We report the first lattice quantum chromodynamics (QCD) study of deuteronlike (<math><mrow><mi>n</mi><mi>p</mi></mrow></math>-like) dibaryons with heavy quark flavors. These include particles with the following dibaryon structures and valence quark contents: <math><mrow><msub><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mi>u</mi><mi>u</mi><mi>c</mi><mi>u</mi><mi>c</mi><mi>c</mi><mo>)</mo></mrow></math>, <math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>c</mi></mrow></msub><msub><mrow><mi>Ω</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mi>s</mi><mi>s</mi><mi>c</mi><mi>s</mi><mi>c</mi><mi>c</mi><mo>)</mo></mrow></math>, <math><msub><mi>Σ</mi><mi>b</mi></msub><msub><mi>Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub><mo>(</mo><mi>u</mi><mi>u</mi><mi>b</mi><mi>u</mi><mi>b</mi><mi>b</mi><mo>)</mo></math>, <math><msub><mi>Ω</mi><mi>b</mi></msub><msub><mi>Ω</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub><mo>(</mo><mi>s</mi><mi>s</mi><mi>b</mi><mi>s</mi><mi>b</mi><mi>b</mi><mo>)</mo></math>, and <math><msub><mi>Ω</mi><mrow><mi>c</mi><mi>c</mi><mi>b</mi></mrow></msub><msub><mi>Ω</mi><mrow><mi>c</mi><mi>b</mi><mi>b</mi></mrow></msub><mo>(</mo><mi>c</mi><mi>c</mi><mi>b</mi><mi>c</mi><mi>b</mi><mi>b</mi><mo>)</mo></math>, and with spin (<math><mi>J</mi></math>) parity (<math><mi>P</mi></math>), <math><msup><mi>J</mi><mi>P</mi></msup><mo>≡</mo><msup><mn>1</mn><mo>+</mo></msup></math>. Using a state-of-the art lattice QCD calculation, after controlling relevant systematic errors, we unambiguously find that the ground state masses of dibaryons <math><msub><mi>Ω</mi><mi>c</mi></msub><msub><mi>Ω</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mi>s</mi><mi>s</mi><mi>c</mi><mi>s</mi><mi>c</mi><mi>c</mi><mo>)</mo></math>, <math><msub><mi>Ω</mi><mi>b</mi></msub><msub><mi>Ω</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub><mo>(</mo><mi>s</mi><mi>s</mi><mi>b</mi><mi>s</mi><mi>b</mi><mi>b</mi><mo>)</mo></math>, and <math><msub><mi>Ω</mi><mrow><mi>c</mi><mi>c</mi><mi>b</mi></mrow></msub><msub><mi>Ω</mi><mrow><mi>c</mi><mi>b</mi><mi>b</mi></mrow></msub><mo>(</mo><mi>c</mi><mi>c</mi><mi>b</mi><mi>c</mi><mi>b</mi><mi>b</mi><mo>)</mo></math> are below their respective two-baryon thresholds, suggesting the presence of bound states that are stable under strong and electromagnetic interactions. We also predict their masses precisely. For dibaryons <math><msub><mi>Σ</mi><mi>c</mi></msub><msub><mi>Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mi>u</mi><mi>u</mi><mi>c</mi><mi>u</mi><mi>c</mi><mi>c</mi><mo>)</mo></math>, and <math><msub><mi>Σ</mi><mi>b</mi></msub><msub><mi>Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub><mo>(</mo><mi>u</mi><mi>u</mi><mi>b</mi><mi>u</mi><mi>b</mi><mi>b</mi><mo>)</mo></math>, we could not reach to a definitive conclusion about the presence of any bound state due to large systematics associated with these states. We also find that the binding of these dibaryons becomes stronger as they become heavier in mass. This study also opens up the possibility of the existence of many other exotic nuclei, which can be formed through the fusion of heavy baryons, similar to the formation of nuclei of elements in the periodic table.

India

Parikshit Junnarkar

Nilmani Mathur

Deuteronlike Heavy Dibaryons from Lattice Quantum Chromodynamics

We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with nonperturbatively improved <math><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> Wilson fermions, covering four values of the lattice spacing and pion masses down to <math><msub><mi>M</mi><mi>π</mi></msub><mo>≈</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Several source-sink separations (typically <math><mo>∼</mo><mn>1.0</mn></math> to <math><mo>∼</mo><mn>1.5</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Renormalization has been performed nonperturbatively using the Rome-Southampton method for all but the finest lattice spacing for which an extrapolation has been used. Physical results are quoted in the <math><mrow><mover><mrow><mi>MS</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> scheme at a scale of <math><mi>μ</mi><mo>=</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and are obtained from a combined chiral, continuum, and finite-size extrapolation. For the nucleon isovector axial, scalar, and tensor charges we find physical values of <math><mrow><msubsup><mrow><mi>g</mi></mrow><mrow><mi>A</mi></mrow><mrow><mi>u</mi><mo>−</mo><mi>d</mi></mrow></msubsup><mo>=</mo><mn>1.242</mn><mo>(</mo><mn>25</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mfrac><mrow><mo>+</mo><mn>00</mn></mrow><mrow><mo>−</mo><mn>31</mn></mrow></mfrac><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub></mrow></math>, <math><mrow><msubsup><mrow><mi>g</mi></mrow><mrow><mi>S</mi></mrow><mrow><mi>u</mi><mo>−</mo><mi>d</mi></mrow></msubsup><mo>=</mo><mn>1.13</mn><mo>(</mo><mn>11</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mfrac><mrow><mo>+</mo><mn>07</mn></mrow><mrow><mo>−</mo><mn>06</mn></mrow></mfrac><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub></mrow></math> and <math><mrow><msubsup><mrow><mi>g</mi></mrow><mrow><mi>T</mi></mrow><mrow><mi>u</mi><mo>−</mo><mi>d</mi></mrow></msubsup><mo>=</mo><mn>0.965</mn><mo>(</mo><mn>38</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mfrac><mrow><mo>+</mo><mn>13</mn></mrow><mrow><mo>−</mo><mn>41</mn></mrow></mfrac><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub></mrow></math>, respectively, where individual systematic errors in each direction from the chiral, continuum, and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by <math><mrow><mo>⟨</mo><mi>x</mi><msub><mrow><mo>⟩</mo></mrow><mrow><mi>u</mi><mo>−</mo><mi>d</mi></mrow></msub><mo>=</mo><mn>0.180</mn><mo>(</mo><mn>25</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mfrac><mrow><mo>+</mo><mn>14</mn></mrow><mrow><mo>−</mo><mn>06</mn></mrow></mfrac><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub></mrow></math>, <math><mrow><mo>⟨</mo><mi>x</mi><msub><mrow><mo>⟩</mo></mrow><mrow><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>Δ</mi><mi>d</mi></mrow></msub><mo>=</mo><mn>0.221</mn><mo>(</mo><mn>25</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mfrac><mrow><mo>+</mo><mn>10</mn></mrow><mrow><mo>−</mo><mn>00</mn></mrow></mfrac><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub></mrow></math>, and <math><mrow><mo>⟨</mo><mi>x</mi><msub><mrow><mo>⟩</mo></mrow><mrow><mi>δ</mi><mi>u</mi><mo>−</mo><mi>δ</mi><mi>d</mi></mrow></msub><mo>=</mo><mn>0.212</mn><mo>(</mo><mn>32</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mfrac><mrow><mo>+</mo><mn>20</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></mfrac><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub></mrow></math>, respectively.

Germany

Italy

Tim Harris

Georg von Hippel

Harvey B. Meyer

Konstantin Ottnad

Jonas Wilhelm

Hartmut Wittig

Sweden

Linus Wrang

Nucleon isovector charges and twist-2 matrix elements with <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> dynamical Wilson quarks

We present the results of a lattice calculation of tetraquark states with quark contents <math><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>2</mn></msub><mover><mi>Q</mi><mo>¯</mo></mover><mover><mi>Q</mi><mo>¯</mo></mover><mo>,</mo><msub><mi>q</mi><mn>1</mn></msub><mo>,</mo><msub><mi>q</mi><mn>2</mn></msub><mo>⊂</mo><mi>u</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>c</mi></math> and <math><mrow><mi>Q</mi><mo>≡</mo><mi>b</mi></mrow></math>, <math><mrow><mi>c</mi></mrow></math> in both spin-0 (<math><mi>J</mi><mo>=</mo><mn>0</mn></math>) and spin-1 (<math><mi>J</mi><mo>=</mo><mn>1</mn></math>) sectors. This calculation is performed on three dynamical <math><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math> highly improved staggered quark ensembles at lattice spacings of about 0.12, 0.09, and 0.06 fm. We use the overlap action for light to charm quarks, while a nonrelativistic action with nonperturbatively improved coefficients with terms up to <math><mrow><mi>O</mi><mo>(</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub><msup><mrow><mi>v</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></mrow></math> is employed for the bottom quark. While considering charm or bottom quarks as heavy, we calculate the energy levels of various four-quark configurations with light quark masses ranging from the physical strange quark mass to that of the corresponding physical pion mass. This enables us to explore the quark mass dependence of the extracted four-quark energy levels over a wide range of quark masses. The results of the spin-1 states show the presence of ground state energy levels which are below their respective thresholds for all the light flavor combinations. Further, we identify a trend that the energy splittings, defined as the energy difference between the ground state energy levels and their respective thresholds, increase with decreasing the light quark masses and are maximum at the physical point for all the spin-1 states. The rate of increase is, however, dependent on the light quark configuration of the particular spin-1 state. We also present a study of hadron mass relations involving tetraquarks, baryons, and mesons arising in the limit of infinitely heavy quarks and find that these relations are more compatible with the heavy quark limit in the bottom sector but deviate substantially in the charm sector. The ground state spectra of the spin-0 tetraquark states with various flavor combinations are seen to lie above their respective thresholds.

M. Padmanath

Study of doubly heavy tetraquarks in lattice QCD