%---------------------------------------------------------------------------------
%       Appendix A: Software programs utilized in research
%---------------------------------------------------------------------------------
\chapter{Important Programs} \label{software}

 In order to perform crucial calculations and predict what we may see we have to develop our own code and methods of both 
 creating and analyzing the data we need in order to make reliable predictions some of the tools we use are: 
 %{\color{red} ref: each code listed below}
 %
 \begin{itemize}
         %
     \item \textbf{MadGraph} \cite{Alwall2014}: a software sweet that allows us to run detector simulations on physical decay processes 
         involving most common models with features that allow for the import of your own models.
         %
     \item \textbf{ROOT}: a data analysis framework developed and maintained by CERN that allow us to analyze data and 
         the detector simulations produced by MadGraph in ways similar to the experimentalists.
         %
     \item \textbf{HIGLU} \cite{Spira1995}: a piece of software specifically designed to numerically evaluate leading order (LO), next to 
         leading order (NLO), and even next-to-next-to leading order (NNLO) $gg \to \phi^0$ production so we can calculate 
         appropriate $K$-factors.
         %
     \item \textbf{2HDMC} \cite{Eriksson2009}: software designed to analyze Higgs decays under several different BSM models, 
         including the 2HDM. This software allows us to calculate total width and branching ratio information for Higgs bosons 
         under a broad phase-space region.
         %
     \item \textbf{MCFM} \cite{Boughezal2016}: software developed at Fermilab to calculate LO, NLO, and NNLO information for several common SM 
         processes such as $WW$ or $t\bar{t}$ production with various decay modes. This software is used to calculate 
         $k$-factors for many of our background processes.
         %
     \item \textbf{VEGAS}: is a linux/unix based numerical integration routine that utilizes important sampling to map out 
         abrupt features of your decay processes so that we can produce realistic collider data for analysis.
         %
     \item \textbf{FeynRules} \cite{Alloul2013}: a Mathematica package used to create model files to use with MadGraph that includes the 
         ability to do process level coupling verification and will check itself for invariance and Hermiticity.
         %
     \item \textbf{FORM}: software developed to calculate traces like the one shown in \Cref{loopTrace} and apply tensor 
         reduction techniques for more reliable simplification.
         %
     \item \textbf{Fortran Code}: self developed Fortran programs and analysis were created and implemented to evaluate the 
         complex integrals involved in cross section calculations, apply necessary selection cuts, construct the kinematics 
         of the process, and generate histogram data for analysis.
         %
 \end{itemize}
 %
 \begin{table}[]
    \centering
     \caption[K-factors calculated from higlu for the production of the light, heavy, and pseudoscalar
     Higgs bosons through glun-gluon fusion via a heavy quark loop (top and bottom)]{K-factors calculated 
     from higlu for the production of the light, heavy, and pseudoscalar Higgs bosons through glun-gluon 
     fusion via a heavy quark loop (top and bottom). For the top loop, these are next-to-next-to leading 
     order (NLLO) to leading order (LO) ratios and for the bottom loop they are next-to leading order of 
     LO ratios.}
    \label{kFac-table}
    \begin{tabular}{|c|c|c|}
    \hline
    $M_{H}$ GeV & top loop kFactor (formula) & bottom loop kFactor (formula) \\ \hline
    125         & 1.92443                    & 1.01226                       \\ \hline
    150         & 1.93552                    & 1.03564                       \\ \hline
    175         & 1.94828                    & 1.0554                        \\ \hline
    200         & 1.96019                    & 1.07253                       \\ \hline
    225         & 1.9708                     & 1.08763                       \\ \hline
    250         & 1.98166                    & 1.10114                       \\ \hline
    275         & 1.99637                    & 1.11336                       \\ \hline
    300         & 2.02058                    & 1.12451                       \\ \hline
    325         & 2.06195                    & 1.13478                       \\ \hline
    350         & 2.13018                    & 1.14428                       \\ \hline
    375         & 1.94282                    & 1.15313                       \\ \hline
    400         & 1.90573                    & 1.1614                        \\ \hline
    425         & 1.88406                    & 1.16918                       \\ \hline
    450         & 1.8687                     & 1.1765                        \\ \hline
    475         & 1.85679                    & 1.18344                       \\ \hline
    500         & 1.84705                    & 1.19001                       \\ \hline
    525         & 1.83883                    & 1.19627                       \\ \hline
    550         & 1.8317                     & 1.20223                       \\ \hline
    575         & 1.82542                    & 1.20793                       \\ \hline
    600         & 1.81979                    & 1.21339                       \\ \hline
    625         & 1.81471                    & 1.21863                       \\ \hline
    650         & 1.81007                    & 1.22365                       \\ \hline
    675         & 1.8058                     & 1.22849                       \\ \hline
    700         & 1.80184                    & 1.23316                       \\ \hline
    725         & 1.79816                    & 1.23766                       \\ \hline
    750         & 1.79472                    & 1.242                         \\ \hline
    775         & 1.79148                    & 1.24621                       \\ \hline
    800         & 1.78844                    & 1.25028                       \\ \hline
    825         & 1.78555                    & 1.25422                       \\ \hline
    850         & 1.78282                    & 1.25805                       \\ \hline
    875         & 1.78021                    & 1.26177                       \\ \hline
    900         & 1.77773                    & 1.26538                       \\ \hline
    925         & 1.77536                    & 1.26889                       \\ \hline
    950         & 1.77309                    & 1.27231                       \\ \hline
    975         & 1.77091                    & 1.27564                       \\ \hline
    1000        & 1.76882                    & 1.27889                       \\ \hline
    \end{tabular}
 \end{table}
