[2025-01-18] For better promotion of the events, the categories in this system will be adjusted. For details, please refer to the announcement of this system. The link is https://indico-tdli.sjtu.edu.cn/news/1-warm-reminder-on-adjusting-indico-tdli-categories-indico
I have calculated tau lepton pair's spin correlation matrix after boosting four-momentum of its decay products pion+ and pion- to the rest frame of tau+ and tau-, respectively.
For Reconstruction level, it shows
$\C_{ij}$ | r | k | n |
r | -0.5976 | 0.0407 | -0.0238 |
k | 0.0057 | 1.2479 | 0.0075 |
n | -0.0112 | -0.0270 | 0.6173 |
And its concurrence is 0.7318.
Here is the distribution of angle between the momentum of pion and n-axis, which is used in the calculation of Asymmetry.
For the data generated through ML, it shows
$\C_{ij}$ | r | k | n |
r | -0.0641 | -0.0230 | 0.0299 |
k | 0.0904 | 0.8288 | -0.0278 |
n | -0.0154 | -0.0291 | 0.0233 |
And its concurrence is 0 (-0.0488).
Since tau lepton pair has the term of net polarization B in its density matrix, the entanglement calculated before is not exactly right.