Discussion

Abstract

In this chapter, we discuss the present results focusing on the narrowness of the width which is the most peculiar property to the $\varTheta ^+$ pentaquark. The mechanism of the $\pi ^-p \rightarrow K^-\varTheta ^+$ reaction was theoretically discussed using the KEK-E522 and E559 results. Knowing that the t-channel and contact term contributions are very small, the s-channel contribution is important in the $\pi ^-p \rightarrow K^-\varTheta ^+$ reaction. Since the s-channel amplitude is related to the $\varTheta ^+$ decay width through the $KN\varTheta$ coupling constant, we can estimate the upper limit of the width from the cross section measured in the experiment. Using both the 2010 and 2012 data together with a theoretical calculation using the effective Lagrangian approach, the upper limits of the width were estimated to be 0.36 and 1.9 MeV for the $\varTheta ^+$ spin-parity of $1/2^+$ and $1/2^-$, respectively. These widths are compared with the past experimental results.