I got confused with Eq.9.7.7 f(x_new) <= f(x_old)+alpha*(del_f dot (x_new-x_old)).
Because delta_x=x_new - x_old (9.7.2), del_f dot delta_x = -F dot F (Eq.9.7.5), and f=1/2 F dot F (Eq.9.7.4), Eq.9.7.7 can be reduced to f(x_new) <= f(x_old)-alpha*(2f), or f(x_new) <= (1-2*alpha)*f.
Therefore, when alpha=1e-4, the criterion Eq.9.7.7 becomes f(x_new)<=0.9998f(x_old).
Is that correct, or I got lost somewhere?

You are correct IF one takes the full Newton step (9.7.3). The point is to develop a robust algorithm even when backtracking along the Newton step.

Saul Teukolsky