B_{22}(p^2,m_I^2,m_+^2) \nn
+  B_{22}(p^2,m_R^2,m_+^2),\\ &-& \frac{1}{2} A_0(m_+^2)-\frac{1}{4} A_0(m_R^2)-\frac{1}{4} A_0(m_I^2)\Big], \nn \\
\delta \Pi_{ZZ}(p^2) &=& \frac{g_1^2 }{2 \pi^2 c^2}\Big[  
(1-2s^2)^2 \left( B_{22}(p^2,m_+^2,m_+^2) -\frac{1}{2} A_0(m_+^2)\right), \nn \\
&+&  B_{22}(p^2,m_R^2,m_I^2 )-\frac{1}{4} A_0(m_R^2)-\frac{1}{4} A_0(m_I^2)\Big], \nn \\
\delta \Pi_{\gamma\gamma}(p^2) &=& \frac{2 e^2 }{ \pi^2 }\Big[  
 B_{22}(p^2,m_+^2,m_+^2) -\frac{1}{2} A_0(m_+^2) \Big], \nn \\
\delta \Pi_{\gamma Z}(p^2) &=& \frac{e g_1(1-2s^2)}{ \pi^2 c }\Big[  
 B_{22}(p^2,m_+^2,m_+^2) -\frac{1}{2} A_0(m_+^2) \Big]. \nn\end{aligned}$$

For $p^2=0$ these expressions become $$\begin{aligned}
\delta \Pi_{WW}(0) &=& \frac{g_1^2 }{8 \pi^2} \left( \frac{1}{2} f(m_+,m_R) +  \frac{1}{2} f(m_+,m_I) \right), \nn \\
\delta \Pi_{ZZ}(0) &=& \frac{g_1^2}{8 \pi^2 c^2} \left( \frac{1}{2} f(m_R,m_I) \right),  \nn\end{aligned}$$ where $$f(m_1,m_2)=m_1^2 +m_2^2 -\frac{2 m_1^2 m_2^2}{m_1^2-m_2^2}\log{ \frac{m_1^2}{m_2^2} }. \nn$$

The derivatives of the vacuum polarizations are $$\begin{aligned}
\delta \Pi'_{\gamma\gamma}(0)&=& - \frac{e^2}{6 \pi^2} B_0(0,m_+^2,m_+^2), \nn \\
\delta \Pi'_{\gamma Z}(0) &=& -\frac{e g_1(1-2s^2)}{12 \pi^2 c } B_0(0,m_+^2,m_+^2), \nn\\
\delta \Pi'_{WW}(p^2) &=& \frac{g_1^2}{2 \pi^2} \Big[ -\frac{1}{6}\Delta + \frac{\partial b_{22}(p^2,m_I^2,m_+^2)}{\partial p^2} , \nn \\ 
&\,& \hspace{1.9cm} + \frac{\partial b_{22}(p^2,m_R^2,m_+^2)}{\partial p^2} \Big], \nn \\
\delta \Pi'_{ZZ}(p^2) &=& \frac{g_1^2}{2 \pi^2 c^2}\Big[  
-  \frac{1}{12}\Delta +\frac{ \partial b_{22}(p^2,m_R^2,m_I^2 )}{\partial p^2}, \nn \\
&\,& (1-2s^2)^2 \left( -\frac{1}{12}\Delta +\frac{\partial b_{22}(p^2,m_+^2,m_+^2)}{\partial p^2} \right) \Big]. \nn \end{aligned}$$

Using these results we can construct the $\rm STUVWX$ parameters with the standard definitions [@Maksymyk:1993zm]

$$\begin{aligned}
 \frac{\alpha S}{4 s^2 \, c^2} &=& \left[\frac{\delta 