A particle \(Q\) of mass \(m\) is attached to a fixed point \(O\) by a light inextensible string of length \(a\). The particle moves in complete vertical circles about \(O\). The points \(A\) and \(B\) are on the path of \(Q\) with \(A B\) a diameter of the circle. \(O A\) makes an angle of \(60^{\circ}\) with the downward vertical through \(O\) and \(O B\) makes an angle of \(60^{\circ}\) with the upward vertical through \(O\). The speed of \(Q\) when it is at \(A\) is \(2 \sqrt{a g}\).

Given that \(T_{A}\) and \(T_{B}\) are the tensions in the string at \(A\) and \(B\) respectively, find the ratio \(T_{A}: T_{B}\).