Spectra of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>b</mml:mi> <mml:mi>c</mml:mi> <mml:mover accent="true"> <mml:mi>b</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> <mml:mover accent="true"> <mml:m

Within the diquark-antidiquark framework, this study investigates the masses of ground-state tetraquarks composed of heavy charm ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>c</a:mi> </a:math> ) and bottom ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>b</c:mi> </c:math> ) quarks and antiquarks, using the Bethe-Salpeter formalism. We establish the Bethe-Salpeter equations for the fully heavy <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>b</e:mi> <e:mi>c</e:mi> <e:mover accent="true"> <e:mi>b</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> <e:mover accent="true"> <e:mi>c</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> </e:math> tetraquarks to the leading order in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mn>1</k:mn> <k:mo>/</k:mo> <k:msub> <k:mi>m</k:mi> <k:mi>Q</k:mi> </k:msub> </k:math> expansion. These equations are subsequently solved numerically under the covariant instantaneous approximation with kernels containing scalar confinement and one-gluon exchange terms. Our results show that the spectra of all possible <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>S</m:mi> </m:math> -wave tetraquark states are above the corresponding two lowest meson decay thresholds via the quark rearrangement. This implies that the ground <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>b</o:mi> <o:mi>c</o:mi> <o:mover accent="true"> <o:mi>b</o:mi> <o:mo stretchy="false">¯</o:mo> </o:mover> <o:mover accent="true"> <o:mi>c</o:mi> <o:mo stretchy="false">¯</o:mo> </o:mover> </o:math> tetraquark states should be broad.