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thesis/chapters/chap2_mu_e_conv.tex

@@ -271,11 +271,11 @@ experimental limits on these two decay modes are set respectively by the MEG
 experiment~\cite{Adam.etal.2013} and the SINDRUM-II
 experiment~\cite{Bertl.etal.2006}:
 \begin{equation}
-  \mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13}\,
+  \mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13}\,,
 \end{equation}
 and:
 \begin{equation}
-  \mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}\.
+  \mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}\,.
 \end{equation}
 
 %\hl{TODO: mueg and muec relations, Lagrangian \ldots}
@@ -307,14 +307,13 @@ In the context of physics beyond the SM, the exotic process of \mueconv where
 a muon decays to an electron without neutrinos is also
 expected, but has never been observed: 
 \begin{equation}
-  \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)\.
+  \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)\,.
 \end{equation}
-The emitted electron in this decay
-mode , the \mueconv electron, is mono-energetic at an energy far above the
-endpoint
+The emitted electron in this decay mode, the \mueconv electron, is
+mono-energetic at an energy far above the endpoint
 of the Michel spectrum (52.8 MeV):
 \begin{equation}
-  E_{\mu e} = m_\mu - E_b - \frac{E^2_\mu}{2m_N}
+  E_{\mu e} = m_\mu - E_b - \frac{E^2_\mu}{2m_N}\,.
 \end{equation}
 where $m_\mu$ is the muon mas; $E_b \simeq Z^2\alpha^2 m_\mu/2$ is the binding
 energy of the muonic atom; and the last term is the nuclear recoil energy
@@ -351,7 +350,10 @@ The mean lifetime $\tau = 1/\Gamma$, then:
 \end{equation}
 The mean lifetimes of free muons and muons in a material are well-known,
 therefore the number of captures can be inferred from the number of stops. For
-aluminium, $\frac{\Gamma_{\textrm{capture}}}{\Gamma_{\textrm{stop}}} = 0.609$
+aluminium, 
+\begin{equation}
+  \frac{\Gamma_{\textrm{capture}}}{\Gamma_{\textrm{stop}}} = 0.609
+\end{equation}
 and the mean lifetime of stopped muons is 864
 ns~\cite{SuzukiMeasday.etal.1987}.