  Theoretical calculations suggest the presence of low-lying excited states in
$^{25}$O. Previous experimental searches by means of proton knockout on
$^{26}$F produced no evidence for such excitations.
  We search for excited states in $^{25}$O using the ${ {}^{24}\text{O} (d,p)
{}^{25}\text{O} }$ reaction. The theoretical analysis of excited states in
unbound $^{25,27}$O is based on the configuration interaction approach that
accounts for couplings to the scattering continuum.
  We use invariant-mass spectroscopy to measure neutron-unbound states in
$^{25}$O. For the theoretical approach, we use the complex-energy Gamow Shell
Model and Density Matrix Renormalization Group method with a finite-range
two-body interaction optimized to the bound states and resonances of
$^{23-26}$O, assuming a core of $^{22}$O. We predict energies, decay widths,
and asymptotic normalization coefficients.
  Our calculations in a large $spdf$ space predict several low-lying excited
states in $^{25}$O of positive and negative parity, and we obtain an
experimental limit on the relative cross section of a possible ${ {J}^{\pi} =
{1/2}^{+} }$ state with respect to the ground-state of $^{25}$O at
$\sigma_{1/2+}/\sigma_{g.s.} = 0.25_{-0.25}^{+1.0}$. We also discuss how the
observation of negative parity states in $^{25}$O could guide the search for
the low-lying negative parity states in $^{27}$O.
  Previous experiments based on the proton knockout of $^{26}$F suffered from
the low cross sections for the population of excited states in $^{25}$O because
of low spectroscopic factors. In this respect, neutron transfer reactions carry
more promise.
