Integrate the given function over the given surface.
\begin{equation}\begin{array}{l}{\text { Spherical cap } H(x, y, z)=y z, \text { over the part of the sphere }} \\ {x^{2}+y^{2}+z^{2}=4 \text { that lies above the cone } z=\sqrt{x^{2}+y^{2}}}\end{array}\end{equation}