fixed typo and logic

Experiment41.log

@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2019/dev/Debian) (preloaded format=pdflatex 2019.11.14)  23 MAR 2021 12:26
+This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2019/dev/Debian) (preloaded format=pdflatex 2019.11.14)  18 MAY 2021 16:31
 entering extended mode
  restricted \write18 enabled.
  %&-line parsing enabled.
@@ -1492,7 +1492,7 @@ Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 71.
 Here is how much of TeX's memory you used:
  23273 strings out of 492615
  407943 string characters out of 6131389
- 463166 words of memory out of 5000000
+ 464166 words of memory out of 5000000
  26640 multiletter control sequences out of 15000+600000
  751046 words of font info for 244 fonts, out of 8000000 for 9000
  1141 hyphenation exceptions out of 8191
@@ -1514,7 +1514,7 @@ exmf-dist/fonts/type1/adobe/utopia/putb8a.pfb></usr/share/texlive/texmf-dist/fo
 nts/type1/adobe/utopia/putr8a.pfb></usr/share/texlive/texmf-dist/fonts/type1/ad
 obe/utopia/putri8a.pfb></usr/share/texmf/fonts/type1/public/cm-super/sftt1200.p
 fb>
-Output written on Experiment41.pdf (39 pages, 2936218 bytes).
+Output written on Experiment41.pdf (39 pages, 2936187 bytes).
 PDF statistics:
  687 PDF objects out of 1000 (max. 8388607)
  546 compressed objects within 6 object streams

Experiment41.tex

@@ -27,7 +27,7 @@
 \renewcommand\cellgape{\Gape[4pt]}
 
 \title{Cosmic muon magnetic moment and lifetime.\\
-	\large v1.4}
+	\large v1.5}
 
 \author{Matei A.V. Climescu}
 \date{Mainz, 2021}

sections/chap3.aux

@@ -10,8 +10,8 @@
 \@writefile{lof}{\contentsline {figure}{\numberline {3.2}{\ignorespaces Magnetic latitude effect at sea level.\relax }}{5}{figure.caption.5}\protected@file@percent }
 \newlabel{fig:magintensity}{{3.2}{5}{Magnetic latitude effect at sea level.\relax }{figure.caption.5}{}}
 \@writefile{toc}{\contentsline {section}{\numberline {3.3}Secondary comic rays}{5}{section.3.3}\protected@file@percent }
-\@writefile{lof}{\contentsline {figure}{\numberline {3.3}{\ignorespaces East-west assymetry measured at different altitudes.\relax }}{6}{figure.caption.6}\protected@file@percent }
-\newlabel{fig:assym}{{3.3}{6}{East-west assymetry measured at different altitudes.\relax }{figure.caption.6}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3.3}{\ignorespaces East-west asymmetry measured at different altitudes.\relax }}{6}{figure.caption.6}\protected@file@percent }
+\newlabel{fig:assym}{{3.3}{6}{East-west asymmetry measured at different altitudes.\relax }{figure.caption.6}{}}
 \@writefile{lof}{\contentsline {figure}{\numberline {3.4}{\ignorespaces Bremsstrahlung pion emission from proton-nucleus scattering.\relax }}{6}{figure.caption.7}\protected@file@percent }
 \newlabel{fig:scat}{{3.4}{6}{Bremsstrahlung pion emission from proton-nucleus scattering.\relax }{figure.caption.7}{}}
 \citation{Tanabashi:2018oca}

sections/chap3.tex

@@ -40,12 +40,12 @@ \section{Primary cosmic rays}
 \text{P}_\Phi=1.5\cdot 10^{10} \cos^4\Phi |z| \text{ eV}.c^{-1}.
 \end{equation}
 
-where $z$ is the particle's charge in units of elementary charge. The discrenpency in the number of positive and negative particles results in an east-west assymetry in particle intensity. At least $90\%$ of the primary particles have a positive charge as shown in Figure \ref{fig:assym}.
+where $z$ is the particle's charge in units of elementary charge. The discrenpency in the number of positive and negative particles results in an east-west asymmetry in particle intensity. At least $90\%$ of the primary particles have a positive charge as shown in Figure \ref{fig:assym}.
 
 \begin{figure}[htbp] %No better figure could be found, it could be remade%
 \centering
 \includegraphics[width=0.8\linewidth]{./fig/assym.png}
-\caption{East-west assymetry measured at different altitudes.}
+\caption{East-west asymmetry measured at different altitudes.}
 \label{fig:assym}
 \end{figure}
 
@@ -164,7 +164,7 @@ \subsection{Hard radiation}
 
 \section{Cosmic ray intensity}
 
-In order to perform the experiment, it is necessary to know the width of each cosmic component, especially muons. Table \ref{tab:flx} shows the muon flux as a function of relevant parameters. Figure \ref{fig:cosflux} indicates the flux of various particle productions for different altitudes. At our latitude the muon assymetry is about 1.3.
+In order to perform the experiment, it is necessary to know the width of each cosmic component, especially muons. Table \ref{tab:flx} shows the muon flux as a function of relevant parameters. Figure \ref{fig:cosflux} indicates the flux of various particle productions for different altitudes. At our latitude the muon asymmetry is about 1.3.
 
 \begin{table}
 \centering

sections/chap4.tex

@@ -186,7 +186,7 @@ \subsection{The decay of free \APmuon}
 \APmuon \rightarrow \APelectron + \Pnue + \APnum.
 \end{equation*}
 
-As a three-body decay, the positron's momentum spectrum is continious, however, due to the parity-violating nature of the weak interaction, an assymetry in the positron's angular distribution can be found as shown in Figure \ref{fig:angassy}
+As a three-body decay, the positron's momentum spectrum is continious, however, due to the parity-violating nature of the weak interaction, an asymmetry in the positron's angular distribution can be found as shown in Figure \ref{fig:angassy}
 
 \begin{figure}
 \centering

sections/chap5.tex

@@ -16,7 +16,7 @@ \section{Experimental principle}
 A muon stop is experimentally defined as an electronic signal from the coincidence circuit of \textit{PMT}1 and \textit{PMT}2 but none from that of \textit{PMT}3 and \textit{PMT}4. Indeed an unstopped muon would traverse both scintillator layers and would thus register a signal in both coincidence circuits while a stopped one would traverse the top layer and not the bottom one. In logic language, a stopped muon would thus be written as:
 
 \begin{equation}
-(\text{\textit{PMT}1} \;\text{\textbf{AND}} \; \text{\textit{PMT}2}) \; \text{\textbf{AND}} \; (\overline{\text{\textit{PMT}3}} \; \text{\textbf{AND}} \; \overline{\text{\textit{PMT}4}}).
+(\text{\textit{PMT}1} \;\text{\textbf{AND}} \; \text{\textit{PMT}2}) \; \text{\textbf{AND}} \; (\overline{\text{\textit{PMT}3} \; \text{\textbf{AND}} \; \text{\textit{PMT}4}}).
 \end{equation}
 
 Two PMTs and a coincidence circuit are used so as to rule out random events and reduce electronic background. Muons generate strong photon bursts that can be seen by both PMTs. A muon decay is defined in the same way as a muon stop meaning that when a particle is sent downwards, it isn't registered, leading to a loss in statistics.

sections/chap6.aux

@@ -11,8 +11,8 @@
 \newlabel{sub@sfig:wigl1}{{a}{31}{\relax }{figure.caption.30}{}}
 \newlabel{sfig:wigl2}{{6.1b}{31}{\relax }{figure.caption.30}{}}
 \newlabel{sub@sfig:wigl2}{{b}{31}{\relax }{figure.caption.30}{}}
-\@writefile{lof}{\contentsline {figure}{\numberline {6.1}{\ignorespaces (a) Components of the expected decay spectrum. The stripped line represents the negative muons, the solid line represents positive muons and the dotted line represents the constant background (b) Total decay (with greatly exagerated assymetry).\relax }}{31}{figure.caption.30}\protected@file@percent }
-\newlabel{fig:wigl}{{6.1}{31}{(a) Components of the expected decay spectrum. The stripped line represents the negative muons, the solid line represents positive muons and the dotted line represents the constant background (b) Total decay (with greatly exagerated assymetry).\relax }{figure.caption.30}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6.1}{\ignorespaces (a) Components of the expected decay spectrum. The stripped line represents the negative muons, the solid line represents positive muons and the dotted line represents the constant background (b) Total decay (with greatly exagerated asymmetry).\relax }}{31}{figure.caption.30}\protected@file@percent }
+\newlabel{fig:wigl}{{6.1}{31}{(a) Components of the expected decay spectrum. The stripped line represents the negative muons, the solid line represents positive muons and the dotted line represents the constant background (b) Total decay (with greatly exagerated asymmetry).\relax }{figure.caption.30}{}}
 \@writefile{toc}{\contentsline {section}{\numberline {6.4}Analysis methods}{31}{section.6.4}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\numberline {6.4.1}Optical fit}{31}{subsection.6.4.1}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\numberline {6.4.2}$\chi ^2$ minimization fit}{31}{subsection.6.4.2}\protected@file@percent }

sections/chap6.tex

@@ -64,13 +64,13 @@ \section{Expected time spectrum}
 N_{\APmuon}(t)\sim \frac{1}{\pi} \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} (1+aP\cos{\Theta}d\Theta)=...=1+aP\frac{2}{\pi}.
 \end{equation}
 
-The geometry factor is thus here about $G=\frac{2}{\pi}\simeq 0.64$. The infinite detector assumption representing the worst case, we in practice find the geometry factor to be $G=0.68\pm0.04$, the expected assymetry is then:
+The geometry factor is thus here about $G=\frac{2}{\pi}\simeq 0.64$. The infinite detector assumption representing the worst case, we in practice find the geometry factor to be $G=0.68\pm0.04$, the expected asymmetry is then:
 
 \begin{equation}
 A \doteq aPG = (0.38 \pm 0.04) \cdot (0.37\pm 0.01) \cdot (0.68 \pm 0.04) = 0.096 \pm 0.019,
 \end{equation}
 
-which is between $7.5\%$ and $11.5\%$. The proportion of positive muons is shown in Figure \ref{fig:wigl} with a greatly exagerated assymetry.
+which is between $7.5\%$ and $11.5\%$. The proportion of positive muons is shown in Figure \ref{fig:wigl} with a greatly exagerated asymmetry.
 
 \begin{figure}
 \centering
@@ -86,7 +86,7 @@ \section{Expected time spectrum}
   \caption{}
 \label{sfig:wigl2}
   \end{subfigure}
-\caption{(a) Components of the expected decay spectrum. The stripped line represents the negative muons, the solid line represents positive muons and the dotted line represents the constant background (b) Total decay (with greatly exagerated assymetry).}
+\caption{(a) Components of the expected decay spectrum. The stripped line represents the negative muons, the solid line represents positive muons and the dotted line represents the constant background (b) Total decay (with greatly exagerated asymmetry).}
 \label{fig:wigl}
 \end{figure}
 
@@ -110,7 +110,7 @@ \section{Analysis methods}
 
 \subsection{Optical fit}
 
-The optical fit is, as it name suggests, a fit made by eye. The measured data points are displayed on a graph and one can then enter parameter values that are believed to well describe the distribution. Since estimating the cosine function form the \APmuon decay spectrum is difficult, the assymetry factor $A$ is set to zero (as if no B-field was set) for optical fits. After recording the calibration of the TDC, it might be necessary to calibrate the data accordingly. For this purpose, the number of channels (each channel corresponds to \SI{50}{\nano\second} by which the measured data points need to be shifted (towards lower values) needs to be recorded in the time calibration field. This method has obvious faults: it's minimization is purely optical and thus quite unreliable, this is why one uses an automated $\chi^2$ minimization fit.
+The optical fit is, as it name suggests, a fit made by eye. The measured data points are displayed on a graph and one can then enter parameter values that are believed to well describe the distribution. Since estimating the cosine function form the \APmuon decay spectrum is difficult, the asymmetry factor $A$ is set to zero (as if no B-field was set) for optical fits. After recording the calibration of the TDC, it might be necessary to calibrate the data accordingly. For this purpose, the number of channels (each channel corresponds to \SI{50}{\nano\second} by which the measured data points need to be shifted (towards lower values) needs to be recorded in the time calibration field. This method has obvious faults: it's minimization is purely optical and thus quite unreliable, this is why one uses an automated $\chi^2$ minimization fit.
 
 \subsection{$\chi^2$ minimization fit}