Applications of a variational method to baryons and supersymmetric hadrons (t̃QQ¯andg̃QQ¯)

We develop a variational model for a three-body system with unequal masses ($m_1\ne m_2\ne m_3$) and compute masses of, for example, $A\mathrm{}\left(\mathrm{usc}\right)\mathrm{}$, $\tilde{g}Q\overline{Q}$ and $\tilde{t}Q\overline{Q}$ ($\tilde{g}=\mathrm{gluino}$ and $\tilde{t}=\mathrm{supersymmetric}\mathrm{partner}$ of $t$ quark). The baryon spectrum is reproduced remarkably well in our model. From our results we conclude that the first radially excited $P_{11}$ state ($2S$) is $N\left(1710\right)\mathrm{}$ and the Roper resonance does not fit in the $Q^3$ spectrum. We discuss the possibility that the Roper resonance might be the lowest $Q^{3}g$ state. We present explicit wave functions for every baryon resonance.