For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to $1$ per unit (pu), and the differences of the voltage phase angles are very small. The line reactances are marked in the figure, where $\alpha, \beta, \gamma$, and $x$ are strictly positive. The bus injections $P_{1}$ and $P_{2}$ are in pu. If $P_{1}=m P_{2}$, where $m>0$, and the real power flow from bus $1$ to bus $2$ is $0$ $\mathrm{pu}$, then which one of the following options is correct?
- $\gamma=m \beta$
- $\beta=m \gamma$
- $\alpha=m \gamma$
- $\alpha=m \beta$