Pentaquark decay width in QCD sum rules

In a diquark-diquark-antiquark picture of the pentaquark we study the decay $\Theta \to K^{+}n$ within the framework of QCD sum rules. After evaluation of the relevant three-point function, we extract the coupling $g_{\Theta nK}$ which is directly related to the pentaquark width. Restricting the decay diagrams to those with color exchange between the mesonlike and baryonlike clusters reduces the coupling constant by a factor of 4. Whereas a small decay width might be possible for a positive parity pentaquark, it seems difficult to explain the measured width for a pentaquark with negative parity.

Figure 1

The basic diagram for the theoretical side of the sum rule.

Figure 2

The main diagrams which contribute to the theoretical side of the sum rule in the relevant structure. (a)–(g) are the color-disconnected diagrams, whereas (h)–(j) are the color-connected diagrams. The cross indicates the insertion of the strange mass.

Figure 3

$|g_{\Theta nK}|$ in case I A with three different continuum threshold parameters. Solid line: ${\Delta }_N=0.5\mathrm{GeV}$; dotted line: ${\Delta }_N=0.4\mathrm{GeV}$; dash-dotted line: ${\Delta }_N=0.6\mathrm{GeV}$.

Figure 4

$|g_{\Theta nK}|$ in case II A. Solid line: ${\Delta }_N=0.5\mathrm{GeV}$; dotted line: ${\Delta }_N=0.4\mathrm{GeV}$; dashed line: ${\Delta }_N=0.6\mathrm{GeV}$. $M^{\prime 2}=1{\mathrm{GeV}}^2$.

Figure 5

$|g_{\Theta nK}|$ in case I B with three different continuum threshold parameters. Solid line: ${\Delta }_N=0.5\mathrm{GeV}$; dotted line: ${\Delta }_N=0.4\mathrm{GeV}$; dash-dotted line: ${\Delta }_N=0.6\mathrm{GeV}$.

Figure 6

$|g_{\Theta nK}|$ in case II B. Solid line: ${\Delta }_N=0.5\mathrm{GeV}$; dotted line: ${\Delta }_N=0.4\mathrm{GeV}$; dashed line: ${\Delta }_N=0.6\mathrm{GeV}$. $M^{\prime 2}=1{\mathrm{GeV}}^2$.