  We present a population study of low- and intermediate-mass X-ray binaries
(LMXBs) with neutron star accretors, performed using the detailed 1D stellar
evolution code MESA. We identify all plausible Roche-lobe overflowing binaries
at the start of mass transfer, and compare our theoretical mass transfer tracks
to the population of well-studied Milky Way LMXBs. The mass transferring
evolution depends on the accepted magnetic braking (MB) law for angular
momentum loss. The most common MB prescription ("Skumanich MB") originated from
observations of the time-dependence of rotational braking of Sun-type stars,
where the angular momentum loss rate depends on the donor mass $M_d$, donor
radius $R_d$, and rotation rate $\Omega$, $\dot{J} \propto M_d R_d^{\gamma}
\Omega^3$. The functional form of the Skumanich MB can be also obtained
theoretically assuming a radial magnetic field, isotropic isothermal winds, and
boosting of the magnetic field by rotation. Here we show that this simple form
of the Skumanich MB law gives mass transfer rates an order of magnitude too
weak to explain most observed persistent LMXBs. This failure suggests that the
standard Skumanich MB law should not be employed to interpret Galactic, or
extragalactic, LMXB populations, with either detailed stellar codes or rapid
binary population synthesis codes. We investigate modifications for the MB law,
and find that including a scaling of the magnetic field strength with the
convective turnover time, and a scaling of MB with the wind mass loss rate, can
reproduce persistent LMXBs, and does a better job at reproducing transient
LMXBs.
