Two Point No Cutoff
Two-point propagator flow without cutoff derivative
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two-point-no-cutoff.tex (56 lines)
\documentclass[tikz]{standalone}
\usetikzlibrary{patterns,decorations.markings}
\tikzset{
dressed/.style={fill=white,postaction={pattern=north east lines}},
momentum/.style={->,semithick,yshift=5pt,shorten >=5pt,shorten <=5pt},
loop/.style 2 args={thick,decoration={markings,mark=at position {#1} with {\arrow{>},\node[anchor=\pgfdecoratedangle-90,font=\footnotesize] {$p_{#2}$};}},postaction={decorate}},
label/.style={thin,gray,shorten <=-1ex}
}
\def\lrad{1}
\def\mrad{0.175*\lrad}
\def\srad{0.15*\lrad}
\begin{document}
% Diagram 1
\begin{tikzpicture}
% Loop
\draw[loop/.list={{0.125}{1},{0.125*3}{2},{0.125*5}{3},{0.125*7}{4}}] (0,0) circle (\lrad);
\draw[dressed] (0,\lrad) circle (\srad) node[above=2pt] {$G_{k,ij}(p_1,p_2)$};
\draw[dressed] (0,-\lrad) circle (\srad) node[below=3pt] {$G_{k,kl}(p_3,p_4)$};
% External lines
\draw (-2*\lrad,0) coordinate (xl) -- (-\lrad,0) node[pos=0.4,below] {$\varphi_a$};
\draw[momentum] (-2*\lrad,0) -- (-1.25*\lrad,0) node[midway,above] {$q_1$};
\draw (\lrad,0) -- (2*\lrad,0) coordinate (xr) node[pos=0.6,below] {$\varphi_b$};
\draw[momentum] (1.25*\lrad,0) -- (2*\lrad,0) node[midway,above] {$q_2$};
% Vertices
\node at (-2.1*\lrad,\lrad) (Gkajk) {$\Gamma_{k,ajk}^{(3)}(q_1,p_2,-p_3)$};
\draw[label] (Gkajk.-30) -- (-\lrad,0);
\draw[dressed] (-\lrad,0) circle (\mrad);
\node at (2.1*\lrad,\lrad) (Gkbli) {$\Gamma_{k,bli}^{(3)}(-q_2,-p_1,p_4)$};
\draw[label] (Gkbli.-150) -- (\lrad,0);
\draw[dressed] (\lrad,0) circle (\mrad);
\end{tikzpicture}
% Diagram 2
\begin{tikzpicture}
% Loop
\draw[loop/.list={{0}{1},{0.125*4}{2}}] (0,0) circle (\lrad);
\draw[dressed] (0,\lrad,0) circle (\srad) node[above=2pt] {$G_{k,ij}(p_1,p_2)$};
% External lines
\draw (-2*\lrad,-\lrad) node[left] {$\varphi_a$} -- (2*\lrad,-\lrad) node[right] {$\varphi_b$};
\draw[momentum] (-2*\lrad,-\lrad) -- (-\lrad,-\lrad) node[midway,above] {$q_1$};
\draw[momentum] (\lrad,-\lrad) -- (2*\lrad,-\lrad) node[midway,above] {$q_2$};
% Vertices
\draw[dressed] (0,-\lrad) circle (\mrad) node[below] {$\Gamma_{k,abji}^{(4)}(q_1,-q_2,-p_1,p_2)$};
\end{tikzpicture}
\end{document}
Typst
two-point-no-cutoff.typ (213 lines)
#import "@preview/cetz:0.3.4": canvas, draw
#import "@preview/modpattern:0.1.0": modpattern
#import draw: line, content, circle, mark
#set page(width: auto, height: auto, margin: 8pt)
// Define styles and constants
#let radius = 1.25
#let med-rad = 0.175 * radius
#let small-rad = 0.15 * radius
// Create hatched pattern for vertices
#let hatched = modpattern(
(.1cm, .1cm),
std.line(start: (0%, 100%), end: (100%, 0%), stroke: 0.5pt),
background: white,
)
// Helper function for dressed vertices
#let dressed-vertex(pos, label: none, rel-label: (0, 0), name: none, radius: small-rad, ..rest) = {
circle(pos, radius: radius, fill: hatched, name: name, stroke: 0.5pt)
if label != none {
let label-pos = if rel-label != none { (rel: rel-label, to: pos) } else { pos }
content(label-pos, $#label$, ..rest)
}
}
#canvas({
// First diagram
// Main loop
circle((0, 0), radius: radius, stroke: 1pt, name: "loop")
// Add momentum arrows and labels around loop
for (ii, pos) in ((1, "0.125"), (2, "0.375"), (3, "0.625"), (4, "0.875")) {
let angle = float(pos) * 360
let label-angle = (angle - 3) * 1deg
// Add momentum labels
let rel-pos = (0.75 * radius * calc.cos(label-angle), 0.75 * radius * calc.sin(label-angle))
content(
(rel: rel-pos, to: "loop"),
$p_#ii$,
size: 8pt,
)
// Add arrow marks
mark(
symbol: "stealth",
(name: "loop", anchor: angle * 1deg),
(name: "loop", anchor: (angle + 1) * 1deg),
..(width: .25, length: .15, stroke: .7pt, angle: 60deg, scale: .7, fill: black),
)
}
// Add dressed vertices with propagators
dressed-vertex(
(0, radius),
label: $G_(k,i j)(p_1,p_2)$,
rel-label: (0, 0.2),
name: "vertex-top",
anchor: "south",
)
dressed-vertex(
(0, -radius),
label: $G_(k,k l)(p_3,p_4)$,
rel-label: (0, -0.3),
name: "vertex-bottom",
anchor: "north",
)
// External lines
line((-2 * radius, 0), (-radius, 0), stroke: 1pt, name: "left-external")
line((radius, 0), (2 * radius, 0), stroke: 1pt, name: "right-external")
// External line labels
content("left-external.start", $phi_a$, anchor: "east", padding: 0.1)
content("right-external.end", $phi_b$, anchor: "west", padding: 0.1)
// External momentum arrows
let arrow-style = (
mark: (end: "stealth", fill: black, scale: .5),
stroke: (thickness: 0.75pt),
)
line(
(-1.9 * radius, 0.15),
(-1.3 * radius, 0.15),
..arrow-style,
name: "q1-arrow",
)
content((rel: (0, 0.3), to: "q1-arrow.mid"), $q_1$)
line(
(1.3 * radius, 0.15),
(1.9 * radius, 0.15),
..arrow-style,
name: "q2-arrow",
)
content((rel: (0, 0.3), to: "q2-arrow.mid"), $q_2$)
// Vertex labels with connecting lines
let label-style = (stroke: gray + 0.3pt)
content(
(-2.1 * radius, radius),
$Gamma_(k,a j k)^((3))(q_1,p_2,-p_3)$,
name: "left-gamma",
)
line(
"left-gamma",
(-radius, 0),
..label-style,
)
content(
(2.1 * radius, radius),
$Gamma_(k,b l i)^((3))(-q_2,-p_1,p_4)$,
name: "right-gamma",
)
line(
"right-gamma",
(radius, 0),
..label-style,
)
// External vertices
dressed-vertex(
(-radius, 0),
radius: med-rad,
name: "vertex-left-external",
)
dressed-vertex(
(radius, 0),
radius: med-rad,
name: "vertex-right-external",
)
})
#pagebreak()
#canvas({
// Second diagram
// Main loop
circle((0, 0), radius: radius, stroke: 1pt, name: "loop")
// Add momentum arrows and labels around loop
for (ii, pos) in ((1, "0"), (2, "0.5")) {
let angle = float(pos) * 360
let label-angle = (angle - 3) * 1deg
// Add momentum labels
let rel-pos = (0.75 * radius * calc.cos(label-angle), 0.75 * radius * calc.sin(label-angle))
content(
(rel: rel-pos, to: "loop"),
$p_#ii$,
size: 8pt,
)
// Add arrow marks
mark(
symbol: "stealth",
(name: "loop", anchor: angle * 1deg),
(name: "loop", anchor: (angle + 1) * 1deg),
..(width: .25, length: .15, stroke: .7pt, angle: 60deg, scale: .7, fill: black),
)
}
// Add dressed vertex with propagator
dressed-vertex(
(0, radius),
label: $G_(k,i j)(p_1,p_2)$,
rel-label: (0, 0.2),
name: "vertex-top",
anchor: "south",
)
// External line
line((-2 * radius, -radius), (2 * radius, -radius), stroke: 1pt, name: "external")
// External line labels
content((rel: (-0.1, 0), to: "external.start"), $phi_a$, anchor: "east")
content((rel: (0.1, 0), to: "external.end"), $phi_b$, anchor: "west")
// External momentum arrows
let arrow-style = (
mark: (end: "stealth", fill: black, scale: .5),
stroke: (thickness: 0.75pt),
)
line(
(-1.9 * radius, -radius + 0.15),
(-1.3 * radius, -radius + 0.15),
..arrow-style,
name: "q1-arrow",
)
content((rel: (0, 0.3), to: "q1-arrow.mid"), $q_1$)
line(
(1.3 * radius, -radius + 0.15),
(1.9 * radius, -radius + 0.15),
..arrow-style,
name: "q2-arrow",
)
content((rel: (0, 0.3), to: "q2-arrow.mid"), $q_2$)
// Four-vertex with label
dressed-vertex(
(0, -radius),
label: $Gamma_(k,a b j i)^((4))(q_1,-q_2,-p_1,p_2)$,
rel-label: (0, -0.3),
radius: med-rad,
anchor: "north",
)
})