Fermi surface arcs and the infrared conductivity of underdoped YBa₂Cu₃O_(6.50)

We reanalyze the data on the in-plane far infrared conductivity of underdoped orthoII YBa$_{2}$Cu$_{3}$O$_{6.50}$ (YBCO$_{6.50}$) in terms of a model in which a pseudogap opens on part of the Fermi surface with the remaining ungaped piece proportional to the temperature. The motivation for our model comes from recent angle-resolved photoemission spectroscopy data in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212), which have revealed the existence of arcs on the Fermi surface. We find the optical data to be consistent with arc formation. In addition we find some evidence that the electronic states lost below the pseudogap energy $\Delta_{pg}$ are recovered in the energy region immediately above it at least for temperatures near $T_c$.