  Directional coupling of Thornber-Feynman polarization with the high-Tc ARPES
distribution specifies the optimum flatband pseudogap \Delta and mobile
localized quasiparticle. This coupling peaks by tuning the statistics and
interaction energy to produce stable short-ranged directional pairing that
reflects the lattice asymmetry. Analogous energy gap and BCS ratio parameters
are identified for low-Tc long-range acoustical phonons and for
quark-anti-quark tightly bound chiral pions in particle physics.
