  A novel approach is introduced for obtaining precise solutions of the pairing
Hamiltonian for tetraquarks, which utilizes an algebraic technique in infinite
dimensions. The parameters involved in the transition phase are calibrated
based on potential tetraquark candidates derived from phenomenology. Our
investigation shows that the rotation and vibration transitional theory
delivers a more accurate explanation for heavy tetraquarks compared to other
methods utilizing the same formalism. To illustrate the concept, we compute the
spectra of several tetraquarks, namely charm, bottom, bottom-charm and open
charm and bottom systems, and contrast them with those of other particles.
