  The accreting millisecond pulsars IGR J00291+5934 and SAX J1808.4-3658 are
two compact binaries with very similar orbital parameters. The latter has been
observed to evolve on a very short timescale of ~70 Myr which is more than an
order of magnitude shorter than expected. There is an ongoing debate on the
possibility that the pulsar spin-down power ablates the companion generating
large amount of mass-loss in the system. It is interesting therefore to study
whether IGR J00291+5934 does show a similar behaviour as its twin system SAX
J1808.4-3658. In this work we present the first measurement of the orbital
period derivative of IGR J00291+5934. By using XMM-Newton data recorded during
the 2015 outburst and adding the previous results of the 2004 and 2008
outbursts, we are able to measure a 90% confidence level upper limit for the
orbital period derivative of -5x10^-13<Pb_dot<6x10^-13. This implies that the
binary is evolving on a timescale longer than ~0.5 Gyr, which is compatible
with the expected timescale of mass transfer driven by angular momentum loss
via gravitational radiation. We discuss the scenario in which the power loss
from magnetic dipole radiation of the neutron star is hitting the companion
star. If this model is applied to SAX J1808.4-3658 then the difference in
orbital behavior can be ascribed to a different efficiency for the conversion
of the spin-down power into energetic relativistic pulsar wind and
X-ray/gamma-ray radiation for the two pulsars, with IGR J00291+5934 requiring
an extraordinarily low efficiency of less than 5% to explain the observations.
Alternatively, the donor in IGR J00291+5934 is weakly/not magnetized which
would suppress the possibility of generating mass-quadrupole variations.
