Constant effective mass across the phase diagram of high-T$_{c}$ cuprates

We investigate the hole dynamics in two prototypical high temperature superconducting systems: La$_{2-x}$Sr$_{x}$CuO$_{4}$ and YBa$_{2}$Cu$_{3}% $O$_{y}$ using a combination of DC transport and infrared spectroscopy. By exploring the effective spectral weight obtained with optics in conjunction with DC Hall results we find that the transition to the Mott insulating state in these systems is of the vanishing carrier number type since we observe no substantial enhancement of the mass as one proceeds to undoped phases. Further, the effective mass remains constant across the entire underdoped regime of the phase diagram. We discuss the implications of these results for the understanding of both transport phenomena and pairing mechanism in high-T$_{c}$ systems.