉ′Qˉ′ states are more probable with a larger mass ratio,
mQ/mQ′. Experimental investigation for these states is desired, which
will enrich our understanding of hadron spectroscopy and probe insights into
the confinement mechanisms within tetraquarks.