Scattering Loop Amplitude Workbench
Simulate high-order Feynman loop diagrams, planar dual momentum kinematics, and infrared dimensional regularization poles from Tree level ($L=0$) to the historic Nine-Loop ($L=9$) amplitude frontier.
Scattering Amplitudes, Loop Expansions & The Nine-Loop Milestone
Why are scattering amplitudes difficult to compute?
In quantum field theory (QFT), predicting collision outcomes requires summing every possible virtual particle path. Each additional closed loop adds four continuous dimensions of unconstrained momentum integration ($d^4 k$), leading to factorial growth in algebraic complexity, tensor reduction, and overlapping infrared singularities.
What makes N=4 Super-Yang-Mills special?
Maximal $\mathcal{N}=4$ supersymmetric Yang-Mills is often described as the "harmonic oscillator of four-dimensional QFT." Due to dual conformal symmetry and the amptuhedron geometry, its amplitudes exhibit maximal transcendentality: an $L$-loop amplitude evaluates purely to multiple polylogarithms of weight $2L$, making it the vanguard for multi-loop methods.
What was achieved at Nine Loops?
Computing an amplitude at nine loops involves evaluating integrals with 28 propagators, managing 18th-order poles in dimensional regularization ($1/\epsilon^{18}$), and resolving the symbol alphabet across thousands of differential equations. AI models assisting in algebraic symbol integration pushed beyond previous eight-loop analytic bounds.