Let $E:\ \dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1,\ a>b$ and $H:\ \dfrac{x^{2}}{A^{2}}-\dfrac{y^{2}}{B^{2}}=1$. Let the distance between the foci of $E$ and the foci of $H$ be $2\sqrt{3}$. If $a-A=2$, and the ratio of the eccentricities of $E$ and $H$ is $\dfrac{1}{3}$, then the sum of the lengths of their latus recta is equal to: