Abstract
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 L\"uscher's 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 ${\Delta}E=(19\pm10)$ MeV. In the 27-plet (dineutron) sector, the finite-volume analysis suggests that the existence of a bound state is unlikely.
Highlights
The strong force between quarks and gluons produces a rich spectrum of bound states and resonances, the color-neutral hadrons
We present a lattice QCD spectroscopy study in the isospin singlet, strangeness −2 sectors relevant for the conjectured H dibaryon
Our initial point-source method for constructing correlators does not allow for bilocal operators at the source; 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
Summary
The strong force between quarks and gluons produces a rich spectrum of bound states and resonances, the color-neutral hadrons. An alternative approach, employed by the HAL QCD Collaboration, is based on determining baryonbaryon potentials from Nambu-Bethe-Salpeter wave functions computed on the lattice, followed by solving the Schrödinger equation to study baryon-baryon scattering and bound states This was done on ensembles with Nf 1⁄4 3 clover fermions for a range of quark masses [21,22,23]. We report initial results from a follow-up study in which we, for the first time, applied the distillation method [31] to the twobaryon sector This allowed us to compute a correlator matrix using operators made from products of two spatially displaced, momentum-projected baryon interpolators at both the source and the sink.
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