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The strange-metal phase of the cuprate high temperature superconductors,above where the superconductivity sets in as a function of temperature, iswidely considered more exotic and mysterious than the superconductivity itself.Here, based upon detailed angle resolved photoemission spectroscopymeasurements of Bi$_2$Sr$_2$CaCu$_2$O$_8$$_+$$_\delta$ over a wide range ofdoping levels, we present a new unifying phenomenology for the non-Fermi liquidnormal-state interactions (scattering rates) in the nodal direction. This newphenomenology has a continuously varying power law exponent (hence named aPower Law Liquid or PLL), which with doping varies smoothly from a quadraticFermi Liquid to a linear Marginal Fermi Liquid and beyond. Using the extractedPLL parameters we can calculate the optics and resistivity over a wide range ofdoping and normal-state temperature values, with the results closely matchingthe experimental curves. This agreement includes the presence of the$"$pseudogap$"$ temperature scale observed in the resistivity curves includingthe apparent quantum critical point. This breaks the direct link to thepseudogapping of antinodal spectral weight observed at similar (but here arguedto be different) temperature scales, and also gives a new direction forsearches of the microscopic mechanism at the heart of these and perhaps manyother non-Fermi-liquid systems.

Power Law Liquid - A Unified Form of Low-Energy Nodal Electronic Interactions in Hole Doped Cuprate Superconductors