Bayesian Analysis of Pentaquark Signals from CLAS Data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a ${\Theta }^{+}$ pentaquark, while the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis, we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a ${\Theta }^{+}$. Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.

Figure 1

$p{K}^{-}$ missing mass spectra from the five $g10$ subsamples and the original $g2a$ data. The data are sorted into bins of width $10\mathrm{MeV}/c^2$.

Figure 2

Missing mass histograms for ${\Theta }^{+}$ from (a) $g10$, (b) fake, and $\Lambda (1520)$ from (c) $g10$, and (d) $g2a$ data. The data in (a) and (b) are sorted into bins of width $10\mathrm{MeV}/c^2$, and the bins in (c) and (d) have width $5\mathrm{MeV}/c^2$.

Figure 3

Graphical representation of the values of evidence ratios from Table 1, on a logarithmic scale. The horizontal lines correspond to the limits of the regions associated with the different descriptors of the Jeffreys scale.