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.
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