将函数 f(x)=cos2xf\left( x\right) = \cos {2x}f(x)=cos2x 的图象向右平移 φ(0<φ<π2)\varphi \left( {0 < \varphi < \frac{\pi }{2}}\right)φ(0<φ<2π) 个单位后得到函数 g(x)g\left( x\right)g(x) 的图象,若对满足 ∣f(x1)−g(x2)∣=2\left| {f\left( {x}_{1}\right) - g\left( {x}_{2}\right) }\right| = 2∣f(x1)−g(x2)∣=2 的 x1,x2{x}_{1},{x}_{2}x1,x2 ,有 ∣x1−x2∣min=π3{\left| {x}_{1} - {x}_{2}\right| }_{\min } = \frac{\pi }{3}∣x1−x2∣min=3π ,则 φ=\varphi =φ= ( )A. π6\frac{\pi }{6}6πB. π4\frac{\pi }{4}4πC. π3\frac{\pi }{3}3πD. 5π12\frac{5\pi }{12}125π