Spectral-Fluctuations Test of the Quark-Model Baryon Spectrum

We study the low-lying baryon spectrum (up to 2.2 GeV) provided by experiments and different quark models using statistical tools which allow us to postulate the existence of missing levels in spectra. We confirm that the experimental spectrum is compatible with random matrix theory, the paradigmatic model of quantum chaos, and we find that the quark models are more similar to a Poisson distribution, which is not compatible with what should be expected in a correlated spectrum. From our analysis it stems that the spectral fluctuation properties of quark-model spectra are incompatible with experimental data. This result can be used to enlighten the problem of missing resonances.

Figure 1

NNSD for the experimental spectrum provided by the PDG data, the model by Capstick and Isgur, and two parametrizations of the model by Löring et al. The histogram represents the spacings; the solid line, the Wigner surmise; and the dashed line, the Poisson distribution. The inset shows the function $F(x)$ in logarithmic scale.