adding numerical values for alpha_em and alpha_s

doc/chapters/output.tex

@@ -173,9 +173,21 @@ \subsubsection{Matching to the Standard Model}
     -\frac{2}{3} \log{\frac{m_t}{\mu}} \right],\\
   \Delta\alpha_{\text{s},\text{susy}}(\mu) &=
   \frac{\alpha_\text{s}}{2\pi}\left[ \frac{1}{2}-\sum_{\text{susy
-        particle } i} C_i \log{\frac{m_i}{\mu}} \right]
+        particle } i} C_i \log{\frac{m_i}{\mu}} \right] ,\\
+  g_{3,\text{susy}}^{\text{\DRbar}}(M_Z) &=
+  \sqrt{4\pi\alpha_{\text{s},\text{susy}}^{\text{\DRbar}}(M_Z)} ,
 \end{align}
 %
+where
+%
+\begin{align}
+  \alpha_{\text{e.m.},\text{SM}}^{(5),\text{\MSbar}}(M_Z) &= 1/127.944,\\
+  \alpha_{\text{s},\text{SM}}^{(5),\text{\MSbar}}(M_Z) &= 0.1185,
+\end{align}
+%
+are the \MSbar electromagnetic and strong cougling constants in the
+Standard Model including only $5$ quark flavours
+\cite{Beringer:1900zz}.
 
 \subsection{Lattice algorithm}