  We discover a universal scaling law for the quasiparticle Nernst coefficient
in underdoped cuprates, whose magnitude decreases exponentially with increasing
temperature as confirmed in YBa$_2$Cu$_3$O$_y$. We attribute it to the basic
mathematical structure of the conductivity formula with a narrow effective
bandwidth of nonzero Berry curvatures associated with the pseudogap. A unified
scheme is then developed to analyze transverse transport in hole-doped cuprates
and clarify the puzzling disparity in determining the pseudogap temperature
from different measurements. Our proposal opens the avenue for exploring
potential scaling laws in the intermediate temperature region and may have
broad applications in strongly correlated or narrow band systems.
