The

** first figure** compares, for assumed neutrino masses of zero (red) and 0.5 eV (blue) and a total measuring time of one full year, a simulation of the results in a narrow energy interval up to the endpoint. The same amount of measuring time was used for each of the data points.

The inset shows, for a 5 times larger energy window, the difference of the two results, normalized to (i.e. divided by) the statistical error of the difference. Mean values of these residuals are given for the interval below 18572 eV, dominated by electrons from tritium β-decay, and above that energy, dominated by background.

The figure demonstrates how sensitive the experimental setup has to be in order to differentiate neutrino masses even smaller than 0.5 eV from zero within the very small energy window below the endpoint energy! One clearly sees that a longer measuring time will help. Simulations have also shown (see second figure) that for a given total measuring time the sensitivity can be improved by allocating the time for each data point according to its weight for the analysis.

The

**second figure** shows a calculation of the expected accuracy on m

_{ν}^{2} for a data taking of three years. Only statistical uncertainties are shown as a function of the fit interval below the endpoint E

_{0}. The complete transmission and response function of the experimental setup is taken into account as well as the final state distribution of the (

^{3}HeT)

^{+} ionized daughter molecules. Various steps of optimization of the KATRIN configuration as specified in [1] (green squares) can be seen:

1. Increase in diameter of the spectrometer vessel (7m → 10m) and of the tritium source (7cm → 9cm) as well as an improved tritium isotopic purity (70% → 95%) (red circles).

2. Optimized distribution of electron energy thresholds (retarding voltage!) used and time spent for each (blue triangles). This corresponds to the** KATRIN reference setup[2]**.

3. Reduction of the expected overall background from 10 mHz to 1 mHz (black empty squares).

The **third figure** demonstrates the KATRIN discovery potential, in units of the Gaussian uncertainty σ, as a function of the potential neutrino mass for the older setup as outlined in [1] (3 years, 7m spectrometer) and of the current configuration (3 years, 10m, optimized). In both cases the expected overall background is 10mHz. Note the improvement, e.g. from 1.64σ to 5σ for an assumed mass of m_{ν}=0.35eV!

The constant line at 1.64σ indicates the expected upper limit on m_{ν} with 90% confidence in case of a zero-mass result.

**References**

[1] KATRIN Collab.,

Letter of Intent (2001)

[2] G.Drexlin, Eur. Phys.J.C33, s01 (2004)