  Dynamical mean field theory is used to study the quantum critical point (QCP)
in the doped Hubbard model on a square lattice. The QCP is characterized by a
universal scaling form of the self energy and a spin density wave instability
at an incommensurate wave vector. The scaling form unifies the low energy kink
and the high energy waterfall feature in the spectral function, while the spin
dynamics includes both the critical incommensurate and high energy
antiferromagnetic paramagnons. We use the frequency dependent four-point
correlation function of spin operators to calculate the momentum dependent
correction to the electron self energy. Our results reveal a substantial
difference with the calculations based on the Spin-Fermion model which
indicates that the frequency dependence of the the quasiparitcle-paramagnon
vertices is an important factor.
