クォークセクター」タグアーカイブ

素粒子標準模型:クォークセクター:クォークセクターのまとめ

\begin{eqnarray}
\lagrangian_{quark}
&=&
\sum_{I=1,2,3}
\left[
i\bar{Q}^F_{I_i}\bar{\sigma}^\mu (D_\mu Q_I)^F_{i}
+
i\bar{u}_{I_R}^F\sigma^\mu (D_\mu u_{I_R})^F
+
i\bar{d}_{I_R}^F\sigma^\mu (D_\mu d_{I_R})^F
\right]\nonumber\\
&&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-\sum_{I,J=1,2,3}
\left(
y^u_{IJ}\bar{Q}^F_{I_i}H^c_iu^F_{J_R}
+
y^d_{IJ}\bar{Q}^F_{I_i}H_id^F_{J_R}
+h.c\right)\\
&\Downarrow&SSB&ユニタリ変換\nonumber\\
&=&
\sum_{I,J=1,2,3}\left[
\frac{}{}
\bar{\psi}^F_{u_I}((i\Slash{\nabla}-m_{u_I})\psi_{u_I})^F
+
\bar{\psi}^F_{d_I}((i\Slash{\nabla}-m_{d_I})\psi_{d_I})^F

\frac{m_{u_I}}{v}h\bar{\psi}^F_{u_I}\psi^F_{u_I}

\frac{m_{d_I}}{v}h\bar{\psi}^F_{d_I}\psi^F_{d_I}
\right.\nonumber\\
&&~~~~~~~~~~
+
\left(
\frac{2e}{3}\bar{\psi}^F_{u_I}\gamma^\mu\psi_{u_I}^F

\frac{e}{3}\bar{\psi}^F_{d_I}\gamma^\mu\psi_{d_I}^F
\right)A_\mu
+\frac{e}{\sqrt{2}\sin\theta_w}\left[
U_{IJ}\bar{\psi}_{u_I}^F\gamma^\mu P_L\psi^F_{d_J}W^+_\mu
+
U^\dagger_{IJ}\bar{\psi}_{d_I}^F\gamma^\mu P_L\psi^F_{u_J}W^-_\mu \right]
\nonumber\\
&&\left.~~~~~~~~~~
+\left\{
\frac{e}{2\sin\theta_w\cos\theta_w}\left(
\bar{\psi}^F_{u_I}\gamma^\mu P_L\psi^F_{u_I}

\bar{\psi}^F_{d_I}\gamma^\mu P_L\psi^F_{d_I}
\right)
-\frac{2e\tan\theta_w}{3}
\bar{\psi}^F_{u_I}\gamma^\mu{\psi}^F_{u_I}
+\frac{e\tan\theta_w}{3}
\bar{\psi}^F_{d_I}\gamma^\mu{\psi}^F_{d_I}
\right\}Z_\mu\right]\nonumber\\
\\
&=&
\sum_{I,J=1,2,3}\left[
\frac{}{}
\bar{\psi}^F_{u_I}((i\Slash{\nabla}-m_{u_I})\psi_{u_I})^F
+
\bar{\psi}^F_{d_I}((i\Slash{\nabla}-m_{d_I})\psi_{d_I})^F

\frac{m_{u_I}}{v}h\bar{\psi}^F_{u_I}\psi^F_{u_I}

\frac{m_{d_I}}{v}h\bar{\psi}^F_{d_I}\psi^F_{d_I}
\right.\nonumber\\
&&\left.~~~~~~~~~~~
+J^\mu_{q,em}A_\mu+J^\mu_{q,Z}Z_\mu
+J^{\mu}_{q,+}W^-_\mu+J^{\mu}_{q,-}W^+_\mu
\right]
\end{eqnarray}