Likelihood scan of the Super-Kamiokande I time series data
  In this work a detailed spectral analysis of the time series of the 8B solar neutrino flux published by the Super-Kamiokande Collaboration is presented, performed through a likelihood scan approach. Preliminarily a careful review of the analysis methodology is given, showing that the traditional periodicity search via the Lomb-Scargle periodogram is a special case of a more general likelihood based method. Since the data are published together with the relevant asymmetric errors, it is then shown how the likelihood analysis can be performed either with or without a prior error averaging. A key point of this work is the detailed illustration of the mathematical model describing the statistical properties of the estimated spectra obtained in the various cases, which is also validated through extensive Monte Carlo computations; the model includes a calculation for the prediction of the possible alias effects. In the successive investigation of the data, such a model is used to derive objective, mathematical predictions which are quantitatively compared with the features observed in the experimental spectra. This article clearly demonstrates that the handling of the errors is the origin of the discrepancy between published null observations and claimed significant periodicity in the same SK-I data sample. Moreover, the comprehensive likelihood analysis with asymmetric errors developed in this work provides results which cannot exclude the null hypothesis of constant rate, even though some indications stemming from the model at odd with such conclusion point towards the desirability of additional investigations with alternative methods to shed further light on the characteristics of the data. 
Gioacchino Ranucci