Maximum likelihood analysis of the first KamLAND results

A maximum likelihood approach has been used to analize the first results from KamLAND emphasizing the application of this method for low statistics samples. The goodness of fit has been determined exploiting a simple Monte Carlo approach in order to test two different null hytpotheses. It turns out that with the present statistics the neutrino oscillation hypothesis has a significance of about 90% (the best-fit for the oscillation parameters from KamLAND are found to be: $\delta m_{12}^2 \sim 7.1 \times 10^{-5}$ eV$^2$ and $\sin^2 \theta_{12} = 0.424/0.576$), while the no-oscillation hypothesis of about 50%. Through the likelihood ratio the hypothesis of no disappearence is rejected at about 99.9% C.L. with the present data from the positron spectrum. A comparison with other analyses is presented.Comment: 14 pages, 5 figure