  In underdoped cuprates, only a portion of the Fermi surface survives as Fermi
arcs due to pseudogap opening. In hole-doped La$_{2}$CuO$_4$, we have deduced
the "coherence temperature" $T_{coh}$ of quasi-particles on the Fermi arc above
which the broadened leading edge position in angle-integrated photoemission
spectra is shifted away from the Fermi level and the quasi-particle concept
starts to lose its meaning. $T_{coh}$ is found to rapidly increase with hole
doping, an opposite behavior to the pseudogap temperature $T^*$. The
superconducting dome is thus located below both $T^*$ and $T_{coh}$, indicating
that the superconductivity emerges out of the coherent Fermionic
quasi-particles on the Fermi arc. $T_{coh}$ remains small in the underdoped
region, indicating that incoherent charge carriers originating from the Fermi
arc are responsible for the apparently metallic transport at high temperatures.
