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====== Proton-proton collisions with a hard process ======

Full code to produce a {{latex:feynman:proton-proton_collisions_hard_process.pdf|multipage PDF}} with the [[latex:feynman#proton-proton_collisions_with_a_hard_process|standalone diagrams]] depicting diffractive proton-proton collisions:

<code latex proton-proton_collisions_hard.tex>
% !TEX program = pdflatexmk
% !TEX parameter = -shell-escape
% Author: Izaak Neutelings (February 2023)
\documentclass[10pt,border=2pt,multi=page,crop]{standalone}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{feynmp-auto}

\def\protons{
  % proton 1
  \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{ip}
  \fmf{phantom}{ip,vp}
  \fmfi{fermion,l=$p_1$,l.s=left,l.d=8}
                {vpath (__ip,__vp) scaled 1.01 shifted (-2.4, 6)}
  \fmfi{fermion}{vpath (__ip,__vp) scaled 1.01 shifted (-2.4, 0)}
  \fmfi{fermion}{vpath (__ip,__vp) scaled 1.01 shifted (-2.4,-6)}
  % proton 2
  \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{iq}
  \fmf{phantom}{iq,vq}
  \fmfi{fermion}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4, 6)}
  \fmfi{fermion}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4, 0)}
  \fmfi{fermion,l=$p_2$,l.s=right,l.d=8}
                {vpath (__iq,__vq) scaled 1.01 shifted (-2.4,-6)}
}
\def\debris{
  % X 2
  \fmfshift{25 left}{x1}
  \fmfshift{20 left}{x2,x3}
  \fmf{phantom}{vp,x1} % to help \fmfi
  \fmf{phantom}{vp,x2} % to help \fmfi
  \fmf{phantom}{vp,x3} % to help \fmfi
  \fmfi{fermion}{vpath (__vp,__x1) scaled 1.0 shifted ( 0.0, 2.0)}
  \fmfi{fermion}{vpath (__vp,__x2) scaled 1.0 shifted ( 0.0, 0.0)}
  \fmfi{fermion}{vpath (__vp,__x3) scaled 1.0 shifted ( 0.0,-2.0)}
  \fmfblob{25}{vp}
  % X 2
  \fmfshift{25 left}{y1}
  \fmfshift{20 left}{y2,y3}
  \fmf{phantom}{vq,y1} % to help \fmfi
  \fmf{phantom}{vq,y2} % to help \fmfi
  \fmf{phantom}{vq,y3} % to help \fmfi
  \fmfi{fermion}{vpath (__vq,__y1) scaled 1.0 shifted ( 0.0,-2.0)}
  \fmfi{fermion}{vpath (__vq,__y2) scaled 1.0 shifted ( 0.0, 0.0)}
  \fmfi{fermion}{vpath (__vq,__y3) scaled 1.0 shifted ( 0.0, 2.0)}
  \fmfblob{25}{vq}
}

\begin{document}
\large

% PP COLLISION - Generic hard process
\begin{page}
\fmfframe(10,6)(-6,6){ % padding (LTRB)
\begin{fmffile}{feynmp-pp-hard-generic}
  \begin{fmfgraph*}(160,160)
    \fmfleft{i1,iq,i2,ip,i3}
    \fmfright{y1,y2,y3,o1,o2,o3,o4,o5,x3,x2,x1}
    \fmfset{arrow_len}{10}
    % skeleton
    \fmf{phantom,tension=0.50}{vq,vp}
    \fmf{phantom}{ip,vp,x1}
    \fmf{phantom}{iq,vq,y1}
    \fmffreeze
    % parton
    \fmf{fermion,tension=2,label=$x_1p_1$,label.side=right}{vp,v}
    \fmf{fermion,tension=2,label=$x_2p_2$,label.side=left}{vq,v}
    % hard interaction
    \fmf{phantom,tension=1}{v,o2} % to help \fmfi
    \fmf{phantom,tension=1}{v,o3} % to help \fmfi
    \fmf{phantom,tension=1}{v,o4} % to help \fmfi
    \fmffreeze
    \fmfi{fermion}{vpath (__v,__o2) scaled 1.01 shifted ( 0,-2)}
    \fmfi{fermion}{vpath (__v,__o3) scaled 1.01 shifted ( 0, 0)}
    \fmfi{fermion}{vpath (__v,__o4) scaled 1.01 shifted ( 0, 2)}
    \fmfblob{20}{v}
    % protons
    \protons
    % debris
    \debris
  \end{fmfgraph*}
\end{fmffile}
}
\end{page}

% PP COLLISION - Drell-Yan
\begin{page}
\fmfframe(10,6)(27,6){ % padding (LTRB)
\begin{fmffile}{feynmp-pp-hard-drell-yan}
  \begin{fmfgraph*}(160,160)
    \fmfleft{i1,iq,i2,ip,i3}
    \fmfright{y1,y2,y3,o1,f1,o2,o3,o4,f2,o5,x3,x2,x1}
    \fmfset{arrow_len}{10}
    % skeleton
    \fmf{phantom,tension=0.48}{vq,vp}
    \fmf{phantom}{ip,vp,x1}
    \fmf{phantom}{iq,vq,y1}
    \fmffreeze
    % parton
    \fmfv{l=$x_1p_1$,l.a=-90,l.d=22}{vp} % cheat: actually a line label
    \fmfv{l=$x_2p_2$,l.a=90,l.d=22}{vq} % cheat: actually a line label
    \fmf{fermion,tension=1.6}{vp,v}
    \fmf{fermion,tension=1.6}{v,vq}
    % hard process
    \fmfshift{20 right}{f1,f2}
    \fmfv{l.a=-25,l.d=3,l=$\ell^+$}{f1}
    \fmfv{l.a=25,l.d=5,l=$\ell^-$}{f2}
    \fmf{boson,tension=2,label=$\text{Z}^0/\gamma^*$,label.side=left}{v,vf}
    \fmf{fermion,tension=2}{f1,vf,f2}
    % protons
    \protons
    % debris
    \debris
  \end{fmfgraph*}
\end{fmffile}
}
\end{page}

% PP COLLISION - Higgs production through gluon-fusion
\begin{page}
\fmfframe(10,6)(27,6){ % padding (LTRB)
\begin{fmffile}{feynmp-pp-hard-higgs}
  \begin{fmfgraph*}(160,160)
    \fmfleft{i1,iq,i2,ip,i3}
    \fmfright{y1,y2,y3,o1,o2,o3,o4,o5,x3,x2,x1}
    \fmfset{arrow_len}{10}
    \fmfset{curly_len}{8}
    % skeleton
    \fmf{phantom,tension=0.48}{vq,vp}
    \fmf{phantom}{ip,vp,x1}
    \fmf{phantom}{iq,vq,y1}
    \fmffreeze
    % parton
    \fmf{gluon,tension=1.4,label=$x_1p_1$,label.side=left}{v1,vp}
    \fmf{gluon,tension=1.4,label=$x_2p_2$,label.side=left}{vq,v2}
    % hard process
    \fmfshift{20 right}{o3}
    \fmfv{l=H}{o3}
    \fmf{fermion,tension=0.3,arrow.size=2mm}{v1,v2}
    \fmf{fermion,tension=2.0}{v1,vh,v2}
    \fmf{dashes,tension=2.5}{vh,o3}
    % protons
    \protons
    % debris
    \debris
  \end{fmfgraph*}
\end{fmffile}
}
\end{page}

\end{document}
</code>
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