\section{The Standard Model}
\label{sect:standard_model}

The standard model \index{standard model|(} of modern particle physics developed in the 1970's attempts to describe on the most basic level, the particle structure of matter and its interactions via the fundamental forces.  Within the standard model all matter consists of a finite irreducible set of spin-1/2 particles denoted as fermions \index{fermion} that interact via the exchange of integral spin bosons\index{boson}.  The bosons in the theory act as the force carriers for the electro-weak and strong nuclear forces.  The fermions are subdivided into the classifications of leptons and quarks \index{lepton} \index{quark} based on their electric charge and their ability to interact with the strong nuclear force.

Leptons are observed to exist with integral or zero electric charge as defined in units of the charge of the electron.  There are three flavors of leptons forming a progressive mass hierarchy in a doublet \index{lepton!flavor!doublets} arranged structure whereby each charged lepton is associated with a light, neutrally charged particle denoted as a \index{neutrino} \index{lepton!neutrino|see{neutrino}} neutrino,
\begin{equation}
\label{eqn:lepton_flavor_doublets}
\begin{pmatrix} e       \\ \nu_e      \end{pmatrix} \qquad
\begin{pmatrix} \mu     \\ \nu_{\mu}  \end{pmatrix} \qquad
\begin{pmatrix} \tau    \\ \nu_{\tau} \end{pmatrix}
\end{equation}
%
The three leptons, the \index{electron} \index{lepton!electron|see{electron}} electron, \index{muon} \index{lepton!muon|see{muon}} muon, and \index{tau} \index{lepton!tau|see{tau}} tau each with negative charge are taken as the base particles states while their charge conjugates the $e^{+}$, $\mu^{+}$, and $\tau^{+}$ are denoted as their anti-particles states.  The neutrinos are taken to be essentially massless, grouped into three generations corresponding to their associated leptons.  Within the standard model there exists no mechanism which in a direct fashion provides for horizontal mixing between the \index{lepton!family} \index{lepton!horizonal mixing} lepton families; as a result members of each family are assigned a \index{lepton!lepton number} quantum number $L_{\ell}$ corresponding to the lepton flavor of the particle.

%%%%%%%%%%%%%%%%%%%%%%%%
% Begin Table Block
\begin{table}
\begin{center}
\begin{tabular}{|c|c|c| c c c|}
\hline
Lepton        & Mass           & Charge & $L_{e}$ & $L_{\mu}$ & $L_{\tau}$ \\
\hline
$e^{-}$      & $0.51 \mbox{ MeV}$     & $-1 e$ & 1       & 0         & 0 \\
$\mu^{-}$    & $105.65 \mbox{ MeV}$   & $-1 e$ & 0       & 1         & 0 \\
$\tau^{-}$   & $1777.03 \mbox{ MeV}$  & $-1 e$ & 0       & 0         & 1 \\
\hline
$\nu_{e}$    & $< 3 \mbox{ eV}$       & $0$    & 1       & 0         & 0 \\
$\nu_{\mu}$  & $< 0.19 \mbox{ MeV}$   & $0$    & 0       & 1         & 0 \\
$\nu_{\tau}$ & $< 18.2 \mbox{ MeV}$   & $0$    & 0       & 0         & 1 \\
\hline
\end{tabular}
\caption{Lepton Properties}
\label{table:lepton_properties}
\end{center}
\end{table}
% End Table Block
%%%%%%%%%%%%%%%%%%%%%%%%
The distinguishing feature of the leptons is that they do not experience a direct interaction with the strong nuclear force.  All lepton interactions occur through primitive \index{electro-weak interactions} electro-weak interaction couplings, shown in Fig.~\ref{fig:lepton_electro_weak}, and as such are a sensitive probe into the structure of the \index{weak current} weak currents.
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Begin Figure Block
\begin{figure}
\begin{center}
\input{lepton_electro_weak_1_psfrags.tex}
\subfigure[Electromagnetic Interaction]{%
\includegraphics*[width=\textwidth/3]{lepton_electro_weak_1.eps}}
\subfigure[Weak Neutral Current]{%
\input{lepton_electro_weak_2_psfrags.tex}
\includegraphics*[width=\textwidth/3]{lepton_electro_weak_2.eps}}
\subfigure[Weak Charged Current]{%
\input{lepton_electro_weak_3_psfrags.tex}
\includegraphics*[width=\textwidth/3]{lepton_electro_weak_3.eps}}
\caption{Primitive electro-weak lepton interactions}
\label{fig:lepton_electro_weak}
\end{center}
\end{figure}
% End Figure Block
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Omit{
all matter and interactions of matter with its surroundings can be broken down into a finite system of fundamental particles interacting with a set of four fundamental forces.  The standard model of modern physics asserts that all mater consists of irreducible set of fundamental spin-1/2 particles denoted as fermions.  The fermions interact through the exchange of particles of integral spin that act as the force carriers for the fundamental forces and are denoted as bosons.}

In contrast to leptons, quarks are distinguished by their interactions with the strong nuclear force and their fractional electric charge.  Strong force \index{strong force} \index{quark!confinement} binding and confinement lead quarks to form the fundamental substructure for all hadronic matter, either in the form of a color neutral three quark bound states that form the common baryons such as the proton and neutron, or in quark-antiquark bound state mesons such as the $\pi,K,\eta$, and $\rho$.  Free quarks are not accessible due to the requirements of color neutrality and strong force confinement at low energies.  Similar to the leptons there exists a generational hierarchy of distinct quark flavor doublets \index{quark!flavor!doublets} based on the masses of each quark and their associated quantum properties. Each generation consists of two quarks each with fractional electric charges equal to $-\frac{1}{3}$ and $\frac{2}{3}$ the charge magnitude of the electron.  There exists evidence for three such quark generations whose associated quarks we label as \textit{up}, \textit{down}, \textit{charm}, \textit{strange}, \textit{top}, \textit{bottom}.  They are arranged in flavors doublets as: \index{quark!up|see{up quark}} \index{quark!down|see{down quark}} \index{quark!strange|see{strange quark}} \index{quark!charm|see{charm quark}} \index{quark!top|see{top quark}} \index{quark!bottom|see(bottom quark)} \index{up quark} \index{down quark} \index{strange quark} \index{charm quark} \index{top quark} \index{bottom quark}
\begin{equation}
\label{eqn:quark_flavor_doublets}
\begin{pmatrix} u \\ d \end{pmatrix} \qquad
\begin{pmatrix} c \\ s \end{pmatrix} \qquad
\begin{pmatrix} t \\ b \end{pmatrix}
\end{equation}
The mass hierarchy of the quark doublets is clear from Table~\ref{table:quark_properties}.  As with the leptons, each quark flavor has a corresponding anti-particle state leading to a total of 12 distinct particles.  These quarks have strong, weak, and electro-magnetic interactions as shown in Fig.~\ref{fig:quark_interactions}.  Unlike the lepton sector the weak interaction vertex can mix quark \index{quark!mixing} flavors between generations leading to $s \rightarrow u$ like processes arising via weak currents. \index{weak current} 
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Begin Figure Block
\begin{figure}
\begin{center}
\subfigure[Strong Color Exchange]{%
\input{quark_strong_psfrags.tex}
\includegraphics*[width=\textwidth/3]{quark_strong.eps}}
\subfigure[Electro-magnetic]{%
\input{quark_em_psfrags.tex}
\includegraphics*[width=\textwidth/3]{quark_em.eps}}
\subfigure[Weak Charged Current]{%
\label{fig:quark_interactions_weak_charged}
\input{quark_weak_1_psfrags.tex}
\includegraphics*[width=\textwidth/3]{quark_weak_1.eps}}
\subfigure[Weak Neutral Current]{%
\label{fig:quark_interactions_weak_neutral}
\input{quark_weak_2_psfrags.tex}
\includegraphics*[width=\textwidth/3]{quark_weak_2.eps}}
\caption{Primitive strong, E\&M, and weak quark interactions}
\label{fig:quark_interactions}
\end{center}
\end{figure}
% End Figure Block
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
% Begin Table Block
\begin{table}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Quark & Mass & Charge & Properties \\
\hline
u & $1-5 \mbox{ MeV/c}^2$         & $\phantom{-}\frac{2}{3} e$  & $I_{z} = \frac{1}{2}$ \\
d & $3-9 \mbox{ MeV/c}^2$         & $-\frac{1}{3} e$ & $I_{z} = -\frac{1}{2}$ \\
c & $1.15-1.35 \mbox{ GeV/c}^2$   & $\phantom{-}\frac{2}{3} e$  & Charm = +1 \\
s & $75-170 \mbox{ MeV/c}^2$      & $-\frac{1}{3} e$ & Strangeness = -1 \\
t & $\approx 174 \mbox{ GeV/c}^2$ & $\phantom{-}\frac{2}{3} e$  & Top = +1 \\
b & $4.0-4.4 \mbox{ GeV/c}^2$     & $-\frac{1}{3} e$ & Bottom = -1 \\
\hline
\end{tabular}
\caption{Quark Properties}
\label{table:quark_properties}
\end{center}
\end{table}
% End Table Block
%%%%%%%%%%%%%%%%%%%%%%%%
\index{standard model|)}

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