Spectral-statistics properties of the experimental and theoretical light baryon and meson spectra

We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical properties are close to those predicted by random matrix theory for chaotic systems, while for the theoretical ones they are in general closer to those predicted for integrable systems and safely incompatible with those of chaotic systems. We stress the importance of the agreement of the fluctuation properties between experiment and theoretical models, as they determine the dynamical regime and the complexity of the real interactions. We emphasize the new statistical method we use, adapted to properly analyze the fluctuation properties for very short spectral sequences.

Figure 1

Nearest-neighbor spacing distribution for GOE (up) and Poisson (down) spectra (histograms) divided into sequences of length $l=3,4,10$ levels in which a local unfolding has been performed, compared to the theoretical predictions, the Wigner surmise, and the Poisson distribution (solid lines).

Figure 2

NNSD for the experimental baryon spectrum from the RPP (histogram) compared to the distorted reference distributions [Wigner, $P_{\mathrm{DW}}\left(s\right)$ (diamonds) and Poisson, $P_{\mathrm{DP}}\left(s\right)$ (crosses)] and to the theoretical distributions [Wigner surmise (dash-dotted) and Poisson distribution (dashed)].

Figure 3

Moments of the NNSD, $M^{\left(k\right)}$, for the experimental baryon spectrum (solid line with error bars), compared to those of the distorted distributions: Wigner (diamonds) and Poisson (crosses).

Figure 4

Distributions of the $p$ values of the K-S test for the 1000 “realizations” of the experimental baryon spectrum within the error bars, for the null hypothesis that the distribution coincides with Wigner (solid histogram) and with Poisson (dashed histogram).

Figure 5

NNSD for the theoretical baryon spectra: (i) top, set CI by Capstick and Isgur [2]; (ii) middle, set L1 by Löring et al. [3]; (iii) bottom, set L2 by Löring et al. [3]. They are compared to the distorted distributions: Wigner, $P_{\mathrm{DW}}\left(s\right)$ (diamonds) and Poisson, $P_{\mathrm{DP}}\left(s\right)$ (crosses).

Figure 6

NNSD for the experimental meson spectrum from the RPP (histogram) compared to the distorted distributions: Wigner, $P_{\mathrm{DW}}\left(s\right)$ (diamonds), Poisson, $P_{\mathrm{DP}}\left(s\right)$ (crosses), and Berry-Robnik with $f=0.78, P_{\mathrm{DBR}}(0.78,s)$ (dots).

Figure 7

Moments of the NNSD, $M^{\left(k\right)}$, for the experimental meson spectrum (solid line with error bars), compared to those of the distorted distributions: Wigner (diamonds), Poisson (crosses), and Berry-Robnik with $f=0.78$ (dots).

Figure 8

Distributions of the $p$ values of the K-S test for the 1000 “realizations” of the experimental meson spectrum within the error bars, for the null hypothesis that the distribution coincides with Poisson (dashed histogram) and with Berry-Robnik for $f=0.78$ (solid histogram).

Figure 9

NNSDs for the theoretical meson spectra: (i) Top left, set GI by Godfrey and Isgur [18]; (ii) middle left, set K1 by Koll et al. [15]; (iii) bottom left, set K2 by Koll et al. [15]; (iv) top right, set E by Ebert et al. [17]; (v) middle right, set V by Vijande et al. [16] and ad hoc distorted Berry-Robnik with $f=0.63$; (vi) bottom right, set LQCD by Dudek et al. [20]. Distorted Wigner, $P_{\mathrm{DW}}\left(s\right)$, is represented with diamonds; distorted Poisson, $P_{\mathrm{DP}}\left(s\right)$, with crosses; and distorted Berry-Robnik, $P_{\mathrm{DBR}}(f,s)$, with dots.