Determination of exotic hadron structure by constituent-counting rule for hard exclusive processes

We propose to use hard exclusive production of an exotic hadron for finding its internal quark-gluon configuration by the constituent-counting rule in perturbative QCD. In particular, the cross section for the exclusive process $\pi^- + p \to K^0 + \Lambda (1405)$ is estimated at the scattering angle $\theta=90^\circ$ in the center-of-mass frame by using current experimental data. In comparison, the cross section for the ground-state $\Lambda$ production $\pi^- + p \to K^0 + \Lambda$ is also shown. We suggest that the internal quark configuration of $\Lambda (1405)$ should be determined by the asymptotic scaling behavior of the cross section. If it is an ordinary three-quark baryon, the scaling of the cross section is $s^{8} d\sigma /dt=$constant, whereas it is $s^{10} d\sigma /dt=$constant if $\Lambda (1405)$ is a five-quark hadron, where $s$ and $t$ are Mandelstam variables. Such a measurement will be possible, for example, by using the high-momentum beamline at J-PARC. In addition, another exclusive process $\gamma + p \to K^+ + \Lambda (1405)$ could be investigated at LEPS and JLab for finding the nature of $\Lambda (1405)$. We indicate that the constituent-counting rule could be used as a valuable quantity in determining internal structure of exotic hadrons by high-energy exclusive processes, where quark-gluon degrees of freedom explicitly appear. Furthermore, it is interesting to investigate the transition from hadron degrees of freedom to quark-gluon ones for exclusive exotic-hadron production processes.