# 龐蒂科夫-牧-中川-坂田矩陣

（重定向自PMNS矩陣

## 矩陣

${\displaystyle {\begin{bmatrix}{\nu _{e}}\\{\nu _{\mu }}\\{\nu _{\tau }}\end{bmatrix}}={\begin{bmatrix}U_{e1}&U_{e2}&U_{e3}\\U_{\mu 1}&U_{\mu 2}&U_{\mu 3}\\U_{\tau 1}&U_{\tau 2}&U_{\tau 3}\end{bmatrix}}{\begin{bmatrix}\nu _{1}\\\nu _{2}\\\nu _{3}\end{bmatrix}}\ }$

${\displaystyle {\begin{bmatrix}U_{e1}&U_{e2}&U_{e3}\\U_{\mu 1}&U_{\mu 2}&U_{\mu 3}\\U_{\tau 1}&U_{\tau 2}&U_{\tau 3}\end{bmatrix}}={\begin{bmatrix}\cos \theta _{12}\cos \theta _{13}&\sin \theta _{12}\cos \theta _{13}&\sin \theta _{13}e^{-i\delta }\\-\sin \theta _{12}\cos \theta _{23}-\cos \theta _{12}\sin \theta _{23}\sin \theta _{13}e^{i\delta }&\cos \theta _{12}\cos \theta _{23}-\sin \theta _{12}\sin \theta _{23}\sin \theta _{13}e^{i\delta }&\sin \theta _{23}\cos \theta _{13}\\\sin \theta _{12}\sin \theta _{23}-\cos \theta _{12}\cos \theta _{23}\sin \theta _{13}e^{i\delta }&-\cos \theta _{12}\sin \theta _{23}-\sin \theta _{12}\cos \theta _{23}\sin \theta _{13}e^{i\delta }&\cos \theta _{23}\cos \theta _{13}\end{bmatrix}}}$

${\displaystyle {\begin{bmatrix}U_{e1}&U_{e2}&U_{e3}\\U_{\mu 1}&U_{\mu 2}&U_{\mu 3}\\U_{\tau 1}&U_{\tau 2}&U_{\tau 3}\end{bmatrix}}={\begin{bmatrix}\cos \theta _{12}\cos \theta _{13}&\sin \theta _{12}&0\\-\sin \theta _{12}\cos \theta _{23}&\cos \theta _{12}\cos \theta _{23}&\sin \theta _{23}\\\sin \theta _{12}\sin \theta _{23}&-\cos \theta _{12}\sin \theta _{23}&\cos \theta _{23}\end{bmatrix}}={\begin{bmatrix}0.85&0.53&0\\-0.37&0.60&0.71\\0.37&-0.60&0.71\end{bmatrix}}\ }$

## 註釋

1. ^ 翹翹板模型中，PMNS矩陣並不是么正矩陣。

## 參考資料

1. ^ Z. Maki, M. Nakagawa, and S. Sakata. Remarks on the Unified Model of Elementary Particles. Progress of Theoretical Physics. 1962, 28: 870. Bibcode:1962PThPh..28..870M. doi:10.1143/PTP.28.870.
2. ^ B. Pontecorvo. Mesonium and anti-mesonium. Zh. Eksp. Teor. Fiz. 1957, 33: 549–551. 英語譯本見Sov. Phys. JETP. 1957, 6: 429. 缺少或|title=为空 (帮助)
3. ^ B. Pontecorvo. Neutrino Experiments and the Problem of Conservation of Leptonic Charge. Zh. Eksp. Teor. Fiz. 1967, 53: 1717. 英語譯本見Sov. Phys. JETP. 1968, 26: 984. Bibcode:1968JETP...26..984P. 缺少或|title=为空 (帮助)
4. ^ J.W.F. Valle. Neutrino physics overview. Journal of Physics: Conference Series. 2006, 53: 473. arXiv:hep-ph/0608101. doi:10.1088/1742-6596/53/1/031.
5. ^ http://www.hep.phy.cam.ac.uk/~thomson/partIIIparticles/handouts/Handout11_2010.pdf
6. ^ Daya Bay Collaboration. Observation of electron-antineutrino disappearance at Daya Bay. 8 March 2012. arXiv:1203.1669.