We present a lattice QCD spectroscopy study in the isospin singlet, strangeness $-2$ sectors relevant for the conjectured $H$ dibaryon. We employ both local and bilocal interpolating operators to isolate the ground state in the rest frame and in moving frames. Calculations are performed using two flavors of O($a$)-improved Wilson fermions and a quenched strange quark. Our initial point-source method for constructing correlators does not allow for bilocal operators at the source; nevertheless, results from using these operators at the sink indicate that they provide an improved overlap onto the ground state in comparison with the local operators. We also present results, in the rest frame, using a second method based on distillation to compute a hermitian matrix of correlators with bilocal operators at both the source and the sink. This method yields a much more precise and reliable determination of the ground-state energy. In the flavor-SU(3) symmetric case, we apply Luschers finite-volume quantization condition to the rest-frame and moving-frame energy levels to determine the $S$-wave scattering phase shift, near and below the two-particle threshold. For a pion mass of 960 MeV, we find that there exists a bound $H$ dibaryon with binding energy ${Delta}E=(19pm10)$ MeV. In the 27-plet (dineutron) sector, the finite-volume analysis suggests that the existence of a bound state is unlikely.
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