 Period invariant for constant-fraction donor-wind mass loss

For a slowly evolving circular orbit with constant retained fraction $f$ and donor-wind angular-momentum loss, logarithmic differentiation of the circular-binary orbital angular momentum gives $d\log P=-3fd\log M_d-3d\log M_a-2d\log (M_d+M_a)$. Integration gives the displayed invariant. At $f=1$ it becomes the period-product invariant for conservative mass transfer, while at $f=0$ it becomes $P{M}^2=\mathrm{constant}$. A varying retained fraction does not give this simple power-law invariant.