  Cuprate high-T_c superconductors on the Mott-insulating side of "optimal
doping" (with respect to the highest T_c's) exhibit enigmatic behavior in the
non-superconducting state. Near optimal doping the transport and spectroscopic
properties are unlike those of a Landau-Fermi liquid. For carrier
concentrations below optimal doping a pseudogap removes quasi-particle spectral
weight from parts of the Fermi surface, and causes a break-up of the Fermi
surface into disconnected nodal and anti-nodal sectors. Here we show that the
near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. Our
optical measurements reveal that the dynamical relaxation rate 1/tau(omega,T)
collapses on a universal function proportional to (hbar omega)^2+(1.5 pi k_B
T)^2. Hints at possible Fermi liquid behavior came from the recent discovery of
quantum oscillations at low temperature and high magnetic field in underdoped
YBa2Cu3O6+d and YBa2Cu4O8, from the observed T^2-dependence of the DC
({\omega}=0) resistivity for both overdoped and underdoped cuprates, and from
the two-fluid analysis of nuclear magnetic resonance data. However, the direct
spectroscopic determination of the energy dependence of the life-time of the
excitations -provided by our measurements- has been elusive up to now. This
observation defies the standard lore of non-Fermi liquid physics in high T_c
cuprates on the underdoped side of the phase diagram.
