Below are some code examples of photon-induced processes in proton-proton collisions. See for example this CMS observation of γγ → ττ and the constrains on the τ anomalous electromagnetic moments, which I worked on. I presented some of the diagrams below in this seminar talk (UZH, 2024) and this conference talk (ICHEP, 2024).
Click on a diagram to jump to the code & download links below:
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{collep}{rgb}{.1,.6,.1} % lepton (green)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-4,10)(8,10){ % padding (L,T)(R,B)
\begin{fmfgraph*}(110,80) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% photons
\fmf{photon}{i1,v1}
\fmf{photon}{i2,v2}
% taus
\fmf{fermion,t=0.9,label=\color{collep}$\tau$,l.s=right,f=(.1,,.6,,.1)}{v1,v2} % t channel
\fmf{fermion,f=(.1,,.6,,.1)}{o1,v1} % outgoing top lepton
\fmf{fermion,f=(.1,,.6,,.1)}{v2,o2} % outgoing bottom lepton
% labels
\fmfv{l=$\gamma$,l.a=160,l.d=5}{i1}
\fmfv{l=$\gamma$,l.a=-158,l.d=6}{i2}
\fmfv{l=\strut\color{collep}$\tau^+$,l.a=12,l.d=5}{o1}
\fmfv{l=\strut\color{collep}$\tau^-$\vspace{-7pt},l.a=-12,l.d=5}{o2}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{v1}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{v2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{collep}{rgb}{.1,.6,.1} % lepton (green)
\definecolor{colbl}{rgb}{.1,.1,.7} % vertex (dark blue)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-4,10)(8,10){ % padding (L,T)(R,B)
\begin{fmfgraph*}(110,80) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% photons
\fmf{photon}{i1,v1}
\fmf{photon}{i2,v2}
% taus
\fmf{fermion,t=0.9,label=\color{collep}$\tau$,l.s=right,f=(.1,,.6,,.1)}{v1,v2} % t channel
\fmf{fermion,f=(.1,,.6,,.1)}{o1,v1} % outgoing top lepton
\fmf{fermion,f=(.1,,.6,,.1)}{v2,o2} % outgoing bottom lepton
% labels
\fmfv{l=$\gamma$,l.a=160,l.d=5}{i1}
\fmfv{l=$\gamma$,l.a=-158,l.d=6}{i2}
\fmfv{l=\strut\color{collep}$\tau^+$,l.a=12,l.d=5}{o1}
\fmfv{l=\strut\color{collep}$\tau^-$\vspace{-7pt},l.a=-12,l.d=5}{o2}
\fmfv{decor.shape=circle,decor.filled=empty,decor.size=15,
f=(.1,,.1,,.7),b=(.92,,.92,,.98),l=\large\color{colbl}$g$,l.a=0,l.d=0}{v1}
\fmfv{decor.shape=circle,decor.filled=empty,decor.size=15,
f=(.1,,.1,,.7),b=(.92,,.92,,.98),l=\large\color{colbl}$g$,l.a=0,l.d=0}{v2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{collep}{rgb}{.1,.6,.1} % lepton (green)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-4,10)(8,10){ % padding (L,T)(R,B)
\begin{fmfgraph*}(110,80) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% photons
\fmf{photon}{i1,v1}
\fmf{photon}{i2,v2}
% taus
\fmf{fermion,t=0.9,label=\color{collep}$\ell$,l.s=right,f=(.1,,.6,,.1)}{v1,v2} % t channel
\fmf{fermion,f=(.1,,.6,,.1)}{o1,v1} % outgoing top lepton
\fmf{fermion,f=(.1,,.6,,.1)}{v2,o2} % outgoing bottom lepton
% labels
\fmfv{l=$\gamma$,l.a=160,l.d=5}{i1}
\fmfv{l=$\gamma$,l.a=-158,l.d=6}{i2}
\fmfv{l=\strut\color{collep}$\ell^+$,l.a=12,l.d=5}{o1}
\fmfv{l=\strut\color{collep}$\ell^-$\vspace{-7pt},l.a=-20,l.d=5}{o2}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{v1}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{v2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{coldis}{rgb}{.9,.5,.0} % disassociated (orange)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-4,10)(8,10){ % padding (L,T)(R,B)
\begin{fmfgraph*}(110,80) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% photons
\fmf{photon}{i1,v1}
\fmf{photon}{i2,v2}
% bosons
\fmf{boson,t=0.9,label=\color{coldis} W,l.s=right,f=(.9,,.5,,.0)}{v1,v2} % t channel
\fmf{boson,f=(.9,,.5,,.0)}{o1,v1} % outgoing top boson
\fmf{boson,f=(.9,,.5,,.0)}{v2,o2} % outgoing bottom boson
% labels
\fmfv{l=$\gamma$,l.a=160,l.d=5}{i1}
\fmfv{l=$\gamma$,l.a=-158,l.d=6}{i2}
\fmfv{l=\strut\color{coldis} W$^+$,l.a=12,l.d=5}{o1}
\fmfv{l=\strut\color{coldis} W$^-$\vspace{-7pt},l.a=-16,l.d=5}{o2}
%\fmfv{decor.shape=circle,f=(.9,,.5,,.0),decor.filled=full,decor.size=4}{v1}
%\fmfv{decor.shape=circle,f=(.9,,.5,,.0),decor.filled=full,decor.size=4}{v2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{collep}{rgb}{.1,.6,.1} % lepton (green)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-4,10)(8,10){ % padding (L,T)(R,B)
\begin{fmfgraph*}(150,95) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
\fmfcmd{ % custom line style: double arrows for protons
style_def proton expr p =
save oldpen; pen oldpen; oldpen := currentpen;
pickup oldpen scaled 1.8; % draw thick line
cdraw p; % draw line
cfill (arrow p) % draw arrow
shifted -center p scaled 1.1 shifted center p; % scale arrow
pickup oldpen; % restore line width
enddef;
}
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp,op}
\fmf{proton}{iq,vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% mediators
\fmf{phantom,t=0.55}{vt1,om,vt2} % pull gtt vertex to left
\fmf{fermion,t=0.35,label=\color{collep}$\tau$,l.s=right,f=(.1,,.6,,.1)}{vt1,vt2} % t channel
\fmf{boson,t=1,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
\fmf{boson,t=1,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
% taus
\fmffreeze
\fmf{fermion,f=(.1,,.6,,.1)}{t1,vt1} % outgoing lepton
\fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2} % outgoing lepton
% labels
\fmfblob{15}{vp}
\fmfblob{15}{vq}
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
\fmfv{l=p$^+$,l.a=20,l.d=6}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\color{collep}$\tau^+$,l.a=10,l.d=5}{t1}
\fmfv{l=\strut\color{collep}$\tau^-$,l.a=-10,l.d=5}{t2}
%\fmfv{decor.shape=circle,decor.filled=full,decor.size=5,f=black}{vp}
%\fmfv{decor.shape=circle,decor.filled=full,decor.size=5,f=black}{vq}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{vt1}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{vt2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{collep}{rgb}{.1,.6,.1} % lepton (green)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-4,18)(8,10){ % padding (L,T)(R,B)
\begin{fmfgraph*}(150,100) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
\fmfcmd{ % custom line style: double arrows for protons
style_def proton expr p =
save oldpen; pen oldpen; oldpen := currentpen;
pickup oldpen scaled 1.8; % draw thick line
cdraw p; % draw line
cfill (arrow p) % draw arrow
shifted -center p scaled 1.1 shifted center p; % scale arrow
pickup oldpen; % restore line width
enddef;
}
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp}
\fmf{phantom}{vp,op}
\fmf{proton}{iq,vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% diffracted proton
\fmfi{fermion,f=(.9,,.5,,.0)}{vpath (__vp,__op) scaled 1.01 shifted(4, 2.5) rotatedaround(vloc(__vp), 9)}
\fmfi{fermion,f=(.9,,.5,,.0)}{vpath (__vp,__op) scaled 1.01 shifted(4, 0.0) rotatedaround(vloc(__vp), 1)}
\fmfi{fermion,f=(.9,,.5,,.0)}{vpath (__vp,__op) scaled 1.01 shifted(4,-2.5) rotatedaround(vloc(__vp),-7)}
% mediators
\fmf{phantom,t=0.55}{vt1,om,vt2} % pull gtt vertex to left
\fmf{fermion,t=0.35,label=\color{collep}$\tau$,l.s=right,f=(.1,,.6,,.1)}{vt1,vt2} % t channel
\fmf{boson,t=1,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
\fmf{boson,t=1,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
% taus
\fmffreeze
\fmf{fermion,f=(.1,,.6,,.1)}{t1,vt1} % outgoing lepton
\fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2} % outgoing lepton
% labels
\fmfblob{15}{vp}
\fmfblob{15}{vq}
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
%\fmfv{l=$X$,l.a=20,l.d=12}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\color{collep}$\tau^+$,l.a=10,l.d=5}{t1}
\fmfv{l=\strut\color{collep}$\tau^-$,l.a=-10,l.d=5}{t2}
%\fmfv{decor.shape=circle,decor.filled=full,decor.size=5,f=black}{vq}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{vt1}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{vt2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{collep}{rgb}{.1,.6,.1} % lepton (green)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-4,18)(8,18){ % padding (L,T)(R,B)
\begin{fmfgraph*}(150,100) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
\fmfcmd{ % custom line style: double arrows for protons
style_def proton expr p =
save oldpen; pen oldpen; oldpen := currentpen;
pickup oldpen scaled 1.8; % draw thick line
cdraw p; % draw line
cfill (arrow p) % draw arrow
shifted -center p scaled 1.1 shifted center p; % scale arrow
pickup oldpen; % restore line width
enddef;
}
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp}
\fmf{phantom}{vp,op}
\fmf{proton}{iq,vq}
\fmf{phantom}{vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% diffracted proton
\fmfi{fermion,f=(.9,,.5,,.0)}{vpath (__vp,__op) scaled 1.01 shifted(4, 2.5) rotatedaround(vloc(__vp), 9)}
\fmfi{fermion,f=(.9,,.5,,.0)}{vpath (__vp,__op) scaled 1.01 shifted(4, 0.0) rotatedaround(vloc(__vp), 1)}
\fmfi{fermion,f=(.9,,.5,,.0)}{vpath (__vp,__op) scaled 1.01 shifted(4,-2.5) rotatedaround(vloc(__vp),-7)}
\fmfi{fermion,f=(.9,,.5,,.0)}{vpath (__vq,__oq) scaled 1.01 shifted(4,-2.5) rotatedaround(vloc(__vq),-9)}
\fmfi{fermion,f=(.9,,.5,,.0)}{vpath (__vq,__oq) scaled 1.01 shifted(4, 0.0) rotatedaround(vloc(__vq),-1)}
\fmfi{fermion,f=(.9,,.5,,.0)}{vpath (__vq,__oq) scaled 1.01 shifted(4, 2.5) rotatedaround(vloc(__vq),7)}
% mediators
\fmf{phantom,t=0.55}{vt1,om,vt2} % pull gtt vertex to left
\fmf{fermion,t=0.35,label=\color{collep}$\tau$,l.s=right,f=(.1,,.6,,.1)}{vt1,vt2} % t channel
\fmf{boson,t=1,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
\fmf{boson,t=1,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
% taus
\fmffreeze
\fmf{fermion,f=(.1,,.6,,.1)}{t1,vt1} % outgoing lepton
\fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2} % outgoing lepton
% labels
\fmfblob{15}{vp}
\fmfblob{15}{vq}
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
%\fmfv{l=$X$,l.a=20,l.d=12}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
%\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\color{collep}$\tau^+$,l.a=10,l.d=5}{t1}
\fmfv{l=\strut\color{collep}$\tau^-$,l.a=-10,l.d=5}{t2}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{vt1}
\fmfv{decor.shape=circle,f=(.1,,.45,,.1),decor.filled=full,decor.size=4}{vt2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{collep}{rgb}{.1,.6,.1} % lepton (green)
\definecolor{colbl}{rgb}{.1,.1,.7} % vertex (dark blue)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-4,10)(8,10){ % padding (L,T)(R,B)
\begin{fmfgraph*}(150,95) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
\fmfcmd{ % custom line style: double arrows for protons
style_def proton expr p =
save oldpen; pen oldpen; oldpen := currentpen;
pickup oldpen scaled 1.8; % draw thick line
cdraw p; % draw line
cfill (arrow p) % draw arrow
shifted -center p scaled 1.1 shifted center p; % scale arrow
pickup oldpen; % restore line width
enddef;
}
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp,op}
\fmf{proton}{iq,vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% mediators
\fmf{phantom,t=1.5}{vt,om} % pull gtt vertex to left
\fmf{boson,t=1.12,label=$\gamma$,l.d=4,l.s=right}{vp,vt}
\fmf{boson,t=1.12,label=$\gamma$,l.d=3,l.s=left}{vq,vt}
% taus
\fmffreeze
\fmf{phantom,f=(.1,,.6,,.1)}{t1,vt} % outgoing lepton
\fmf{phantom,f=(.1,,.6,,.1)}{vt,t2} % outgoing lepton
\fmfi{fermion,f=(.1,,.6,,.1)}{vpath (__t1,__vt) shifted(0,2)} % outgoing lepton
\fmfi{fermion,f=(.1,,.6,,.1)}{vpath (__vt,__t2) shifted(0,-2)} % outgoing lepton
% labels
\fmfblob{15}{vq}
\fmfblob{15}{vp}
\fmfv{d.s=circle,f=(.1,,.1,,.7),d.f=(.1,,.1,,.7),d.s=4,l.d=12,l.a=0,
l=\normalsize\color{colbl}$C_{\tau B}/\Lambda^2$}{vt}
\fmfblob{18}{vt} % use \fmfv first to give color
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
\fmfv{l=p$^+$,l.a=20,l.d=6}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\color{collep}$\tau^+$,l.a=22,l.d=5}{t1}
\fmfv{l=\strut\color{collep}$\tau^-$,l.a=-22,l.d=5}{t2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{collep}{rgb}{.1,.6,.1} % lepton (green)
\definecolor{colbl}{rgb}{.1,.1,.7} % vertex (dark blue)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-4,10)(8,10){ % padding (L,T)(R,B)
\begin{fmfgraph*}(150,95) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
\fmfcmd{ % custom line style: double arrows for protons
style_def proton expr p =
save oldpen; pen oldpen; oldpen := currentpen;
pickup oldpen scaled 1.8; % draw thick line
cdraw p; % draw line
cfill (arrow p) % draw arrow
shifted -center p scaled 1.1 shifted center p; % scale arrow
pickup oldpen; % restore line width
enddef;
}
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp,op}
\fmf{proton}{iq,vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% mediators
\fmf{phantom,t=0.55}{vt1,om,vt2} % pull gtt vertex to left
\fmf{fermion,t=0.35,label=\color{collep}$\tau$,l.s=right,f=(.1,,.6,,.1)}{vt1,vt2} % t channel
\fmf{boson,t=1,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
\fmf{boson,t=1,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
% taus
\fmffreeze
\fmf{fermion,f=(.1,,.6,,.1)}{t1,vt1} % outgoing lepton
\fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2} % outgoing lepton
% labels
\fmfblob{15}{vp}
\fmfblob{15}{vq}
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
\fmfv{l=p$^+$,l.a=20,l.d=6}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\color{collep}$\tau^+$,l.a=10,l.d=5}{t1}
\fmfv{l=\strut\color{collep}$\tau^-$,l.a=-10,l.d=5}{t2}
\fmfv{decor.shape=circle,decor.filled=empty,decor.size=15,
f=(.1,,.1,,.7),b=(.92,,.92,,.98),l=\large\color{colbl}$g$,l.a=0,l.d=0}{vt1}
\fmfv{decor.shape=circle,decor.filled=empty,decor.size=15,
f=(.1,,.1,,.7),b=(.92,,.92,,.98),l=\large\color{colbl}$g$,l.a=0,l.d=0}{vt2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
Full code
The LaTeX code below collects all the diagrams above into one big file that produces a multipage PDF. Please find download links below, or edit and compile here if you like:
% !TEX program = pdflatexmk
% !TEX parameter = -shell-escape
% Author: Izaak Neutelings (February 2024)
% Description: Anomalous magnetic moment in pp collisions
% Sources: https://cms.cern.ch/iCMS/analysisadmin/cadilines?line=EXO-23-005
% Instructions: To compile via command line, run the following twice
% pdflatex -shell-escape anomalous_momentum_pp.tex
\documentclass[11pt,border=4pt,multi=page,crop]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\usepackage{pgffor} % for \foreach
% DEFINE TEXT COLORS
\definecolor{collep}{rgb}{.1,.6,.1} % lepton (green)
%\definecolor{collep}{rgb}{.75,.0,.0} % lepton (red)
\definecolor{colvtx}{rgb}{.1,.45,.1} % vertex (dark green)
%\definecolor{colvtx}{rgb}{.45,.0,.0} % vertex (dark red)
\definecolor{coldis}{rgb}{.9,.5,.0} % disassociated (orange)
\definecolor{colbl}{rgb}{.1,.1,.7} % vertex (dark blue)
% DEFINE COLOR MACROS
% The following loops over the user color names and defines
% a handy \<colname> command to set text color, as well as
% defines colors in MetaPost of the same and value for lines
\usepackage{pgffor} % for \foreach
\def\MPcolors{} % MetaPost code importing xcolor names
\foreach \colname in {collep,colvtx,coldis,colbl}{ % create command & MetaPost code
\expandafter\xdef\csname\colname\endcsname{\noexpand\color{\colname}}% \newcommand\<colname>
\convertcolorspec{named}{\colname}{rgb}\tmprgb % get rgb code
\xdef\MPcolors{\MPcolors color \colname; \colname := (\tmprgb); } % add color name
}
% DEFINE fmfpicture ENVIRONMENT
% The following defines a custom picture environment that
% helps to create standalone pages with common settings,
% and correctly padding the diagram with \fmfframe
\usepackage{environ} % for \NewEnviron
\NewEnviron{fmfpicture}[3]{%
\begin{page} % to create standalone page
\fmfframe(#1)(#2){ % padding (LT)(RB)
\begin{fmffile}{feynmp-#3} % auxiliary files (use unique name!)
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
\fmfcmd\MPcolors % define custom line colors in MetaPost (does not work in \fmfv)
\fmfcmd{ % custom line style: double arrows for protons
style_def proton expr p =
save oldpen; pen oldpen; oldpen := currentpen;
pickup oldpen scaled 1.8; % draw thick line
cdraw p; % draw line
cfill (arrow p) % draw arrow
shifted -center p scaled 1.1 shifted center p; % scale arrow
pickup oldpen; % restore line width
enddef;
}
\BODY % main code
\end{fmffile}
}
\end{page}
}
\begin{document}
% gamma gamma -> tautau (g-2)
\begin{fmfpicture}{-4,10}{8,10}{gammagamma-tautau} % padding (LT)(RB)
\begin{fmfgraph*}(110,80) % canvas (W,H)
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% photons
\fmf{photon}{i1,v1}
\fmf{photon}{i2,v2}
% taus
\fmf{fermion,t=0.9,label=\collep$\tau$,l.s=right,f=collep}{v1,v2} % t channel
\fmf{fermion,f=collep}{o1,v1} % outgoing top lepton
\fmf{fermion,f=collep}{v2,o2} % outgoing bottom lepton
% labels
\fmfv{l=$\gamma$,l.a=160,l.d=5}{i1}
\fmfv{l=$\gamma$,l.a=-158,l.d=6}{i2}
\fmfv{l=\strut\collep$\tau^+$,l.a=12,l.d=5}{o1}
\fmfv{l=\strut\collep$\tau^-$\vspace{-7pt},l.a=-12,l.d=5}{o2}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{v1}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{v2}
\end{fmfgraph*}
\end{fmfpicture}
% gamma gamma -> tautau (g-2)
\begin{fmfpicture}{-4,10}{8,10}{gammagamma-tautau-blob-g} % padding (LT)(RB)
\begin{fmfgraph*}(110,80) % canvas (W,H)
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% photons
\fmf{photon}{i1,v1}
\fmf{photon}{i2,v2}
% taus
\fmf{fermion,t=0.9,label=\collep$\tau$,l.s=right,f=collep}{v1,v2} % t channel
\fmf{fermion,f=collep}{o1,v1} % outgoing top lepton
\fmf{fermion,f=collep}{v2,o2} % outgoing bottom lepton
% labels
\fmfv{l=$\gamma$,l.a=160,l.d=5}{i1}
\fmfv{l=$\gamma$,l.a=-158,l.d=6}{i2}
\fmfv{l=\strut\collep$\tau^+$,l.a=12,l.d=5}{o1}
\fmfv{l=\strut\collep$\tau^-$\vspace{-7pt},l.a=-12,l.d=5}{o2}
\fmfv{decor.shape=circle,decor.filled=empty,decor.size=15,
f=colbl,b=(.92,,.92,,.98),l=\large\colbl$g$,l.a=0,l.d=0}{v1}
\fmfv{decor.shape=circle,decor.filled=empty,decor.size=15,
f=colbl,b=(.92,,.92,,.98),l=\large\colbl$g$,l.a=0,l.d=0}{v2}
\end{fmfgraph*}
\end{fmfpicture}
% gamma gamma -> ellell (g-2)
\begin{fmfpicture}{-4,10}{8,10}{gammagamma-ellell} % padding (LT)(RB)
\begin{fmfgraph*}(110,80) % canvas (W,H)
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% photons
\fmf{photon}{i1,v1}
\fmf{photon}{i2,v2}
% taus
\fmf{fermion,t=0.9,label=\collep$\ell$,l.s=right,f=collep}{v1,v2} % t channel
\fmf{fermion,f=collep}{o1,v1} % outgoing top lepton
\fmf{fermion,f=collep}{v2,o2} % outgoing bottom lepton
% labels
\fmfv{l=$\gamma$,l.a=160,l.d=5}{i1}
\fmfv{l=$\gamma$,l.a=-158,l.d=6}{i2}
\fmfv{l=\strut\collep$\ell^+$,l.a=12,l.d=5}{o1}
\fmfv{l=\strut\collep$\ell^-$\vspace{-7pt},l.a=-20,l.d=5}{o2}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{v1}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{v2}
\end{fmfgraph*}
\end{fmfpicture}
% gamma gamma -> WW
\begin{fmfpicture}{-4,10}{8,10}{gammagamma-WW} % padding (LT)(RB)
\begin{fmfgraph*}(110,80) % canvas (W,H)
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% photons
\fmf{photon}{i1,v1}
\fmf{photon}{i2,v2}
% bosons
\fmf{boson,t=0.9,label=\coldis W,l.s=right,f=coldis}{v1,v2} % t channel
\fmf{boson,f=coldis}{o1,v1} % outgoing top boson
\fmf{boson,f=coldis}{v2,o2} % outgoing bottom boson
% labels
\fmfv{l=$\gamma$,l.a=160,l.d=5}{i1}
\fmfv{l=$\gamma$,l.a=-158,l.d=6}{i2}
\fmfv{l=\strut\coldis W$^+$,l.a=12,l.d=5}{o1}
\fmfv{l=\strut\coldis W$^-$\vspace{-7pt},l.a=-16,l.d=5}{o2}
%\fmfv{decor.shape=circle,f=coldis,decor.filled=full,decor.size=4}{v1}
%\fmfv{decor.shape=circle,f=coldis,decor.filled=full,decor.size=4}{v2}
\end{fmfgraph*}
\end{fmfpicture}
% pp -> tautau (g-2)
\begin{fmfpicture}{-4,10}{8,10}{pp-tautau} % padding (LT)(RB)
\begin{fmfgraph*}(150,95) % canvas (W,H)
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp,op}
\fmf{proton}{iq,vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% mediators
\fmf{phantom,t=0.55}{vt1,om,vt2} % pull gtt vertex to left
\fmf{fermion,t=0.35,label=\collep$\tau$,l.s=right,f=collep}{vt1,vt2} % t channel
\fmf{boson,t=1,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
\fmf{boson,t=1,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
% taus
\fmffreeze
\fmf{fermion,f=collep}{t1,vt1} % outgoing lepton
\fmf{fermion,f=collep}{vt2,t2} % outgoing lepton
% labels
\fmfblob{15}{vp}
\fmfblob{15}{vq}
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
\fmfv{l=p$^+$,l.a=20,l.d=6}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\collep$\tau^+$,l.a=10,l.d=5}{t1}
\fmfv{l=\strut\collep$\tau^-$,l.a=-10,l.d=5}{t2}
%\fmfv{decor.shape=circle,decor.filled=full,decor.size=5,f=black}{vp}
%\fmfv{decor.shape=circle,decor.filled=full,decor.size=5,f=black}{vq}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{vt1}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{vt2}
\end{fmfgraph*}
\end{fmfpicture}
% pp -> tautau (g-2), single diffractive
\begin{fmfpicture}{-4,18}{8,10}{pp-tautau-SD} % padding (LT)(RB)
\begin{fmfgraph*}(150,100) % canvas (W,H)
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp}
\fmf{phantom}{vp,op}
\fmf{proton}{iq,vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% diffracted proton
\fmfi{fermion,f=coldis}{vpath (__vp,__op) scaled 1.01 shifted(4, 2.5) rotatedaround(vloc(__vp), 9)}
\fmfi{fermion,f=coldis}{vpath (__vp,__op) scaled 1.01 shifted(4, 0.0) rotatedaround(vloc(__vp), 1)}
\fmfi{fermion,f=coldis}{vpath (__vp,__op) scaled 1.01 shifted(4,-2.5) rotatedaround(vloc(__vp),-7)}
% mediators
\fmf{phantom,t=0.55}{vt1,om,vt2} % pull gtt vertex to left
\fmf{fermion,t=0.35,label=\collep$\tau$,l.s=right,f=collep}{vt1,vt2} % t channel
\fmf{boson,t=1,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
\fmf{boson,t=1,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
% taus
\fmffreeze
\fmf{fermion,f=collep}{t1,vt1} % outgoing lepton
\fmf{fermion,f=collep}{vt2,t2} % outgoing lepton
% labels
\fmfblob{15}{vp}
\fmfblob{15}{vq}
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
%\fmfv{l=$X$,l.a=20,l.d=12}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\collep$\tau^+$,l.a=10,l.d=5}{t1}
\fmfv{l=\strut\collep$\tau^-$,l.a=-10,l.d=5}{t2}
%\fmfv{decor.shape=circle,decor.filled=full,decor.size=5,f=black}{vq}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{vt1}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{vt2}
\end{fmfgraph*}
\end{fmfpicture}
% pp -> tautau (g-2), double diffractive
\begin{fmfpicture}{-4,18}{8,18}{pp-tautau-DD} % padding (LT)(RB)
\begin{fmfgraph*}(150,100) % canvas (W,H)
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp}
\fmf{phantom}{vp,op}
\fmf{proton}{iq,vq}
\fmf{phantom}{vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% diffracted proton
\fmfi{fermion,f=coldis}{vpath (__vp,__op) scaled 1.01 shifted(4, 2.5) rotatedaround(vloc(__vp), 9)}
\fmfi{fermion,f=coldis}{vpath (__vp,__op) scaled 1.01 shifted(4, 0.0) rotatedaround(vloc(__vp), 1)}
\fmfi{fermion,f=coldis}{vpath (__vp,__op) scaled 1.01 shifted(4,-2.5) rotatedaround(vloc(__vp),-7)}
\fmfi{fermion,f=coldis}{vpath (__vq,__oq) scaled 1.01 shifted(4,-2.5) rotatedaround(vloc(__vq),-9)}
\fmfi{fermion,f=coldis}{vpath (__vq,__oq) scaled 1.01 shifted(4, 0.0) rotatedaround(vloc(__vq),-1)}
\fmfi{fermion,f=coldis}{vpath (__vq,__oq) scaled 1.01 shifted(4, 2.5) rotatedaround(vloc(__vq),7)}
% mediators
\fmf{phantom,t=0.55}{vt1,om,vt2} % pull gtt vertex to left
\fmf{fermion,t=0.35,label=\collep$\tau$,l.s=right,f=collep}{vt1,vt2} % t channel
\fmf{boson,t=1,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
\fmf{boson,t=1,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
% taus
\fmffreeze
\fmf{fermion,f=collep}{t1,vt1} % outgoing lepton
\fmf{fermion,f=collep}{vt2,t2} % outgoing lepton
% labels
\fmfblob{15}{vp}
\fmfblob{15}{vq}
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
%\fmfv{l=$X$,l.a=20,l.d=12}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
%\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\collep$\tau^+$,l.a=10,l.d=5}{t1}
\fmfv{l=\strut\collep$\tau^-$,l.a=-10,l.d=5}{t2}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{vt1}
\fmfv{decor.shape=circle,f=colvtx,decor.filled=full,decor.size=4}{vt2}
\end{fmfgraph*}
\end{fmfpicture}
% pp -> tautau blob (g-2)
\begin{fmfpicture}{-4,10}{8,10}{pp-tautau-blob} % padding (LT)(RB)
\begin{fmfgraph*}(150,95) % canvas (W,H)
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp,op}
\fmf{proton}{iq,vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% mediators
\fmf{phantom,t=1.5}{vt,om} % pull gtt vertex to left
\fmf{boson,t=1.12,label=$\gamma$,l.d=4,l.s=right}{vp,vt}
\fmf{boson,t=1.12,label=$\gamma$,l.d=3,l.s=left}{vq,vt}
% taus
\fmffreeze
\fmf{phantom,f=collep}{t1,vt} % outgoing lepton
\fmf{phantom,f=collep}{vt,t2} % outgoing lepton
\fmfi{fermion,f=collep}{vpath (__t1,__vt) shifted(0,2)} % outgoing lepton
\fmfi{fermion,f=collep}{vpath (__vt,__t2) shifted(0,-2)} % outgoing lepton
% labels
\fmfblob{15}{vq}
\fmfblob{15}{vp}
\fmfv{d.s=circle,f=colbl,d.f=full,d.s=4,l.d=12,l.a=0,
l=\normalsize\colbl$C_{\tau B}/\Lambda^2$}{vt}
\fmfblob{18}{vt} % use \fmfv first to give color
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
\fmfv{l=p$^+$,l.a=20,l.d=6}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\collep$\tau^+$,l.a=22,l.d=5}{t1}
\fmfv{l=\strut\collep$\tau^-$,l.a=-22,l.d=5}{t2}
\end{fmfgraph*}
\end{fmfpicture}
% pp -> tautau (g-2)
\begin{fmfpicture}{-4,10}{8,10}{pp-tautau-blob-g} % padding (LT)(RB)
\begin{fmfgraph*}(150,95) % canvas (W,H)
% external vertices
\fmfleft{iq,im,ip}
\fmfright{oq,t2,om,t1,op}
\fmfshift{2 down}{t1}
\fmfshift{2 up}{t2}
% protons
\fmf{proton}{ip,vp,op}
\fmf{proton}{iq,vq,oq}
% skeleton
\fmf{phantom,t=0.4}{ip,vp} % pull to right
\fmf{phantom,t=0.4}{iq,vq} % pull to right
\fmf{phantom,t=0.2}{vp,vq} % t channel
\fmffreeze
% mediators
\fmf{phantom,t=0.55}{vt1,om,vt2} % pull gtt vertex to left
\fmf{fermion,t=0.35,label=\collep$\tau$,l.s=right,f=collep}{vt1,vt2} % t channel
\fmf{boson,t=1,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
\fmf{boson,t=1,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
% taus
\fmffreeze
\fmf{fermion,f=collep}{t1,vt1} % outgoing lepton
\fmf{fermion,f=collep}{vt2,t2} % outgoing lepton
% labels
\fmfblob{15}{vp}
\fmfblob{15}{vq}
\fmfv{l=p$^+$,l.a=160,l.d=5}{ip}
\fmfv{l=p$^+$,l.a=20,l.d=6}{op}
\fmfv{l=p$^+$,l.a=-160,l.d=5}{iq}
\fmfv{l=p$^+$,l.a=-20,l.d=6}{oq}
\fmfv{l=\strut\collep$\tau^+$,l.a=10,l.d=5}{t1}
\fmfv{l=\strut\collep$\tau^-$,l.a=-10,l.d=5}{t2}
\fmfv{decor.shape=circle,decor.filled=empty,decor.size=15,
f=colbl,b=(.92,,.92,,.98),l=\large\colbl$g$,l.a=0,l.d=0}{vt1}
\fmfv{decor.shape=circle,decor.filled=empty,decor.size=15,
f=colbl,b=(.92,,.92,,.98),l=\large\colbl$g$,l.a=0,l.d=0}{vt2}
\end{fmfgraph*}
\end{fmfpicture}
\end{document}Click to download: g-2_pp_tautau.tex • g-2_pp_tautau.pdf
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