Results

 

 

 

Home         KamLAND Experiment        Our Research          Results           About Me

 

  

After testing the real N1 from the 4th KamLAND Data Release file, we got the following graph:

 

 

                                           http://latex.codecogs.com/gif.latex?P_%7B1_%7Bestimate%7D%7D%20%3D%20%5Cbegin%7Bpmatrix%7D%200.39%5C%5C%200.78%5C%5C%200.60%5C%5C%200.86%5C%5C%200.46%5C%5C%200.31%5C%5C%200.29%5C%5C%20-0.11%5C%5C%200.75%5C%5C%200.52%5C%5C%200.59%20%5Cend%7Bpmatrix%7D                             

 

 

 

Comparing our N estimated from the P1estimate above with KamLAND’s N’1 obtained from the experiment, we got:

 

 

 

      http://latex.codecogs.com/gif.latex?N%5E%7B%27%7D_%7B1%7D%20%3D%20%5Cbegin%7Bpmatrix%7D%2050.1%5C%5C%2088.2%5C%5C%20106.8%5C%5C%2073.7%5C%5C%2079.3%5C%5C%2092.5%5C%5C%2066.6%5C%5C%2065.8%5C%5C%2083.0%5C%5C%2097.0%5C%5C%20137.3%5C%5C%20119.4%5C%5C%20126.2%5C%5C%20169.0%5C%5C%20112.2%5C%5C%20104.9%5C%5C%20102.6%20%5Cend%7Bpmatrix%7D                                     http://latex.codecogs.com/gif.latex?N%5E%7B%27%7D_%7B1_%7Bestimate%7D%7D%20%3D%20%5Cbegin%7Bpmatrix%7D%2053.1%5C%5C%2085.5%5C%5C%20102.5%5C%5C%2081.4%5C%5C%2083.3%5C%5C%2084.1%5C%5C%2065.4%5C%5C%2069.8%5C%5C%2087.8%5C%5C%2089.0%5C%5C%20129.1%5C%5C%20136.0%5C%5C%20126.5%5C%5C%20157.0%5C%5C%20115.5%5C%5C%20109.9%5C%5C%2099.2%20%5Cend%7Bpmatrix%7D

 

 

 

 

Chi square of the N between our estimate and the N observed:    

6.68

 

Chi square of the P between our estimate and the closest straight line of 0.44 without taking into account covariance:    

 9.65

 

The above chi square with covariance:  

 67.95

 

 

The results from the chi squares show that the P1estimate that we obtained through our method is a good fit for the appearance probability, while a constant probability is not.

 

 

 

 

Covariance Matrix of C

 

 

 

 

 

 

Conclusions

 

After KamLAND’s counts data was run through our method, we obtained appearance probabilities for 11 values of L/Eν without assuming an average L. Even though the errors appear large,

 the chi square accounting for covariance shows that not even the best fitted horizontal line of P(l) = 0.44 will fit the data obtained due to correlations between the data points.

Using the appearance probability graph obtained in this research, the predicted N matched KamLAND’s observed N based on the chi square.

We intend to apply the methods learned and used in this research to current and future experiments.

 

 

 

 

References

 

•      KamLAND 4th Data Release File:  http://www.awa.tohoku.ac.jp/KamLAND/4th_result_data_release/4th_result_data_release.html 

•      KamLAND Probability graph: http://arxiv.org/pdf/1009.4771v2.pdf 

•      All detector pictures:  http://kamland.lbl.gov/ 

 

 

 

 

This program is funded by the National Science Foundation through grant number PHY-1157044.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.