External substrate Core Counter-rotating boundary (width δ) Incoming dc1 / modon wavevector k b θ Fermion vortex boundary Phase shift δ₀ from core scattering K_d (dissipative) Energy transfer → g' K_r (reactive) Phase shift → g K_d / K_r = α_mf = tan²θ_W sin²θ_W = α_mf / (1 + α_mf)

Scattering geometry of a dc1 quasiparticle (or modon) approaching a fermion’s counter-rotating boundary. The dissipative channel K_d transfers energy across the boundary (→ hypercharge coupling g’), while the reactive channel K_r deflects without energy transfer (→ isospin coupling g). Their ratio determines the Weinberg angle: sin²θ_W = K_d/(K_d + K_r).