ar X iv : h ep - p h / 01 10 41 4 v 1 3 1 O ct 2 00 1 CP violating neutrino oscillation and uncertainties in Earth matter density

We propose a statistical formulation to estimate possible errors in long baseline neutrino oscillation experiments caused by uncertainties in the Earth matter density. A quantitative investigation of the effect is made on the CP asymmetry in future neutrino factory experiments. Leptonic CP violation (CPV) is one of the main challenges in future long baseline (LBL) neutrino oscillation experiments [1], where more accurate measurements of the neutrino oscillation parameters are anticipated. However, since the neutrino beam travels a long path through the Earth, the MSW matter effect [2] can mimic a non-vanishing CP phase and makes it non-trivial to extract the intrinsic CP phase. Therefore, a thorough quantitative understanding of the matter effect and its possible uncertainties is necessary before an accurate account of the CPV effect can be achieved. The critical quantity in discerning the matter effect is the value of the Earth matter density as a function of the baseline. A number of approaches have been suggested on using different Earth density profiles of the Earth for the electron number density (DEN). In these works, DEN is taken either as a distance-averaging effective constant [3], an adiabatic approximation profile [4], mantle-core-mantle layers approximation [5], multi-step functions [6], or the preliminary reference Earth model (PREM) [7]. We refer to Ref. [8] for a review of some of the available Earth density models. It is clear from these works that the analysis of the leptonic CPV will depend on the Earth density model adopted to analyze the experimental data. From the geophysics point of view, a density model is understood to be an approximation of the Earth and has its inherent uncertainties. For a brief discussion on the uncertainty of DEN, we refer to Refs. [9] and [5]. Detailed discussions can be found in geophysics review[10, 11, 12]. As to PREM, significant deviations from PREM due to local variation have been documented[13] and averaged per spherical shell with thickness of 100 Km, its precision is roughly 5%. Instead of examining quantitatively all the schemes of the Earth density to find out the preferred density scheme to use, we would like to raise and attempt to provide at least a partial answer to the following basic questions: What is the effect of uncertainties in the Earth matter density on the measurement of CPV? Can the effect be so severe that it demands a more accurate knowledge of the Earth density before a reliable CP phase can be extracted in LBL experiments? We propose in this paper to estimate the error due to the uncertainty in the Earth matter density as the variance of a CP odd oscillation probability. As described below the procedure in making the estimate is a weighted average over the whole sample space of possible Earth density profiles. We first introduce a local variance function σ(x) to characterize the density uncertainties at each point of the Earth along a given baseline. With the variance function we sample the earth density profiles, then construct an averaging process to calculate the deviation of a physical quantity from its mean value. The probability of the various DEN examples is taken as a logarithmic distribution suitable for non-negative quantities, although other statistics approach may be used. [email protected]