2. For a regular quadrilateral pyramid, the ratio of the area of a diagonal section to the area of a side face is $\sqrt{6}: 2$, then the angle between the side face and the base is . $\qquad$
2. $\frac{\pi}{3}$ Detailed Explanation: Let the side length of the square base be 1, the height of the pyramid be $h$, and the height of the side triangle be $l$, then $A C=\sqrt{2}, \frac{\sqrt{6}}{2}=$ $\frac{\sqrt{2} h}{l}$, then $\sin \angle P M H=\frac{h}{l}=\frac{\sqrt{3}}{2}, \angle P M H=\frac{\pi}{3}$.