  We study the systematic doping evolution of nodal dispersions by in-situ
angle-resolved photoemission spectroscopy on the continuously doped surface of
a high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$. We reveal that
the nodal dispersion has three segments separated by two kinks, located at ~10
meV and roughly 70 meV, respectively. The three segments have different band
velocities and different doping dependence. In particular, the velocity of the
high-energy segment increases monotonically as the doping level decreases and
can even surpass the bare band velocity. We propose that electron
fractionalization is a possible cause for this anomalous nodal dispersion and
may even play a key role in the understanding of exotic properties of cuprates.
