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latex:feynman [2018/11/10 15:29] – [Leptoquark] iwnlatex:feynman [2023/06/06 18:16] (current) – [Simple example: electron - muon scattering] iwn
Line 11: Line 11:
   * [[https://twiki.cern.ch/twiki/bin/viewauth/CMS/SUSYSimplifiedModelDiagrams|ready-made SUSY diagrams (images)]], with the [[https://github.com/CMS-SUS-XPAG/SUSYDiagrams|code (GitHub)]];   * [[https://twiki.cern.ch/twiki/bin/viewauth/CMS/SUSYSimplifiedModelDiagrams|ready-made SUSY diagrams (images)]], with the [[https://github.com/CMS-SUS-XPAG/SUSYDiagrams|code (GitHub)]];
   * [[http://osksn2.hep.sci.osaka-u.ac.jp/~taku/osx/feynmp_latexit.html|how to set up feynMP in LaTeXiT on Mac OS X]] to make Feynman diagrams as standalone images (strongly recommended);   * [[http://osksn2.hep.sci.osaka-u.ac.jp/~taku/osx/feynmp_latexit.html|how to set up feynMP in LaTeXiT on Mac OS X]] to make Feynman diagrams as standalone images (strongly recommended);
 +  * [[https://www.overleaf.com/learn/latex/Feynman_diagrams#Other_packages_for_drawing_Feynman_diagrams|Excelent tutorial by Overleaf]];
   * [[latex:feynman_file|macro for typesetting Feynman graphs in a LaTeX file]];   * [[latex:feynman_file|macro for typesetting Feynman graphs in a LaTeX file]];
-  * [[latex:feynman_equation_file|using Feynman diagrams in equation in a LaTeX text]]. +  * [[latex:feynman_equation_file|using Feynman diagrams in equation in a LaTeX text]]; 
- +  * [[latex:tikz|more general TikZ diagrams]].
  
  ===== Simple example: electron - muon scattering =====  ===== Simple example: electron - muon scattering =====
Line 62: Line 62:
 Checkout the [[http://www.pd.infn.it/TeX/doc/latex/feynmf/manual.pdf|feynMF manual]] for all the available line styles, line options, vertex options and all their parameters. Checkout the [[http://www.pd.infn.it/TeX/doc/latex/feynmf/manual.pdf|feynMF manual]] for all the available line styles, line options, vertex options and all their parameters.
  
-<WRAP group><WRAP half column 55% centeralign> +<WRAP group><WRAP half column 60% centeralign> 
-**Table 1**: Available line styles  of ''\fmf''+\\ \\ \\ \\ 
-{{ latex:fmfmp_line_styles_table.png ? 420 }} +**Table 1**: Available line styles  for ''\fmf''
-</WRAP><WRAP half column 37% centeralign > +{{ latex:fmfmp_line_styles_table.png ? 500 }} 
-**Table 2**: Available line options of ''\fmf''+</WRAP><WRAP half column 36% centeralign > 
-{{ latex:fmfmp_line_options_table.png ? 270 }}+**Table 2**: Available style parameters for ''\fmf''
 +{{ latex:fmfmp_line_styles_table2.png ? 600 }} 
 +\\ 
 +**Table 3**: Available line options for ''\fmf''
 +{{ latex:fmfmp_line_options_table.png ? 600 }}
 \\ \\
-**Table 3**: Available vertex options of ''\fmfv''+**Table 4**: Available vertex options for ''\fmfv''
-{{ latex:fmfmp_vertex_options_table.png ? 300 }}+{{ latex:fmfmp_vertex_options_table.png ? 600 }}
 </WRAP></WRAP> </WRAP></WRAP>
  
Line 298: Line 302:
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
-\\ \\ 
  
  
  
 + ===== Bent lines and loop ===== 
  
 +Lines can be bent by simply adding ''right'' or ''left''. Here is for example the one-loop correction to the electron-photon vertex to compute the anomalous magnetic momentum:
 +
 +<WRAP group><WRAP half column lo 55%>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(70,100)
 +    \fmfleft{f2,f1}
 +    \fmfright{p} % outgoing photon
 +    \fmf{boson,l.s=left,t=0.8}{p,v}
 +    \fmf{fermion}{f2,v1}
 +    \fmf{plain,t=1.5}{v1,v,v2}
 +    \fmf{fermion}{v2,f1}
 +    \fmfv{l.a=165,l=e$^-$}{f1} % outcoming electron
 +    \fmfv{l.a=-165,l=e$^-$}{f2} % incoming electron
 +    \fmffreeze
 +    \fmf{boson,left}{v1,v2} % bend photon line to the left
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column lo 40%>
 +{{ latex:feynman:electron_vertex_loop.png ? 210 }}
 +</WRAP></WRAP>
 +
 +More examples can be found below in the sections on [[#higgs_mass_loop_corrections_with_susy_and_vlqs|Higgs mass corrections]] and [[#penguin_diagrams|Penguin diagrams]].
 +\\ \\
  ====== Intermediate mode: How to use MetaPost ======  ====== Intermediate mode: How to use MetaPost ======
  
Line 505: Line 535:
  
 Some Feynman diagrams contributing to top quark pair production via gluon-gluon fusion: Some Feynman diagrams contributing to top quark pair production via gluon-gluon fusion:
 +
 +Full code for a {{latex:feynman:ttbar.pdf|multipage PDF}} including all figures below can be found [[latex:feynman:ttbar|here]].
  
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
Line 512: Line 544:
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
 +    % main
 +    \fmf{fermion}{i1,v1,i2}
     \fmf{fermion}{o2,v2,o1}     \fmf{fermion}{o2,v2,o1}
-    \fmf{gluon}{i2,v1,i1} +    \fmf{gluon,label=$g$,label.side=right,label.dist=10}{v2,v1} 
-    \fmf{gluon,label=$g$}{v1,v2+    % labels 
-    \fmflabel{$g$}{i1} +    \fmflabel{$q$}{i1} 
-    \fmflabel{$g$}{i2}+    \fmflabel{$\overline{q}$}{i2}
     \fmflabel{$\overline{\text{t}}$}{o2}     \fmflabel{$\overline{\text{t}}$}{o2}
     \fmflabel{t}{o1}     \fmflabel{t}{o1}
Line 524: Line 558:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\
-{{ latex:ggttbar1.png ? 220 }}+{{ latex:feynman:qqttbar.png ? 220 }}
 \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 532: Line 566:
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
   \begin{fmfgraph*}(110,60)   \begin{fmfgraph*}(110,60)
-    \fmfleft{i2,i1}  +    \fmfleft{i2,i1} 
-    \fmfright{o2,o1}  +    \fmfright{o2,o1} 
-    \fmf{gluon}{v1,i1}  +    \fmfshift{2 left}{i1} 
-    \fmf{fermion}{v1,o1} +    \fmf{fermion}{o2,v2,o1} 
-    \fmf{gluon}{i2,v2+    \fmf{gluon}{v1,i1
-    \fmf{fermion}{o2,v2+    \fmf{gluon}{v1,i2
-    \fmf{fermion,label=t}{v2,v1+    \fmf{gluon,label=$g$}{v1,v2
-    \fmflabel{$g$}{i2} +    % labels 
-    \fmflabel{$g$}{i1}+    \fmfv{l.d=4,l=$g$}{i1
 +    \fmfv{l.d=6,l=$g$}{i2} 
 +    \fmflabel{$\overline{\text{t}}$}{o2}
     \fmflabel{t}{o1}     \fmflabel{t}{o1}
-    \fmflabel{$\overline{\text{t}}$}{o2} 
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 548: Line 583:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\
-{{ latex:ggttbar2.png ? 220 }}+{{ latex:feynman:ggttbar1.png ? 220 }}
 \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 558: Line 593:
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
-    \fmf{fermion}{i1,v1,i2} +    % main 
-    \fmf{fermion}{o2,v2,o1+    \fmf{gluon}{v1,i1} 
-    \fmf{gluon,label=$g$,label.side=right,label.dist=10}{v2,v1} +    \fmf{fermion}{v1,o1} 
-    \fmflabel{$q$}{i1+    \fmf{gluon}{i2,v2
-    \fmflabel{$\overline{q}$}{i2+    \fmf{fermion}{o2,v2} 
-    \fmflabel{$\overline{\text{t}}$}{o2+    \fmf{fermion,label=t}{v2,v1} 
-    \fmflabel{t}{o1}+    % labels 
 +    \fmflabel{$g$}{i2
 +    \fmflabel{$g$}{i1} 
 +    \fmfv{l.d=7,l.a=22,l=t}{o1
 +    \fmfv{l.d=7,l.a=-20,l=$\overline{\text{t}}$}{o2}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 570: Line 609:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\
-{{ latex:qqttbar.png ? 220 }}+{{ latex:feynman:ggttbar3.png ? 220 }}
 \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
  
- +With radiated quarks or gluons that will form hard jets:
- +
-With jets:+
  
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
Line 582: Line 619:
 \large \large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(125,75)+  \begin{fmfgraph*}(120,70)
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
     \fmftop{t}     \fmftop{t}
 +    \fmfshift{5 up}{t}
 +    % skeleton
     \fmf{phantom}{i1,v1,i2}     \fmf{phantom}{i1,v1,i2}
     \fmf{phantom}{o1,v2,o2}     \fmf{phantom}{o1,v2,o2}
     \fmf{phantom}{v1,v2}     \fmf{phantom}{v1,v2}
     \fmffreeze     \fmffreeze
-    \fmfshift{5 left}{i1} +    % main 
-    \fmfshift{5 up}{i1,t+    \fmf{fermion}{i1,g
-    \fmf{gluon,tension=0.8}{g,i1+    \fmf{plain,tension=2.8}{g,v1
-    \fmf{fermion}{v1,g+    \fmf{fermion}{v1,i2
-    \fmf{gluon}{v1,i2} +    \fmf{gluon,tension=0}{t,g}
-    \fmf{fermion,tension=0}{g,t}+
     \fmf{gluon}{v1,v2}     \fmf{gluon}{v1,v2}
     \fmf{fermion}{o2,v2,o1}     \fmf{fermion}{o2,v2,o1}
-    \fmflabel{$g$}{i1} +    % labels 
-    \fmflabel{$g$}{i2} +    \fmflabel{$q$}{i1} 
-    \fmflabel{$\overline{\text{t}}$}{o2} +    \fmflabel{$\overline{q}$}{i2
-    \fmflabel{t}{o1}+    \fmfv{l.d=5,l.a=25,l=$g$}{t
 +    \fmflabel{$\bar{\text{t}}$}{o2} 
 +    \fmflabel{$\text{t}$}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 607: Line 647:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\ \\ \\
-{{ latex:ggttbar_quark.png ? 220 }}+{{ latex:feynman:qqttbar_gluon.png ? 220 }}
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
- 
  
  
Line 617: Line 656:
 \large \large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(125,75)+  \begin{fmfgraph*}(120,75)
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
     \fmftop{t}     \fmftop{t}
 +    \fmfshift{4 left}{i1}
 +    \fmfshift{2 left}{i2}
 +    \fmfshift{5 up}{t}
 +    % skeleton
     \fmf{phantom}{i1,v1,i2}     \fmf{phantom}{i1,v1,i2}
     \fmf{phantom}{o1,v2,o2}     \fmf{phantom}{o1,v2,o2}
-    \fmf{phantom}{v1,v2}+    \fmf{phantom,tension=1.2}{v1,v2}
     \fmffreeze     \fmffreeze
-    %\fmfshift{5 left}{i1} +    % main
-    %\fmfshift{5 up}{i1,t}+
     \fmf{gluon,tension=0.8}{g,i1}     \fmf{gluon,tension=0.8}{g,i1}
     \fmf{fermion}{v1,g}     \fmf{fermion}{v1,g}
-    \fmf{fermion}{i2,v1}+    \fmf{gluon}{v1,i2}
     \fmf{fermion,tension=0}{g,t}     \fmf{fermion,tension=0}{g,t}
     \fmf{gluon}{v1,v2}     \fmf{gluon}{v1,v2}
     \fmf{fermion}{o2,v2,o1}     \fmf{fermion}{o2,v2,o1}
-    \fmflabel{$g$}{i1} +    % labels 
-    \fmflabel{$q$}{i2} +    \fmfv{l.d=4,l=$g$}{i1} 
-    \fmflabel{$\overline{\text{t}}$}{o2} +    \fmfv{l.d=6,l=$g$}{i2
-    \fmflabel{t}{o1}+    \fmfv{l.d=5,l.a=25,l=$q$}{t
 +    \fmflabel{$\bar{\text{t}}$}{o2} 
 +    \fmflabel{$\text{t}$}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 642: Line 686:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\ \\ \\
-{{ latex:gqttbar_quark.png ? 220 }}+{{ latex:feynman:ggttbar_quark.png ? 220 }}
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 652: Line 696:
 \large \large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(120,70)+  \begin{fmfgraph*}(120,75)
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
     \fmftop{t}     \fmftop{t}
 +    \fmfshift{4 left}{i1}
 +    \fmfshift{2 left}{i2}
 +    \fmfshift{5 up}{t}
 +    % skeleton
     \fmf{phantom}{i1,v1,i2}     \fmf{phantom}{i1,v1,i2}
     \fmf{phantom}{o1,v2,o2}     \fmf{phantom}{o1,v2,o2}
-    \fmf{phantom}{v1,v2}+    \fmf{phantom,tension=1.2}{v1,v2}
     \fmffreeze     \fmffreeze
-    \fmf{fermion}{i1,g} +    % main 
-    \fmf{plain,tension=2.8}{g,v1+    \fmf{gluon,tension=0.8}{g,i1
-    \fmf{fermion}{v1,i2} +    \fmf{fermion}{v1,g} 
-    \fmf{gluon,tension=0}{t,g}+    \fmf{fermion}{i2,v1
 +    \fmf{fermion,tension=0}{g,t}
     \fmf{gluon}{v1,v2}     \fmf{gluon}{v1,v2}
     \fmf{fermion}{o2,v2,o1}     \fmf{fermion}{o2,v2,o1}
-    \fmflabel{$q$}{i1} +    % labels 
-    \fmflabel{$\overline{q}$}{i2+    \fmfv{l.d=4,l=$g$}{i1} 
-    \fmflabel{$\overline{\text{t}}$}{o2} +    \fmfv{l.d=6,l=$q$}{i2} 
-    \fmflabel{t}{o1}+    \fmfv{l.d=5,l.a=25,l=$q$}{t
 +    \fmflabel{$\bar{\text{t}}$}{o2} 
 +    \fmflabel{$\text{t}$}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 675: Line 726:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\ \\ \\
-{{ latex:gqttbar_quark.png ? 220 }}+{{ latex:feynman:gqttbar_quark.png ? 220 }}
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 699: Line 750:
     \fmf{boson,label=$\text{Z}/\gamma^*$,label.side=right}{v1,v2}     \fmf{boson,label=$\text{Z}/\gamma^*$,label.side=right}{v1,v2}
     \fmflabel{$q$}{i1}     \fmflabel{$q$}{i1}
-    \fmflabel{$q'$}{i2} +    \fmflabel{$\overline{q}$}{i2} 
-    \fmflabel{$\bar{\ell}$}{o2} +    \fmflabel{$\ell^+$}{o2} 
-    \fmflabel{$\ell$}{o1}+    \fmflabel{$\ell^-$}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 736: Line 787:
     \fmflabel{$g$}{i1}     \fmflabel{$g$}{i1}
     \fmflabel{$q$}{i2}     \fmflabel{$q$}{i2}
-    \fmflabel{$q'$}{t} +    \fmfv{l.a=25,l=$q$}{t} 
-    \fmflabel{$\bar{\ell}$}{o2} +    \fmflabel{$\ell^+$}{o2} 
-    \fmflabel{$\ell$}{o1}+    \fmflabel{$\ell^-$}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 768: Line 819:
     \fmflabel{$q$}{i1}     \fmflabel{$q$}{i1}
     \fmflabel{$q'$}{i2}     \fmflabel{$q'$}{i2}
-    \fmflabel{$\bar{\ell}$}{o2} +    \fmflabel{$\ell^+$}{o2} 
-    \fmflabel{$\ell$}{o1}+    \fmflabel{$\ell^-$}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 1629: Line 1680:
     \fmf{fermion}{v,q}     \fmf{fermion}{v,q}
     \fmf{fermion}{v,l}     \fmf{fermion}{v,l}
-    \fmfv{l=$\text{LQ}_3$}{LQ} +    \fmfv{l=LQ}{LQ} 
-    \fmfv{l.a=-28,l=$\text{b}$}{q} +    \fmfv{l.a=-28,l=$q$}{q} 
-    \fmfv{l.a=28,l=$\tau$}{l}+    \fmfv{l.a=28,l=$\ell$}{l}
     \fmfdot{v}     \fmfdot{v}
-    \fmfv{l.a=115,l=\large$\lambda_{\tau\text{b}}$}{v}+    \fmfv{l.a=115,l=\large$\lambda_{\ell q}$}{v}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 1639: Line 1690:
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
 \\ \\ \\ \\
-{{ latex:feynman:lq_coupling_btau.png ? 250 }}+{{ latex:feynman:lq_coupling_lq.png ? 250 }}
 \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 1670: Line 1721:
     \fmfshift{ 8 up}{o3}     \fmfshift{ 8 up}{o3}
     \fmfshift{16 up}{o4}     \fmfshift{16 up}{o4}
-    \fmf{fermion,tension=1.8}{o2,v1,o1+    \fmf{fermion,tension=1.8}{o1,v1,o2
-    \fmf{fermion,tension=1.8}{o3,v2,o4}+    \fmf{fermion,tension=1.8}{o4,v2,o3}
     % labels     % labels
     \fmflabel{$g$}{g1}     \fmflabel{$g$}{g1}
     \fmflabel{$g$}{g2}     \fmflabel{$g$}{g2}
-    \fmflabel{$\ell$}{o1} +    \fmflabel{$\overline{\ell}$}{o1} 
-    \fmflabel{$\overline{q}$}{o2} +    \fmflabel{$q$}{o2} 
-    \fmflabel{$\overline{\ell}$}{o3} +    \fmflabel{$\ell$}{o3} 
-    \fmflabel{$q$}{o4}+    \fmflabel{$\overline{q}$}{o4}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 1709: Line 1760:
     \fmfshift{ 8 up}{o3}     \fmfshift{ 8 up}{o3}
     \fmfshift{16 up}{o4}     \fmfshift{16 up}{o4}
-    \fmf{fermion,tension=1.8}{o2,v1,o1+    \fmf{fermion,tension=1.8}{o1,v1,o2
-    \fmf{fermion,tension=1.8}{o3,v2,o4}+    \fmf{fermion,tension=1.8}{o4,v2,o3}
     % labels     % labels
     \fmflabel{$g$}{g}     \fmflabel{$g$}{g}
-    \fmflabel{$\tau^-$}{o1} +    \fmflabel{$\tau^+$}{o1} 
-    \fmflabel{$\overline{\text{b}}$}{o2} +    \fmflabel{b}{o2} 
-    \fmflabel{$\tau^+$}{o3} +    \fmflabel{\vspace{8pt}$\tau^-$}{o3} 
-    \fmflabel{b}{o4}+    \fmflabel{$\overline{\text{b}}$}{o4}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 1722: Line 1773:
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
 \\ \\ \\ \\
-{{ latex:feynman:lq_pair_ttnunu_short.png ? 250 }}+{{ latex:feynman:lq_pair_bbtautau_short.png ? 250 }}
 \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 1739: Line 1790:
     % gluon + quarks     % gluon + quarks
     \fmf{gluon}{i1,v1}     \fmf{gluon}{i1,v1}
-    \fmf{fermion}{i2,v2,o2}+    \fmf{fermion}{i2,v1} 
 +    \fmf{fermion,label=$q$,label.side=left}{v1,v2} 
 +    \fmf{fermion}{v2,o2}
     \fmflabel{$g$}{i1}     \fmflabel{$g$}{i1}
     \fmflabel{$q$}{i2}     \fmflabel{$q$}{i2}
     \fmflabel{$\ell$}{o2}     \fmflabel{$\ell$}{o2}
-    % LQs +    % LQ 
-    \fmf{dashes_arrow,label=LQ,label.side=left}{v2,v1,LQ}+    \fmf{dashes,label=LQ,label.side=left}{v2,LQ}
     % LQ -> lepton + quark     % LQ -> lepton + quark
     \fmf{fermion}{l2,LQ,l1}     \fmf{fermion}{l2,LQ,l1}
 +    \fmfshift{20 right}{l1,l2}
     \fmflabel{$q$}{l1}     \fmflabel{$q$}{l1}
     \fmflabel{$\overline{\ell}$}{l2}     \fmflabel{$\overline{\ell}$}{l2}
Line 1753: Line 1807:
 </code> </code>
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
-\\ \\ 
-{{ latex:lq_single_t-channel_llq.png ? 250 }} 
 \\ \\ \\ \\ \\ \\
 +{{ latex:feynman:lq_single_qll_skewed.png ? 250 }}
 +\\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
  
Line 1764: Line 1818:
   \begin{fmfgraph*}(120,100)   \begin{fmfgraph*}(120,100)
     \fmfstraight     \fmfstraight
-    \fmfleft{i2,i1}+    \fmfleft{i2,m,i1}
     \fmfright{o2,l2,l1}     \fmfright{o2,l2,l1}
     % skeleton     % skeleton
-    \fmf{phantom,tension=1.8}{i1,v1} +    \fmf{phantom,tension=1.0}{i1,v1} 
-    \fmf{phantom,tension=1.0}{v1,l1} +    \fmf{phantom,tension=1.0}{v2,l1} 
-    \fmf{phantom,tension=1.8}{v1,v2} +    \fmf{phantom,tension=1.5}{v1,v2} 
-    \fmf{phantom,tension=1.8}{i2,v2}+    \fmf{phantom,tension=1.0}{i2,v1}
     \fmf{phantom,tension=1.0}{v2,o2}     \fmf{phantom,tension=1.0}{v2,o2}
 +    \fmf{phantom,tension=0.6}{i1,t1,m}
 +    \fmf{phantom,tension=0.6}{t1,LQ}
 +    \fmf{phantom,tension=2.0}{l1,LQ,l2}
     \fmffreeze     \fmffreeze
     % gluon + quarks     % gluon + quarks
-    \fmf{gluon}{i1,v1} +    \fmf{phantom,tension=5.0}{i1,g} % shorten leg 
-    \fmf{fermion}{i2,v2,o2+    \fmf{phantom,tension=5.0}{i2,q} % shorten leg 
-    \fmflabel{$g$}{i1+    \fmf{phantom,tension=5.0}{o2,l} % shorten leg 
-    \fmflabel{$q$}{i2+    \fmf{gluon}{g,v1} 
-    \fmflabel{$\ell$}{o2+    \fmf{fermion}{q,v1} 
-    % LQs +    \fmf{fermion,label=$q$,label.side=right}{v1,v2} 
-    \fmf{dashes_arrow,tension=1.2,label=LQ,label.side=left}{v1,LQ} +    \fmf{fermion}{v2,l
-    \fmf{dashes_arrow,label=LQ,label.side=left}{v2,v1}+    \fmflabel{$g$}{g
 +    \fmflabel{$q$}{q
 +    \fmflabel{$\ell$}{l
 +    % LQ 
 +    \fmf{dashes,tension=1.2,label=LQ,label.side=left}{v2,LQ}
     % LQ -> lepton + quark     % LQ -> lepton + quark
     \fmf{fermion}{l2,LQ,l1}     \fmf{fermion}{l2,LQ,l1}
-    \fmfshift{right}{l1,l2+    \fmfshift{20 right}{l1,l2}
-    \fmfshift{20 left}{o2}+
     \fmflabel{$q$}{l1}     \fmflabel{$q$}{l1}
     \fmflabel{$\overline{\ell}$}{l2}     \fmflabel{$\overline{\ell}$}{l2}
Line 1793: Line 1853:
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
 \\ \\ \\ \\ \\ \\ \\ \\
-{{ latex:lq_single_t-channel_llq_straight.png ? 250 }}+{{ latex:feynman:lq_single_qll.png ? 250 }}
 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
 +
  
 <WRAP group><WRAP 55% column lo> <WRAP group><WRAP 55% column lo>
Line 1806: Line 1867:
     % gluon + quarks     % gluon + quarks
     \fmf{gluon}{i1,v1}     \fmf{gluon}{i1,v1}
-    \fmf{fermion}{i2,v1} +    \fmf{fermion}{i2,v2,o2}
-    \fmf{fermion,label=$q$,label.side=left}{v1,v2} +
-    \fmf{fermion}{v2,o2}+
     \fmflabel{$g$}{i1}     \fmflabel{$g$}{i1}
     \fmflabel{$q$}{i2}     \fmflabel{$q$}{i2}
     \fmflabel{$\ell$}{o2}     \fmflabel{$\ell$}{o2}
-    % LQ +    % LQs 
-    \fmf{dashes_arrow,label=LQ,label.side=left}{v2,LQ}+    \fmf{dashes,label=LQ,label.side=left}{v2,v1,LQ}
     % LQ -> lepton + quark     % LQ -> lepton + quark
     \fmf{fermion}{l2,LQ,l1}     \fmf{fermion}{l2,LQ,l1}
-    \fmfshift{20 right}{l1,l2} 
     \fmflabel{$q$}{l1}     \fmflabel{$q$}{l1}
     \fmflabel{$\overline{\ell}$}{l2}     \fmflabel{$\overline{\ell}$}{l2}
Line 1823: Line 1881:
 </code> </code>
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
 +\\ \\
 +{{ latex:feynman:lq_single_qll2_skewed.png ? 250 }}
 \\ \\ \\ \\ \\ \\
-{{ latex:lq_single_s-channel_llq.png ? 250 }} 
-\\ \\ \\ \\ 
 </WRAP></WRAP> </WRAP></WRAP>
  
Line 1834: Line 1892:
   \begin{fmfgraph*}(120,100)   \begin{fmfgraph*}(120,100)
     \fmfstraight     \fmfstraight
-    \fmfleft{i2,m,i1}+    \fmfleft{i2,i1}
     \fmfright{o2,l2,l1}     \fmfright{o2,l2,l1}
     % skeleton     % skeleton
-    \fmf{phantom,tension=1.0}{i1,v1} +    \fmf{phantom,tension=1.8}{i1,v1} 
-    \fmf{phantom,tension=1.0}{v2,l1} +    \fmf{phantom,tension=1.0}{v1,l1} 
-    \fmf{phantom,tension=1.5}{v1,v2} +    \fmf{phantom,tension=1.4}{v1,v2} 
-    \fmf{phantom,tension=1.0}{i2,v1}+    \fmf{phantom,tension=1.8}{i2,v2}
     \fmf{phantom,tension=1.0}{v2,o2}     \fmf{phantom,tension=1.0}{v2,o2}
-    \fmf{phantom,tension=0.6}{i1,t1,m} 
-    \fmf{phantom,tension=0.6}{t1,LQ} 
-    \fmf{phantom,tension=2.0}{l1,LQ,l2} 
     \fmffreeze     \fmffreeze
     % gluon + quarks     % gluon + quarks
-    \fmf{phantom,tension=5.0}{i1,g} % shorten leg +    \fmf{gluon}{i1,v1} 
-    \fmf{phantom,tension=5.0}{i2,q} % shorten leg +    \fmf{fermion}{i2,v2,o2
-    \fmf{phantom,tension=5.0}{o2,l} % shorten leg +    \fmflabel{$g$}{i1
-    \fmf{gluon}{g,v1} +    \fmflabel{$q$}{i2
-    \fmf{fermion}{q,v1} +    \fmflabel{$\ell$}{o2
-    \fmf{fermion,label=$q$,label.side=right}{v1,v2} +    % LQs 
-    \fmf{fermion}{v2,l+    \fmf{dashes,tension=1.2,label=LQ,label.side=left}{v1,LQ} 
-    \fmflabel{$g$}{g+    \fmf{dashes,label=LQ,label.side=left}{v2,v1}
-    \fmflabel{$q$}{q+
-    \fmflabel{$\ell$}{l+
-    % LQ +
-    \fmf{dashes_arrow,tension=1.2,label=LQ,label.side=left}{v2,LQ}+
     % LQ -> lepton + quark     % LQ -> lepton + quark
     \fmf{fermion}{l2,LQ,l1}     \fmf{fermion}{l2,LQ,l1}
-    \fmfshift{20 right}{l1,l2}+    \fmfshift{right}{l1,l2
 +    \fmfshift{20 left}{o2}
     \fmflabel{$q$}{l1}     \fmflabel{$q$}{l1}
     \fmflabel{$\overline{\ell}$}{l2}     \fmflabel{$\overline{\ell}$}{l2}
Line 1869: Line 1921:
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
 \\ \\ \\ \\ \\ \\ \\ \\
-{{ latex:lq_single_s-channel_llq_straight.png ? 250 }}+{{ latex:feynman:lq_single_qll2.png ? 250 }}
 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +% preamble
 +\usepackage{xcolor}
 +\definecolor{myblue}{rgb}{.0,.13,.98} % 0,32,250
 +
 +% body
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,180)
 +    \fmfleft{i1,iq,i2,ip,i3}
 +    \fmfright{y1,y2,y3,d,o1,o2,f1,o3,f2,d,x3,x2,x1}
 +    \fmfset{arrow_len}{10}
 +    % skeleton
 +    \fmf{phantom,t=0.48}{vq,vp}
 +    \fmf{phantom}{ip,vp,x1}
 +    \fmf{phantom}{iq,vq,y1}
 +    \fmffreeze
 +    \fmf{phantom,t=1.8}{vq,v1,vp}
 +    \fmf{phantom,t=1.8}{v1,v2}
 +    \fmf{phantom,t=1}{o3,v2,o2}
 +    \fmffreeze
 +    % partons
 +    \fmf{fermion,lab=$q$,l.s=right}{vp,v1}
 +    \fmf{gluon,lab=$g$,l.s=left}{vq,v1}
 +    % hard process
 +    \fmf{fermion,lab=$q$,l.s=right}{v1,v2}
 +    \fmf{fermion}{v2,o1}
 +    \fmfshift{10 right}{f1,f2}
 +    \fmf{dashes,t=2,lab=LQ,l.s=left}{v2,vf}
 +    \fmf{phantom,t=0.4}{x1,vf} % pull vf
 +    \fmf{fermion,t=1.4}{f1,vf,f2}
 +    % proton 1
 +    \fmf{phantom}{ip,vp}
 +    \fmfi{fermion}{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
 +    \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}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4,-6)}
 +    % X
 +    \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}
 +    % outgoing proton
 +    \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}
 +    % labels
 +    \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{ip}
 +    \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{iq}
 +    \fmfv{l=$\overline{\ell}$}{f1}
 +    \fmfv{l=$q$}{f2}
 +    \fmfv{l=$\ell$,l.a=-20}{o1}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(.0,,.13,,.98),
 +          l=$\color{myblue}\lambda$,l.d=7,l.a=-10}{v2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:lq_single_qll_protons.png ? 1000 }}
 +\\ \\ \\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,90)
 +    \fmfstraight
 +    \fmfleft{i2,i1}
 +    \fmfright{o2,l2,l1}
 +    % skeleton
 +    \fmf{phantom,tension=1.8}{i1,v1}
 +    \fmf{phantom,tension=1.1}{v1,l1}
 +    \fmf{phantom,tension=1.6}{v1,v2}
 +    \fmf{phantom,tension=1.8}{i2,v2}
 +    \fmf{phantom,tension=1.1}{v2,o2}
 +    \fmffreeze
 +    % gluon + quarks
 +    \fmf{fermion}{i1,v1}
 +    \fmf{photon}{i2,v2}
 +    \fmf{fermion}{v2,o2}
 +    % LQs
 +    \fmf{dashes,tension=1.2,label=LQ,label.side=left}{v1,LQ}
 +    \fmf{fermion}{v1,v2}
 +    % LQ -> lepton + quark
 +    \fmf{fermion}{l2,LQ,l1}
 +    \fmfshift{5 right}{l1,l2}
 +    \fmfshift{2 down}{l2}
 +    \fmfshift{20 left}{o2}
 +    \fmfv{l.a=160,l=$q$}{i1}
 +    \fmfv{l.a=-165,l=$\gamma$}{i2}
 +    \fmfv{l.a=-20,l=$\ell$}{o2}
 +    \fmfv{l.a=20,l=$\overline{q}$}{l1}
 +    \fmfv{l.a=-10,l=$\overline{\ell}$}{l2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(.0,,.13,,.98),
 +          l=$\color{myblue}\lambda$,l.d=6,l.a=-45}{v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:lq_single_qll_lepton-induced.png ? 250 }}
 +\\ \\ \\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,190)
 +    \fmfleft{i1,iq,i2,ip,i3}
 +    \fmfright{y1,y2,y3,d,o1,o2,f1,o3,f2,d,x3,x2,x1}
 +    \fmfset{arrow_len}{10}
 +    % skeleton
 +    \fmf{phantom,t=0.48}{vq,vp}
 +    \fmf{phantom,t=1.3}{ip,vp}
 +    \fmf{phantom,t=1.3}{iq,vq}
 +    \fmf{phantom}{vp,x1}
 +    \fmf{phantom}{vq,y1}
 +    \fmffreeze
 +    \fmf{phantom,t=1.6}{vq,v2,v1,vp}
 +    \fmf{phantom,t=0.7}{v1,o3}
 +    \fmf{phantom,t=0.7}{v2,o2}
 +    \fmffreeze
 +    % parton
 +    \fmf{fermion,t=1.6,lab=$q$}{vp,v1}
 +    \fmf{photon,t=1.6,lab=$\gamma$,l.d=3,l.s=left}{vq,v2}
 +    \fmf{fermion,t=1,lab=$\ell$,l.s=right}{v1,v2}
 +    \fmf{fermion,t=1}{v2,o1}
 +    % hard process
 +    \fmfshift{5 right}{f1,f2}
 +    \fmf{dashes,t=2,lab=LQ,l.d=3,l.s=left}{v1,vf}
 +    \fmf{fermion,t=1.4}{f1,vf,f2}
 +    %\fmf{fermion,t=1}{v2,o1}
 +    % proton 1
 +    \fmf{phantom}{ip,vp}
 +    \fmfi{fermion}{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
 +    \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}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4,-6)}
 +    % X
 +    \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, 2.5)}
 +    \fmfi{fermion}{vpath (__vp,__x2) scaled 1.0 shifted ( 0.0, 0.0)}
 +    \fmfi{fermion}{vpath (__vp,__x3) scaled 1.0 shifted ( 0.0,-3.0)}
 +    \fmfblob{22}{vp}
 +    % outgoing proton
 +    \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,__y3) scaled 1.0 shifted (-1.5,-6.0)}
 +    \fmfi{fermion}{vpath (__vq,__y3) scaled 1.0 shifted ( 0.0, 0.0)}
 +    \fmfi{fermion}{vpath (__vq,__y3) scaled 1.0 shifted ( 1.5, 6.0)}
 +    \fmfblob{22}{vq}
 +    % labels
 +    \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{ip}
 +    \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{iq}
 +    \fmfv{l=$\text{p}^+$,l.a=-20,l.d=8}{y3}
 +    \fmfv{l=$\overline{\ell}$}{f1}
 +    \fmfv{l=$q$}{f2}
 +    \fmfv{l=$\ell$,l.a=-20}{o1}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(.0,,.13,,.98),
 +          l=$\color{myblue}\lambda$,l.d=6,l.a=-45}{v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:lq_single_qll_lepton-induced_protons.png ? 1000 }}
 +\\ \\ \\ \\ \\
 +</WRAP></WRAP>
 +
 +
 + ==== Nonresonant (t-channel) production ====
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(110,60)
 +    \fmfleft{i2,i1}
 +    \fmfright{o2,o1}
 +    \fmf{fermion}{i1,v1,o1}
 +    \fmf{fermion}{o2,v2,i2}
 +    \fmf{dashes,label=LQ,l.s=right,t=0.8}{v1,v2}
 +    \fmfv{l.a=150,l=$q$}{i1}
 +    \fmfv{l.a=30,l=$\ell$}{o1}
 +    \fmfv{l.a=-150,l=$\overline{q}$}{i2}
 +    \fmfv{l.a=-30,l=$\overline{\ell}$}{o2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\
 +{{ latex:feynman:lq_t-channel_ll.png ? 250 }}
 +\\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,120)
 +    \fmfleft{d,d,g2,d,d,g1,d,d}
 +    \fmfright{b2,d,t2,d,d,t1,d,b1}
 +    % gluons
 +    \fmf{gluon,tension=1.8}{v1,g1}
 +    \fmf{gluon,tension=1.8}{g2,v2}
 +    \fmf{phantom}{v1,t1}
 +    \fmf{phantom}{v2,t2}
 +    \fmffreeze
 +    % b quarks
 +    \fmf{fermion}{b2,v2,vl2}
 +    \fmf{fermion}{vl1,v1,b1}
 +    % LQ (t-channel)
 +    \fmf{dashes,tension=1,label=LQ,l.s=left}{vl1,vl2}
 +    % tau leptons
 +    \fmf{fermion}{t1,vl1}
 +    \fmf{fermion}{vl2,t2}
 +    % labels
 +    \fmfv{l=$g$,l.a=160,l.d=6}{g1}
 +    \fmfv{l=$g$,l.a=-160,l.d=6}{g2}
 +    \fmfv{l=b,l.a=20,l.d=5}{b1}
 +    \fmfv{l=$\overline{\text{b}}$,l.a=-20,l.d=5}{b2}
 +    \fmfv{l=$\tau^+$,l.a=20,l.d=5}{t1}
 +    \fmfv{l=$\tau^-$,l.a=-5,l.d=5}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\
 +{{ latex:feynman:lq_t-channel_bbtautau.png ? 1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 + ===== Z' and W' =====
 +
 +Here are some examples of processes with Z' and W'.
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,60)
 +    \fmfset{arrow_len}{10}
 +    \fmfstraight
 +    \fmfleft{i3,i1}
 +    \fmfright{o3,o2,o1}
 +    % fermions
 +    \fmf{fermion}{i1,v1,o1}
 +    \fmffreeze
 +    \fmf{fermion,tension=1.5}{o3,v3,o2}
 +    \fmf{phantom,tension=1.8}{i3,v3}
 +    \fmflabel{b}{i1}
 +    \fmflabel{c}{o1}
 +    \fmflabel{$\tau$}{o2}
 +    \fmflabel{$\nu_\tau$}{o3}
 +    % boson
 +    \fmf{boson,label=W$'$,label.side=left}{v3,v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\
 +{{ latex:feynman:wprime_b_ctaunu.png ? 250 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,60)
 +    \fmfset{arrow_len}{10}
 +    \fmfstraight
 +    \fmfleft{i3,i1}
 +    \fmfright{o3,o2,o1}
 +    % fermions
 +    \fmf{fermion}{i1,v1,o1}
 +    \fmffreeze
 +    \fmf{fermion,tension=1.5}{o3,v3,o2}
 +    \fmf{phantom,tension=1.8}{i3,v3}
 +    \fmflabel{b}{i1}
 +    \fmflabel{s}{o1}
 +    \fmflabel{$\mu$}{o2}
 +    \fmflabel{$\mu$}{o3}
 +    % boson
 +    \fmf{boson,label=Z$'$,label.side=left}{v3,v1}
 +    \fmfblob{16}{v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:zprime_b_smumu.png ? 250 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(110,100)
 +    \fmfleft{i2,i1}
 +    \fmfright{o2,m2,m1,o1}
 +    \fmfshift{30 right}{m1,m2}
 +    \fmf{fermion}{i1,v1,i2}
 +    \fmf{phantom}{o2,v2,o1}
 +    \fmf{boson,label=$\text{Z}/\gamma^*$,label.side=right}{v1,v2}
 +    \fmffreeze
 +    \fmf{fermion}{o2,v2,z,o1}
 +    \fmffreeze
 +    \fmf{boson,label=$\text{Z}'$,label.side=left}{z,m}
 +    \fmf{fermion,tension=1.4}{m2,m,m1}
 +    \fmf{phantom,tension=0.6}{i2,m}
 +    \fmflabel{$\mu^-$}{m1}
 +    \fmflabel{$\mu^+$}{m2}
 +    \fmflabel{$\mu^-$}{o1}
 +    \fmflabel{$\mu^+$}{o2}
 +    \fmflabel{$q$}{i1}
 +    \fmflabel{$\overline{q}'$}{i2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\
 +{{ latex:feynman:zprime_4mu.png ? 450 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +
 +
 + ===== SUSY =====
 +
 +More SUSY diagram are available [[https://twiki.cern.ch/twiki/bin/viewauth/CMS/SUSYSimplifiedModelDiagrams|here (images]] and [[https://github.com/CMS-SUS-XPAG/SUSYDiagrams|here (GitHub)]].
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(80,120)
 +    %\fmfstraight
 +    \fmfleft{i2,b,i1}
 +    \fmfright{o4,o3,o2,o1}
 +    \fmftop{top}
 +    \fmfbottom{bot}
 +    % blob
 +    \fmfblob{16}{b}
 +    \fmf{dashes,tension=1.3,label=$\tilde{\text{t}}$,l.s=right}{v1,b}
 +    \fmf{dashes,tension=1.3,label=$\overline{\tilde{\text{t}}}$,l.s=right}{b,v2}
 +    % decay products
 +    %\fmf{phantom,tension=1.0}{top,v1}
 +    %\fmf{phantom,tension=1.0}{v2,bot}
 +    \fmfshift{16 down}{o1}
 +    \fmfshift{ 8 down}{o2}
 +    \fmfshift{ 8 up}{o3}
 +    \fmfshift{16 up}{o4}
 +    \fmf{dots,tension=1.8}{v1,o1}
 +    \fmf{fermion,tension=1.8}{o2,v1}
 +    \fmf{fermion,tension=1.8}{v2,o4}
 +    \fmf{dots,tension=1.8}{o3,v2}
 +    % labels
 +    \fmflabel{$\tilde{\chi}_1^0$}{o1}
 +    \fmflabel{$\overline{\text{t}}$}{o2}
 +    \fmflabel{$\tilde{\chi}_1^0$}{o3}
 +    \fmflabel{t}{o4}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:susy_stop_pair_ttxx.png ? 250 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +
  ===== Top quark pair decay into a W boson pair and a b quark pair =====  ===== Top quark pair decay into a W boson pair and a b quark pair =====
  
Line 3239: Line 3696:
  
 Here are some proton-proton collisions with hard processes. Note the use of ''\fmfshift'' to shorten the proton debris lines, and make the hard process stick out, without changing the aspect ratio of diagram's other parts. Here are some proton-proton collisions with hard processes. Note the use of ''\fmfshift'' to shorten the proton debris lines, and make the hard process stick out, without changing the aspect ratio of diagram's other parts.
 +
 +Full code for a {{latex:feynman:proton-proton_collisions_hard_process.pdf|multipage PDF}} including all figures below can be found [[latex:feynman:pp_hard|here]].
  
 A generic proces: A generic proces:
Line 3334: Line 3793:
     % hard process     % hard process
     \fmfshift{20 right}{f1,f2}     \fmfshift{20 right}{f1,f2}
-    \fmfv{l=$\bar{f}$}{f1} +    \fmfv{l.a=-25,l.d=3,l=$\ell^+$}{f1} 
-    \fmfv{l=$f$}{f2}+    \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{boson,tension=2,label=$\text{Z}^0/\gamma^*$,label.side=left}{v,vf}
     \fmf{fermion,tension=2}{f1,vf,f2}     \fmf{fermion,tension=2}{f1,vf,f2}
Line 3377: Line 3836:
 </WRAP><WRAP half column 35%> </WRAP><WRAP half column 35%>
 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-{{ latex:proton-proton_drell-yan.png ? 0x1000 }}+{{ latex:feynman:proton-proton_drell-yan.png ? 0x1000 }}
 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 3458: Line 3917:
  
 Diffractive processes involving a Pomeron, after [[https://arxiv.org/abs/1208.4968|this ALICE]], [[https://cds.cern.ch/record/2005230?ln=en|this CMS (FSQ-15-005)]] and [[https://cds.cern.ch/record/2194234?ln=en|this ATLAS (ATL-PHYS-PROC-2016-079)]] paper. Note the Pomeron symbol is made with ''${\rm I\!P}$'' instead of ''${\mathbb{P}$''. Diffractive processes involving a Pomeron, after [[https://arxiv.org/abs/1208.4968|this ALICE]], [[https://cds.cern.ch/record/2005230?ln=en|this CMS (FSQ-15-005)]] and [[https://cds.cern.ch/record/2194234?ln=en|this ATLAS (ATL-PHYS-PROC-2016-079)]] paper. Note the Pomeron symbol is made with ''${\rm I\!P}$'' instead of ''${\mathbb{P}$''.
 +
 +Full code for a {{latex:feynman:proton-proton_collisions_diffractive.pdf|multipage PDF}} including all figures below can be found [[latex:feynman:pp_diffractive|here]].
  
 Elastic scattering with Pomeron exchange: Elastic scattering with Pomeron exchange:
Line 3689: Line 4150:
  
  
 + ===== Anomalous momentum measurement (g-2) =====
 +
 +The text colors in the diagrams below are defined with the following in the preamble:
 +<code latex>
 +\usepackage{xcolor}
 +\definecolor{myblue}{rgb}{.1,.1,.7}
 +\definecolor{mygreen}{rgb}{.1,.6,.1}
 +</code>
 +
 +Tree level of photon-tautau vertex:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v1}
 +    \fmf{plain,f=(.1,,.6,,.1),t=0.9}{v1,v,v2}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{v2,f1}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmffreeze
 +    \fmf{boson,right=0.36,label=$\gamma$,l.s=right}{v1,v2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_loop_bent.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +Photon loop:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v1}
 +    \fmf{plain,f=(.1,,.6,,.1),t=0.9}{v1,v,v2}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{v2,f1}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmffreeze
 +    \fmf{boson,right=0.36,label=$\gamma$,l.s=right}{v1,v2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_loop.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +With vacuum polarization quark loop:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(160,120)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v1}
 +    \fmf{fermion,f=(.1,,.6,,.1),t=0.6}{v1,v,v2}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{v2,f1}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmffreeze
 +    \fmf{boson,t=2}{v1,vl1}
 +    \fmf{boson,t=2}{vl2,v2}
 +    \fmf{fermion,left=1,tension=1,label=\Large$q$}{vl1,vl2,vl1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_quarkloop.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +Vertex with blob:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1.3}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v,f1}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmfv{decor.shape=circle,decor.filled=shaded,
 +          decor.size=28,f=(.1,,.1,,.7)}{v}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_blob.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1.3}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v,f1}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmfv{decor.shape=circle,decor.filled=empty,decor.size=35,
 +          f=(.1,,.1,,.7),b=(.92,,.92,,.98),l=\large\color{myblue}$g-2$,l.a=0,l.d=0}{v}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_blob_g-2.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v1}
 +    \fmf{dashes,left=0.48,t=0.7}{v1,v}
 +    \fmf{dashes,left=0.48,t=0.7,l.d=1pt,label=\Large slepton}{v,v2}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{v2,f1}
 +    \fmf{phantom,t=0.3}{v2,v1}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmffreeze
 +    \fmf{fermion,l.s=right,l.d=4,l.s=right,
 +         label=\huge$\substack{\text{dark}\\\text{matter}}$}{v1,v2}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_susy_dm.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +
 +
 + ===== Lepton flavor violating decays =====
 +
 +Some examples of lepton flavor violating (LFV) decays of heavy leptons (muon, tau),
 +which is possible in the Standard Model thanks to neutrino oscillations, but still heavily suppressed due to the small neutrino masses.
 +
 +LVF decay of a heavy leptons (muon, tau) to a lepton plus photon.
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(170,50)
 +    \fmfleft{i1,i2}
 +    \fmfright{o1,o2}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{plain,l.d=3,label=$\nu_\ell$\;,t=1.5}{v1,x} % left neutrino line
 +    \fmf{plain,l.d=3,label=\;$\nu_{\ell'}$,t=1.5}{x,v2} % right neutrino line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmfv{decor.shape=cross,decor.size=10}{x} % cross
 +    \fmffreeze
 +    % loop
 +    \fmf{phantom,t=1}{vl,i2} % support left
 +    \fmf{phantom,t=1.8}{vl,vr} % support middle
 +    \fmf{phantom,t=1}{vr,o2} % support right
 +    \fmf{boson,left=0.25,t=1.2}{v1,vl,vr,v2} % loop
 +    % photon
 +    \fmfshift{30 left}{t2}
 +    \fmf{boson,t=0}{vr,t2} % photon
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=8,l.a=70,l=$\mathrm{W}^-$}{vl}
 +    \fmfv{l.d=5,l.a=15,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_gamma.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +LVF decay of a heavy leptons (muon, tau) to a three leptons, which proceeds through a penguin diagram.
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(140,60)
 +    \fmfstraight
 +    \fmfleft{i1,i2,i3}
 +    \fmfright{o1,o2,o3}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{plain,l.d=3,label=$\nu_\ell$\;,t=1.5}{v1,x} % left neutrino line
 +    \fmf{plain,l.d=3,label=\;$\nu_{\ell'}$,t=1.5}{x,v2} % right neutrino line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmfv{decor.shape=cross,decor.size=10}{x} % cross
 +    \fmffreeze
 +    % loop
 +    \fmf{phantom,t=1.7}{vl,i2} % support left
 +    \fmf{phantom,t=2.4}{vl,vr} % support middle
 +    \fmf{phantom,t=1.7}{vr,o2} % support right
 +    \fmf{boson,left=0.25,t=0.7}{v1,vl,vr,v2} % loop
 +    \fmffreeze
 +    % photon
 +    \fmf{phantom,t=0.9}{t1,vg} % support
 +    \fmfshift{5 right}{o2}
 +    \fmfshift{5 right}{o3}
 +    \fmf{boson,t=1,l.d=4,label=$\gamma$}{vr,vg} % photon
 +    \fmf{fermion,t=1.8}{o3,vg,o2} % fermion
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=-10,l=$\ell'^-$}{o2}
 +    \fmfv{l.d=5,l.a=20,l=$\ell'^+$}{o3}
 +    \fmfv{l.d=8,l.a=70,l=$\mathrm{W}^-$}{vl}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_3lepton.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +LVF decay of a heavy leptons (muon, tau) to a lepton and a photon through a LQ mediator.
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(170,50)
 +    \fmfleft{i1,i2}
 +    \fmfright{o1,o2}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{fermion,l.d=6,label=$q$,t=0.75}{v1,v2} % quark line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % loop
 +    \fmf{phantom,t=1}{vl,i2} % support left
 +    \fmf{phantom,t=1.8}{vl,vr} % support middle
 +    \fmf{phantom,t=1}{vr,o2} % support right
 +    \fmf{boson,left=0.25,t=1.2}{v1,vl,vr,v2} % loop
 +    % photon
 +    \fmfshift{30 left}{t2}
 +    \fmf{boson,t=0}{vr,t2} % photon
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=7,l.a=110,l=LQ}{vl}
 +    \fmfv{l.d=5,l.a=15,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_gamma_lq.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(170,35)
 +    \fmfleft{i1,i2}
 +    \fmfright{o1,o2}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{phantom,t=1.2}{v1,v} % support line
 +    \fmf{phantom,t=2.0}{v,v2} % support line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % internal quark line
 +    \fmf{fermion,l.d=6,l.s=left,label=$q$,t=1}{v1,vm} % quark line
 +    \fmf{plain,t=8}{vm,v2} % quark line
 +    % loop
 +    \fmf{boson,right=0.9,t=1}{v1,v2} % loop
 +    % photon
 +    \fmfshift{30 left}{t2}
 +    \fmf{boson,t=0}{v,t2} % photon
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=22,l.a=-85,l=LQ}{v1}
 +    \fmfv{l.d=5,l.a=15,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_gamma_lq2.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(170,45)
 +    \fmfleft{i1,i2}
 +    \fmfright{o1,o2}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{phantom,t=0.85}{v1,v2}
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % loop top
 +    \fmf{phantom,t=1}{vtl,i2} % support left
 +    \fmf{phantom,t=0.6}{vtl,vtr} % support middle
 +    \fmf{phantom,t=1}{vtr,o2} % support right
 +    \fmf{plain,left=0.26,t=1.6}{v1,vtl} % support loop
 +    \fmf{fermion,left=0.26,t=1.6,l.d=5,label=$q$}{vtl,vtr} % fermion loop
 +    \fmf{plain,left=0.26,t=1.6}{vtr,v2} % quark loop
 +    % loop bottom
 +    \fmf{boson,right=1,t=1,label=LQ}{v1,v2} % LQ loop
 +    % photon
 +    \fmfshift{30 left}{t2}
 +    \fmf{boson,t=0}{vtr,t2} % photon
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=20,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_gamma_lq3.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +LVF decay of a heavy leptons (muon, tau) to a three leptons through a LQ mediator.
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(140,60)
 +    \fmfstraight
 +    \fmfleft{i1,i2,i3}
 +    \fmfright{o1,o2,o3}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{fermion,l.d=6,label=$q$,t=0.75}{v1,v2} % quark line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % loop
 +    \fmf{phantom,t=1.7}{vl,i2} % support left
 +    \fmf{phantom,t=2.4}{vl,vr} % support middle
 +    \fmf{phantom,t=1.7}{vr,o2} % support right
 +    \fmf{boson,left=0.25,t=0.7}{v1,vl,vr,v2} % loop
 +    \fmffreeze
 +    % photon
 +    \fmf{phantom,t=0.9}{t1,vg} % support
 +    \fmfshift{5 right}{o2}
 +    \fmfshift{5 right}{o3}
 +    \fmf{boson,t=1,l.d=4,label=$\gamma$}{vr,vg} % photon
 +    \fmf{fermion,t=1.8}{o3,vg,o2} % fermion
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=-10,l=$\ell'^-$}{o2}
 +    \fmfv{l.d=5,l.a=20,l=$\ell'^+$}{o3}
 +    \fmfv{l.d=8,l.a=70,l=LQ}{vl}
 +    %\fmfv{l.d=5,l.a=15,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_3lepton_lq.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(150,50)
 +    \fmfstraight
 +    \fmfleft{i1,i2,i3}
 +    \fmfright{o1,o2,o3}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{phantom,t=1.2}{v1,v} % support line
 +    \fmf{phantom,t=2.0}{v,v2} % support line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % internal quark line
 +    \fmf{fermion,l.d=6,l.s=left,label=$q$,t=1}{v1,vm} % quark line
 +    \fmf{plain,t=8}{vm,v2} % quark line
 +    % loop
 +    \fmf{boson,right=0.9,t=1}{v1,v2} % loop
 +    % photon -> 2 leptons
 +    \fmf{boson,t=1,l.d=3,l.s=left,label=$\gamma$}{v,vg} % photon
 +    \fmf{fermion,t=1.6}{o3,vg,o2} % lepton lines
 +    \fmf{phantom,t=1}{i3,vg} % support line
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o2}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^+$}{o3}
 +    \fmfv{l.d=22,l.a=-85,l=LQ}{v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_3lepton_lq2.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(130,100)
 +    \fmfleft{i1,i2,i3}
 +    \fmfright{o1,o2,o3}
 +    \fmftop{t1,t2}
 +    \fmfbottom{b1,b2}
 +    % fermion lines
 +    \fmf{fermion}{i2,v1} % lepton line in
 +    \fmf{phantom,t=0.9}{v1,v2}
 +    \fmf{fermion}{v2,o2} % lepton line out
 +    \fmffreeze
 +    % loop top
 +    \fmf{phantom,t=1}{vtl,i3} % support left
 +    \fmf{phantom,t=0.6}{vtl,vtr} % support middle
 +    \fmf{phantom,t=1}{vtr,o3} % support right
 +    \fmf{phantom,left=0.26,t=1.5}{v1,vtl,vtr} % support loop
 +    \fmf{fermion,left=0.26,t=1.5,label=$q$}{vtr,v2} % quark loop
 +    \fmffreeze
 +    \fmf{boson,left=0.57,t=1,l.d=3,label=LQ}{v1,vtr} % LQ loop
 +    % loop bottom
 +    \fmf{phantom,t=1}{vbl,i1} % support left
 +    \fmf{phantom,t=0.6}{vbl,vbr} % support middle
 +    \fmf{phantom,t=1}{vbr,o1} % support right
 +    \fmf{phantom,right=0.26,t=1.5}{v1,vbl,vbr} % support loop
 +    \fmf{boson,right=0.26,t=1.5,l.d=3,label=LQ}{vbr,v2} % LQ loop
 +    \fmffreeze
 +    \fmf{fermion,right=0.57,t=1,label=$q$}{v1,vbr} % quark loop
 +    % fermion
 +    %\fmfshift{10 right}{o1}
 +    %\fmfshift{10 right}{o3}
 +    \fmf{fermion,t=0}{vbr,o1} % fermion
 +    \fmf{fermion,t=0}{o3,vtr} % fermion
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i2}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o2}
 +    %\fmfv{l.d=7,l.a=110,l=LQ}{vtl}
 +    \fmfv{l.d=5,l.a=-15,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=20,l=$\ell'^+$}{o3}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_3lepton_lq_loop.png ? 0x1000 }}
 +</WRAP></WRAP>
 + ===== Ultra-peripheral lead-lead collisions =====
 +
 +The text colors in the diagrams below are defined with the following in the preamble:
 +<code latex>
 +\usepackage{xcolor}
 +\definecolor{myblue}{rgb}{.1,.1,.7}
 +\definecolor{myred}{rgb}{.4,.1,.1}
 +\definecolor{mylightred}{rgb}{.9,.1,.1}
 +\definecolor{mygreen}{rgb}{.1,.6,.1}
 +\definecolor{myorange}{rgb}{.9,.7,.2}
 +</code>
 +
 +Measuring the anomalous momentum (g-2) of tau leptons in electron-positron (e+e-) collisions:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % lead 1
 +    \fmf{fermion}{ip,vp,op}
 +    \fmf{phantom,t=0.3}{ip,vp}
 +    % lead 2
 +    \fmf{fermion}{iq,vq,oq}
 +    \fmf{phantom,t=0.3}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.5}{vt1,t1}
 +    \fmf{phantom,t=0.5}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,t=4,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,t=1,label=\color{mygreen}$\tau$,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,t=4,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut e$^-$,l.a=160,l.d=4}{ip}
 +    \fmfv{l=\strut e$^-$,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut e$^+$,l.a=-160,l.d=4}{iq}
 +    \fmfv{l=\strut e$^+$,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=0,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=0,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(0.4,,0.1,,0.1)}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(0.4,,0.1,,0.1)}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:ee_tautau_green.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +Ultra-peripheral lead-lead collisions (UPC) to measure the anomalous momentum (g-2) for tau leptons:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % lead 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.3}{ip,vp}
 +    % lead 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.3}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.5}{vt1,t1}
 +    \fmf{phantom,t=0.5}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmf{double,width=1.9}{ip,vp,op}
 +    \fmf{double,width=1.9}{iq,vq,oq}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion}{vt2,t2}
 +    \fmf{plain,label=$\tau$\!,l.s=left}{vt2,vt1}
 +    \fmf{fermion}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4}{vt1}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % lead 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.3}{ip,vp}
 +    % lead 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.3}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.5}{vt1,t1}
 +    \fmf{phantom,t=0.5}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$\!,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_green.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % lead 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.3}{ip,vp}
 +    % lead 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.3}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.5}{vt1,t1}
 +    \fmf{phantom,t=0.5}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$\!,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=-40}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=40}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_green_da.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +With a blob for new physics:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % proton 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.5}{ip,vp}
 +    % proton 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.5}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.7}{vt1,t1}
 +    \fmf{phantom,t=0.7}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\;\large$\color{myblue}\delta a_\tau$,l.d=5,l.a=-25}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\;\large$\color{myblue}\delta a_\tau$,l.d=5,l.a=25}{vt2}
 +    \fmfblob{18}{vt2,vt1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_green_blob.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +UPC with neutron emission from electromagnetic dissociation (EMD):
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,d,t2,m,t1,n,op}
 +    \fmfshift{7 right}{op}
 +    \fmfshift{7 right}{oq}
 +    \fmfshift{5 up}{op}
 +    \fmfshift{4 up}{n}
 +    \fmfshift{5 down}{oq}
 +    % lead 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.4}{ip,vp}
 +    % lead 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.4}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmf{phantom,label=\:Pb$^*$,l.s=left}{vp,vn} % excited Pb
 +    \fmf{phantom,t=0.9}{vn,op} % relaxed Pb
 +    \fmffreeze
 +    \fmf{phantom,t=0.1}{vn,n} % neutron
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.3}{vpath (__vn,__n)} % neutron
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.65}{vt1,vt2} % t-channel
 +    \fmf{phantom,t=0.6}{vt1,t1}
 +    \fmf{phantom,t=0.6}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$,l.d=4,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=n$^0$,l.a=10,l.d=6}{n} % neutron
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$\;\;,l.a=110,l.d=9}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautauneutron_green.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +UPC with a pair of tau leptons decaying into a muon and hadrons ("mutau" decay channel):
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,n3,p3,p2,p1,n2,n1,m1,op}
 +    \fmfshift{8 right}{m1}
 +    \fmfshift{8 right}{n1}
 +    \fmfshift{8 right}{n2}
 +    \fmfshift{8 right}{p1}
 +    \fmfshift{8 right}{p2}
 +    \fmfshift{8 right}{p3}
 +    \fmfshift{8 right}{n3}
 +    % proton 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.5}{ip,vp}
 +    % proton 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.5}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.05}{vt1,im,vt2} % pull left
 +    \fmf{phantom,t=0.45}{vt1,vt2} % pull together
 +    \fmf{phantom,t=0.6}{vt1,t1}
 +    \fmf{phantom,t=0.6}{vt2,t2}
 +    \fmf{phantom,t=0.5}{t1,t2} % pull together
 +    \fmf{phantom,t=0.8}{t2,oq} % pull right
 +    \fmf{phantom,t=0.8}{t1,op} % pull right
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,label=$\tau$,l.s=right}{vt2,t2}
 +    \fmf{plain,label=$\tau$\!,l.s=left}{vt2,vt1}
 +    \fmf{fermion,label=$\tau$,l.s=left}{vt1,t1}
 +    % tau decay 1
 +    \fmf{plain,t=1}{p1,t2}
 +    \fmf{plain,t=1}{t2,p2}
 +    \fmf{plain,t=1}{p3,t2}
 +    \fmf{plain,t=1}{n3,t2}
 +    \fmfv{l=$\pi^\mp$,l.a=0,l.d=5}{p1}
 +    \fmfv{l=$\pi^\pm$,l.a=0,l.d=5}{p2}
 +    \fmfv{l=$\pi^\mp$,l.a=0,l.d=5}{p3}
 +    \fmfv{l=$\overline\nu_\tau$,l.a=-20,l.d=5}{n3}
 +    % tau decay 2
 +    \fmf{plain,t=1}{t1,n1}
 +    \fmf{plain,t=1}{t1,n2}
 +    \fmf{plain,t=1}{t1,m1}
 +    \fmfv{l=$\mu^\pm$,l.a=20,l.d=5}{m1}
 +    \fmfv{l=$\nu_\tau$,l.a=0,l.d=5}{n1}
 +    \fmfv{l=$\nu_\mu$,l.a=0,l.d=5}{n2}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=-40}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=40}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_mutau_3p_blue.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,n3,p3,p2,p1,n2,n1,m1,op}
 +    \fmfshift{8 right}{m1}
 +    \fmfshift{8 right}{n1}
 +    \fmfshift{8 right}{n2}
 +    \fmfshift{8 right}{p1}
 +    \fmfshift{8 right}{p2}
 +    \fmfshift{8 right}{p3}
 +    \fmfshift{8 right}{n3}
 +    % proton 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.5}{ip,vp}
 +    % proton 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.5}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.05}{vt1,im,vt2} % pull left
 +    \fmf{phantom,t=0.45}{vt1,vt2} % pull together
 +    \fmf{phantom,t=0.6}{vt1,t1}
 +    \fmf{phantom,t=0.6}{vt2,t2}
 +    \fmf{phantom,t=0.5}{t1,t2} % pull together
 +    \fmf{phantom,t=0.8}{t2,oq} % pull right
 +    \fmf{phantom,t=0.8}{t1,op} % pull right
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,label=\color{mygreen}$\tau$,l.s=right,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$\!,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,label=\color{mygreen}$\tau$,l.s=left,f=(.1,,.6,,.1)}{vt1,t1}
 +    % tau decay 1
 +    \fmf{plain,t=1,f=(.9,,.7,,.2)}{p1,t2}
 +    \fmf{plain,t=1,f=(.9,,.7,,.2)}{t2,p2}
 +    \fmf{plain,t=1,f=(.9,,.7,,.2)}{p3,t2}
 +    \fmf{plain,t=1,f=(.1,,.6,,.1)}{n3,t2}
 +    \fmfv{l=\color{myorange}$\pi^\mp$,l.a=0,l.d=5}{p1}
 +    \fmfv{l=\color{myorange}$\pi^\pm$,l.a=0,l.d=5}{p2}
 +    \fmfv{l=\color{myorange}$\pi^\mp$,l.a=0,l.d=5}{p3}
 +    \fmfv{l=\color{mygreen}$\overline\nu_\tau$,l.a=-20,l.d=5}{n3}
 +    % tau decay 2
 +    \fmf{plain,t=1,f=(.1,,.6,,.1)}{t1,n1}
 +    \fmf{plain,t=1,f=(.1,,.6,,.1)}{t1,n2}
 +    \fmf{plain,t=1,f=(.9,,.1,,.1)}{t1,m1}
 +    \fmfv{l=\color{mylightred}$\mu^\pm$,l.a=20,l.d=5}{m1}
 +    \fmfv{l=\color{mygreen}$\nu_\tau$,l.a=0,l.d=5}{n1}
 +    \fmfv{l=\color{mygreen}$\nu_\mu$,l.a=0,l.d=5}{n2}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=-40}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=40}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_mutau_3p_color.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
  ===== Penguin diagrams =====  ===== Penguin diagrams =====
  
latex/feynman.1541860176.txt.gz · Last modified: 2018/11/10 15:29 by iwn