 codex/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2004/iii/paper-44-compton-diagrams.py

"""Original diagram sketches. Python 3.14, NumPy and Matplotlib from root pyproject."""
from pathlib import Path
import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
from matplotlib.patches import FancyArrowPatch

BLUE="#184e79"
PURPLE="#71498c"
RED="#b13333"

def line(ax,p,q,arrow=True):
    ax.plot([p[0],q[0]],[p[1],q[1]],color=BLUE,lw=1.8)
    if arrow:
        p,q=np.asarray(p),np.asarray(q)
        a=p+.44*(q-p);b=p+.59*(q-p)
        ax.add_patch(FancyArrowPatch(a,b,arrowstyle="-|>",mutation_scale=11,
                                    color=BLUE,linewidth=1.3))

def wave(ax,p,q,cycles=6):
    p,q=np.array(p,float),np.array(q,float)
    d=q-p;n=np.array([-d[1],d[0]])/np.linalg.norm(d)
    t=np.linspace(0,1,260)
    pts=p[:,None]+d[:,None]*t+n[:,None]*(.052*np.sin(cycles*2*np.pi*t))
    ax.plot(pts[0],pts[1],color=PURPLE,lw=1.3)

def arch(ax,a,b,h=.86):
    t=np.linspace(0,1,300)
    dx=b-a
    x=a+dx*t;y=h*np.sin(np.pi*t)
    tangent=np.array([np.full_like(t,dx),h*np.pi*np.cos(np.pi*t)])
    norm=np.array([-tangent[1],tangent[0]])/np.sqrt(np.sum(tangent*tangent,axis=0))
    x,y=np.array([x,y])+norm*(.042*np.sin(14*np.pi*t))
    ax.plot(x,y,color=PURPLE,lw=1.25)
    ax.plot([a,b],[0,0],"o",color=BLUE,ms=3)

def electron(ax,y=0):
    line(ax,(0,y),(5,y))
    ax.text(-.08,y+.16,r"$p$",fontsize=10)
    ax.text(5.0,y+.16,r"$p'$",fontsize=10)

def photons(ax,a,b,crossed=False,bubble=False):
    labels=[r"$k'$ (out)",r"$k$ (in)"] if crossed else [r"$k$ (in)",r"$k'$ (out)"]
    lower=[(a-.35,-1.34),(b+.35,-1.34)]
    for i,(x,lo) in enumerate(zip([a,b],lower)):
        if bubble and i==0:
            cx=x-.35;cy=-.82;rx=.33;ry=.28
            wave(ax,(cx,-1.34),(cx,cy-ry),3)
            ts=np.linspace(0,2*np.pi,160)
            ax.plot(cx+rx*np.cos(ts),cy+ry*np.sin(ts),color=BLUE,lw=1.5)
            t0=2.4;t1=2.8
            p=(cx+rx*np.cos(t0),cy+ry*np.sin(t0))
            q=(cx+rx*np.cos(t1),cy+ry*np.sin(t1))
            ax.add_patch(FancyArrowPatch(p,q,arrowstyle="-|>",mutation_scale=10,color=BLUE))
            for yy in [cy-ry,cy+ry]:ax.plot([cx],[yy],"o",color=BLUE,ms=3)
            wave(ax,(cx,cy+ry),(x,0),3)
        else:wave(ax,lo,(x,0))
        ax.plot([x],[0],"o",color=BLUE,ms=3)
        ax.text(lo[0],-1.58,labels[i],ha="center",fontsize=10)

def cross(ax,x,y=0):
    ax.plot([x-.11,x+.11],[y-.11,y+.11],color=RED,lw=1.8)
    ax.plot([x-.11,x+.11],[y+.11,y-.11],color=RED,lw=1.8)

def panel(ax,title):
    ax.set_xlim(-.4,5.4);ax.set_ylim(-1.95,1.4);ax.axis("off")
    ax.set_title(title,fontsize=12,pad=8)

def main():
    fig,axs=plt.subplots(2,3,figsize=(13.2,8.4),dpi=100,facecolor="white")
    spec=[("Tree: s channel",1.6,3.4,None,False),
          ("Tree: u channel",1.6,3.4,None,True),
          ("Internal electron self-energy",.8,4.2,(2.0,3.0),False),
          ("First photon vertex correction",1.6,4.2,(.65,2.65),False),
          ("Second photon vertex correction",.8,3.4,(2.35,4.4),False),
          ("Virtual photon spans both vertices",1.65,3.35,(.6,4.4),False)]
    for ax,(title,a,b,loop,swapped) in zip(axs.flat,spec):
        panel(ax,title);electron(ax);photons(ax,a,b,swapped)
        if loop:arch(ax,*loop)
    fig.suptitle("Compton scattering: tree order e² and internal one-loop order e⁴",fontsize=16)
    fig.text(.5,.025,"Each of the four loop panels also has the crossed external-photon ordering.",ha="center",fontsize=12)
    fig.subplots_adjust(left=.03,right=.98,top=.91,bottom=.08,wspace=.18,hspace=.40)
    fig.savefig(Path.cwd()/"paper-44-compton-diagrams.png",facecolor="white",transparent=False)
    plt.close(fig)

if __name__=="__main__":
    main()