The vertex of angle $\alpha$ is at the origin, its initial side coincides with the positive $x$-axis, and two points on its terminal side are $A ( 1 , a )$ and $B ( 2 , b )$. If $\cos 2 \alpha = \frac { 2 } { 3 }$, then $| a - b | =$
A. $\frac { 1 } { 5 }$\\
B. $\frac { \sqrt { 5 } } { 5 }$\\
C. $\frac { 2 \sqrt { 5 } } { 5 }$\\
D. (incomplete)