Playground 14

Loop Diagrams and Renormalization Flow

Compare tree and loop diagrams, follow loop momentum into the ultraviolet, then see how bare parameters plus corrections become the measured, scale-dependent quantities.

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Current build step
1. Tree and loop diagrams are compared
0%
Bare
0.48
Correction
0.49
Measured
0.97

Loop Flow Build

treeloop
Where the problem comes from
Tree graphs have fixed kinematics, but loop graphs integrate over internal momentum. The ultraviolet tail is where the divergence pressure comes from.
Renormalized parameter
gmeas=gbare+δgg_{\rm meas} = g_{\rm bare} + \delta g
The bare parameter is not the directly observed one. Counterterms and corrections are organized so the measured quantity stays finite.
Bare
0.48
Correction
+ 0.49
Measured
= 0.97
Running coupling
coupling at scale μ1.00