Exotic-Hadron Signature by Constituent-Counting Rule in Perturbative QCD

We explain a method to find internal quark configurations of exotic hadron candidates by using the constituent counting rule. The counting rule was theoretically predicted in perturbative QCD for hard exclusive hadron reactions, and it has been tested in experiments for stable hadrons including compound systems of hadrons such as the deuteron, $^3$H, and $^3$He. It indicates that the cross section scales as $d\sigma /dt \sim 1/s^{n-2}$, where $s$ is the center-of-mass energy squared and $n$ is the total number of constituents. We apply this method for finding internal configurations of exotic hadron candidates, especially $\Lambda (1405)$. There is a possibility that $\Lambda (1405)$ could be five-quark state or a $\bar K N$ molecule, and scaling properties should be different between the ordinary three-quark state or five-quark one. We predict such a difference in $\pi^- + p \to K^0 + \Lambda (1405)$, and it could be experimentally tested, for example, at J-PARC. On the other hand, there are already measurements for $\gamma + p \to K^+ + \Lambda (1405)$ as well as the ground $\Lambda$ in photoproduction reactions. Analyzing such data, we found an interesting indication that $\Lambda (1405)$ looks like a five-quark state at medium energies and a three-quark one at high energies. However, accurate higher-energy measurements are necessary for drawing a solid conclusion, and it should be done at JLab by using the updated 12 GeV electron beam. Furthermore, we discuss studies of exotic hadron candidates, such as $f_0 (980)$ and $a_0 (980)$, in electron-positron annihilation by using generalized distribution amplitudes and the counting rule. These studies should be possible as a KEKB experiment.