The accreting millisecond X-ray pulsar (AMXP) SAX J1808.4-3658, shows a peculiar orbital evolution that proceeds at a much faster pace than predicted by conservative binary evolution models. It is important to identify the underlying mechanism responsible for this behavior because it can help to understand how this system evolves. It has also been suggested that, when in quiescence, SAX J1808.4-3658 turns on as a radio pulsar, a circumstance that might provide a link between AMXPs and black-widow radio pulsars. In this work we report the results of a deep radio pulsation search at 2 GHz using the Green Bank Telescope in August 2014 and an X-ray monitoring of the 2015 outburst with Chandra, Swift, and INTEGRAL. In particular, we present the X-ray timing analysis of a 30-ks Chandra observation executed during the 2015 outburst. We detect no radio pulsations, and place the strongest limit to date on the pulsed radio flux density of any AMXP. We also find that the orbit of SAX J1808.4-3658 continues evolving at a fast pace and we compare it to the bhevior of other accreting and non-accreting binaries. We discuss two scenarios: either the neutron star has a large moment of inertia (I>1.7x10^45 g cm^2) and is ablating the donor (by using its spin-down power) thus generating mass-loss with an efficiency of 40% or the donor star is undergoing quasi-cyclic variations due to a varying mass-quadrupole induced by either a strong (1 kG) field or by some unidentified mechanism probably linked to irradiation.
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