It is commonly believed that millisecond radio pulsars have been spun up by
transfer of matter and angular momentum from a low-mass companion during an
X-ray active mass transfer phase. A subclass of low-mass X-ray binaries is that
of the accreting millisecond X-ray pulsars, transient systems that show periods
of X-ray quiescence during which radio emission could switch on. The aim of
this work is to search for millisecond pulsations from three accreting
millisecond X-ray pulsars, XTE J1751-305, XTE J1814-338, and SAX J1808.4-3658,
observed during their quiescent X-ray phases at high radio frequencies (5 - 8
GHz) in order to overcome the problem of the free-free absorption due to the
matter engulfing the system. A positive result would provide definite proof of
the recycling model, providing the direct link between the progenitors and
their evolutionary products. The data analysis methodology has been chosen on
the basis of the precise knowledge of orbital and spin parameters from X-ray
observations. It is subdivided in three steps: we corrected the time series for
the effects of (I) the dispersion due to interstellar medium and (II) of the
orbital motions, and finally (III) folded modulo the spin period to increase
the signal-to-noise ratio. No radio signal with spin and orbital
characteristics matching those of the X-ray sources has been found in our
search, down to very low flux density upper limits. We analysed several
mechanisms that could have prevented the detection of the signal, concluding
that the low luminosity of the sources and the geometric factor are the most
likely reasons for this negative result.Comment: 5 pages, 3 figures. Accepted for publication by A&