PMNS hâng-lia̍t

Tī lia̍p-chú bu̍t-lí-ha̍k tiong, PMNS hâng-lia̍t sī chi̍t ê (Hàn-jī: PMNS行列; Eng-gí: Pontecorvo-Maki-Nakagawa-Sakata matrix, kán-chheng PMNS matrix), mā kiò-chò neutrino sio-lām hâng-lia̍t (Hàn-jī: neutrino相濫行列; Eng-gí: neutrino mixing matrix) sī chi̍t ê unitary sio-lām hâng-lia̍t, chū-iû thoân-pò ê neutrino kap si jio̍k-la̍t ê neutrino nn̄g-ê chi-kan liōng-chú thài ê chhat-piat. Chit ê hâng-lia̍t siōng chá sī Ziro Maki, Masami Nakagawa, kap Shoichi Sakata tī 1962 nî the̍h-chhut ·ê, ēng-lâi kái-soeh Bruno Pontecorvo ī-chhek ê neutrino tín-tāng hiān-siōng.

Hâng-lia̍t

PMNS hâng-lia̍ chok-iōng tī neutrino ê chit-liōng kò͘-iú thài, tiō chiâⁿ-chò bī ê kò͘-iú thài sī án-ne:

${\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}}\$.

Chham-sò͘-hòa

PMNS ū kúi-nā chióng bô-kâng ê chham-sò͘-hòa. Siōng chiap khòaⁿ-tio̍h ·ê sī bô͘-hóng 3-chhù-goân khong-kan lāi-té ê tńg-se̍h, ū 3 ê sio-lām kak ($\theta _{12}$, $\theta _{23}$ kap $\theta _{13}$), koh ū chi̍t-ê tāi-piáu CP phò-hoāi ê ūi-siòng $\delta _{\text{CP}}$.

${\begin{aligned}&{\begin{bmatrix}1&0&0\\0&c_{23}&s_{23}\\0&-s_{23}&c_{23}\end{bmatrix}}{\begin{bmatrix}c_{13}&0&s_{13}e^{-i\delta _{\text{CP}}}\\0&1&0\\-s_{13}e^{i\delta _{\text{CP}}}&0&c_{13}\end{bmatrix}}{\begin{bmatrix}c_{12}&s_{12}&0\\-s_{12}&c_{12}&0\\0&0&1\end{bmatrix}}\\&={\begin{bmatrix}c_{12}c_{13}&s_{12}c_{13}&s_{13}e^{-i\delta _{\text{CP}}}\\-s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\delta _{\text{CP}}}&c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\delta _{\text{CP}}}&s_{23}c_{13}\\s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\delta _{\text{CP}}}&-c_{12}s_{23}-s_{12}c_{23}s_{13}e^{i\delta _{\text{CP}}}&c_{23}c_{13}\end{bmatrix}}.\end{aligned}}$

kî-tiong $s_{ij}$ kap $c_{ij}$ hun-pia̍t sī tāi-piáu $\sin \theta _{ij}$ kap $\cos \theta _{ij}$.

Koh khòaⁿ

• Neutrino tín-tāng
• CKM hâng-lia̍t