  We investigate constraints on additional planets orbiting the distant M-dwarf
star OGLE-2005-BLG-390L, around which photometric microlensing data has
revealed the existence of the sub-Neptune-mass planet OGLE-2005-BLG-390Lb. We
specifically aim to study potential Jovian companions and compare our findings
with predictions from core-accretion and disc-instability models of planet
formation. We also obtain an estimate of the detection probability for
sub-Neptune mass planets similar to OGLE-2005-BLG-390Lb using a simplified
simulation of a microlensing experiment. We compute the efficiency of our
photometric data for detecting additional planets around OGLE-2005-BLG-390L, as
a function of the microlensing model parameters and convert it into a function
of the orbital axis and planet mass by means of an adopted model of the Milky
Way. We find that more than 50 % of potential planets with a mass in excess of
1 M_J between 1.1 and 2.3 AU around OGLE-2005-BLG-390L would have revealed
their existence, whereas for gas giants above 3 M_J in orbits between 1.5 and
2.2 AU, the detection efficiency reaches 70 %; however, no such companion was
observed. Our photometric microlensing data therefore do not contradict the
existence of gas giant planets at any separation orbiting OGLE-2005-BLG-390L.
Furthermore we find a detection probability for an OGLE-2005-BLG-390Lb-like
planet of around 2-5 %. In agreement with current planet formation theories,
this quantitatively supports the prediction that sub-Neptune mass planets are
common around low-mass stars.
