Pentaquark in $K^{+}\text{‐}d$ total cross section data

An analysis of $K^{+}\text{‐}d$ total cross section data is undertaken to explore possible effects of the recently observed resonance in the $S=+1$ hadronic system with mass around $1.55\mathrm{GeV}$. It is found that a structure corresponding to the resonance is visible in the data. The width consistent with the observed deviation from background is found to be $0.9\pm 0.3\mathrm{MeV}$ and the mass is $1.559\pm 0.003\mathrm{GeV}∕c^2$ for spin parity ${\frac{1}{2}}^{+}$ and $1.547\pm 0.002\mathrm{GeV}∕c^2$ for ${\frac{1}{2}}^{-}$. The errors are one standard deviation and statistical only.

Figure 1

Double scattering contribution to $K^{+}d$ scattering. The common value of $\Lambda$ used for the dipole form factor employed in this work is around $1.4\mathrm{GeV}∕c$.

Figure 2

The measured Fermi momentum distribution compared with the parametrization and that predicted from the one-pion-exchange deuteron.

Figure 3

$K^{+}$ proton total cross section compared with the fit used here. The solid points are from Bowen et al. [24] and the open points are from Carroll et al. [25].

Figure 4

Phase shifts obtained in this work from the $s$-wave fit (solid curves) compared with previously obtained values. The solid points for $I=1$ are from Ref. 22. For $I=0$, the solid circles are from Ref. 28, the open circles are from Ref. 27, the solid squares are from Ref. 29, and the dotted curve is from the “C” fit by Ref. 30.

Figure 5

Background fit used in this work. The highest and lowest momentum points were used. The solid points are from Ref. 24. The dotted curve is only the $I=1$ contribution, the dash-dotted curve includes that plus the $I=0$ contribution, and the solid curve includes the double scattering as well. The horizontal bars indicate the range of masses from Refs. 7, 8. The ranges from all of the experiments can be found on Fig. 7.

Figure 6

Comparison of Fermi motion corrected resonances with the data. The dash-dotted, solid, and dashed curves correspond to widths of 1.2, 0.9, and $0.6\mathrm{MeV}$, respectively. The dotted curve is the background fit. The horizontal bars are the same as in Fig. 5. The vertical dashed line in each panel shows the input value of the mass. For the $s$-wave resonance the theoretical peak occurs almost at this value while, for the $p$-wave resonance, there is a noticeable change due to the fact that the background phase shift is considerably larger.

Figure 7

${\chi }^2$ contour plots as a function of $\Gamma$ and mass. The inner contour corresponds to one standard deviation, the next to two standard deviations, etc. The solid curves are for the ${\frac{1}{2}}^{+}$ case ($P_{01}$ partial wave) and the dashed curves are for ${\frac{1}{2}}^{-}$ ($S_{01}$ partial wave). The points at the top correspond to mass estimates given by the six discovery experiments cited in the introduction (A–F correspond to Refs. 3, 4, 5, 6, 7, 8). The vertical placement of these points has no significance.