Rotation and Vibration in Tetraquarks

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 reasonable agreement with other works for heavy tetraquarks compared to other methods. 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.