High resolution measurements of superfluid density and broadband quasiparticle conductivity have been used to probe the low energy excitation spectrum of nodal quasiparticles in underdoped YBCO. Penetration depth is measured to temperatures as low as
0.05 K. Microwave conductivity is measured from 0.1 to 20 GHz and is a direct probe of zero-energy quasiparticles. The data are compared with predictions for a number of theoretical scenarios that compete with or otherwise modify pure d-wave superconductivity, in particular commensurate and incommensurate spin and charge density waves; d + i s and d + i d superconductivity; circulating current phases; and the BCS--BEC crossover. We conclude that the data are consistent with a pure d-wave state in the presence of a small amount of strong scattering disorder, and are able to rule out most candidate competing states either completely, or to a level set by the energy scale of the disorder, ~ 4 K. Commensurate spin and charge density orders, however, are not expected to alter the nodal spectrum and therefore cannot be excluded.
