Weakly bound $H$ dibaryon from SU(3)-flavor-symmetric QCD

We present the first study of baryon-baryon interactions in the continuum limit of lattice QCD, finding unexpectedly large lattice artifacts. Specifically, we determine the binding energy of the <math display="inline"><mi>H</mi></math> dibaryon at a single quark-mass point. The calculation is performed at six values of the lattice spacing <math display="inline"><mi>a</mi></math>, using <math display="inline"><mrow><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo></mrow></math>-improved Wilson fermions at the SU(3)-symmetric point with <math display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>=</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>≈</mo><mn>420</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. Energy levels are extracted by applying a variational method to correlation matrices of bilocal two-baryon interpolating operators computed using the distillation technique. Our analysis employs Lüscher’s finite-volume quantization condition to determine the scattering phase shifts from the spectrum and vice versa, both above and below the two-baryon threshold. We perform global fits to the lattice spectra using parametrizations of the phase shift, supplemented by terms describing discretization effects, then extrapolate the lattice spacing to zero. The phase shift and the binding energy determined from it are found to be strongly affected by lattice artifacts. Our estimate of the binding energy in the continuum limit of three-flavor QCD is <math display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>H</mi></mrow><mrow><msub><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></mrow><mrow><mi>f</mi></mrow></msub></mrow></msubsup><mo>=</mo><mn>4.56</mn><mo>±</mo><mn>1.1</mn><msub><mrow><mn>3</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.6</mn><msub><mrow><mn>3</mn></mrow><mrow><mi>syst</mi></mrow></msub><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>.