The order of 1P and 2S states of baryons in the chiral quark model.
The well-known order reverse problem of $1P$ and $2S$ states of baryons in naive quark models is investigated in the chiral quark model. Besides a nonperturbative linear-screened confining interaction and a perturbative one-gluon exchange between quarks, we incorporate the Goldstone-boson exchanges taking into account not only the full octet of pseudoscalar mesons but also the scalar one. The latter has been already admitted as a deficiency of the original model in describing, for instance, the $\rho-\omega$ splitting. The numerical approach to the three-body bound state problem is the so-called Gau\ss ian expansion method, which is able to get a precision as good as Faddeev calculations. With a set of parameters fixed to different hadron and hadron-hadron observables, we find that the $2S$ state is predicted below the $1P$ state in all the cases studied. Therefore, we can assert that the Roper resonance, $N(1440)$, could be explained as the first radial excitation of the nucleon or, at least, it should have an important 3-quark Fock component. We extend the calculation to the $qqQ$ and $qQQ$ sectors (with $q$ representing a light $u$-, $d$-, or $s$-quark and $Q$ denoting the charm quark or the bottom one) in which many new states have been recently observed. Some tentative assignments are done attending to the agreement between theoretical and experimental masses; however, we admit that other sources of information are needed in order to make strong claims about the nature of the states.
Publisher URL: http://arxiv.org/abs/1709.09315