  The emergence of the coherent quasiparticle peak and the development of the
peak-dip-hump structure in the anti-nodal region below $T_{c}$ is the most
prominent non-BCS signature of the underdoped high-$T_{c}$ cuprates, in which
no coherent quasiparticle can be defined in the anti-nodal region above
$T_{c}$. The peak-dip-hump structure has been commonly interpreted as the
result of the coupling of the electron to some Bosonic mode. However, such an
electron-Boson coupling picture does not answer the question of \textit{why the
quasiparticle dispersion is so flat in the anti-nodal region}, a behavior
totally unexpected for Bogoliubov quasiparticle in a d-wave BCS superconductor.
Here we show that the sharp quasiparticle peak in the anti-nodal region should
be understood as a new pole in the electron Green's function generated by the
strong coupling of the electron to diffusive spin fluctuation around the
antiferromagnetic wave vector $\mathbf{Q}=(\pi,\pi)$, rather than a nearly free
Bogoliubov quasiparticle in a d-wave BCS superconductor. More specifically, we
find that the normal self-energy of the electron from the scattering with the
diffusive spin fluctuation manifests itself mainly as a level repulsion effect
and is responsible for the reduction of both the quasiparticle dispersion and
the quasiparticle dissipation rate in the anti-nodal region. We argue that the
peak-dip separation in the anti-nodal spectrum should not be interpreted as the
energy of the pairing glue.
