  We derive analytical $\chi\ll1$ approximations for spin-dependent quantum
radiation reaction for locally constant and locally monochromatic fields. We
show how to factor out fast spin oscillations and obtain the degree of
polarization in the plane orthogonal to the magnetic field from the Frobenius
norm of the Mueller matrix. We show that spin effects lead to a transseries in
$\chi$, with powers $\chi^k$, logarithms $(\ln\chi)^k$ and oscillating terms,
$\cos(\dots/\chi)$ and $\sin(\dots/\chi)$. In our approach we can obtain each
moment, $\langle(kP)^m\rangle$, of the lightfront longitudinal momentum
independently of the other moments and without considering the spectrum. We
show how to obtain a low-energy expansion of the spectrum from the moments by
treating $m$ as a continuous, complex parameter and performing an inverse
Mellin transform. We also show how to obtain the spectrum, without making a
low-energy approximation, from a handful of moments using the principle of
maximum entropy.
