The calculation of multiquark hadrons by the quark model baryon, meson and multiquark states

The 1st new hadron summer school related with the new science field, 'the comprehensive research of new hadron states searched by variable flavor number scheme', was held on August 18-20, 2010. This report is one of the 'quark model' lectures. The chapter 1 describes following problems: 1. The background and the significance as a phenomenological theory of the constituent quark model. 2. The introduction of the quark model. 3. The summary of the properties of hadrons in which the quark model can apply to three quarks (qqq) and, one quark and antiquark (q-q) configurations, but is difficult to apply to some configurations. 4. A brief summary of exotic hadrons and recent problems. In chapter 2, the introduction and some exercises of the stochastic variational method are reported as a technique of solving spatial part of multiquark states. In the chapter 3, spins and color parts in multiquark states are calculated. The group theory is applied to calculate the eigenvalues of the Casimir operators of SU(2), SU(3) and SU(6). In the problems of being unable to apply Casimir operators, the direct matrix diagonalization method, m-scheme, is employed for interacting quarks and for the interaction involving quark mass. To find the attractive interaction in tetraquark (QQqq-bar) state is given as an exercise problem. (Y. Kazumata)