<p>Isospin-1/2 charmed axial-vector <i>D</i><sup>∗</sup><i>π</i> − <i>D</i><sup>∗</sup><i>η</i> − <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∗</mo> </msubsup> <mover accent="true"> <mi>K</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( {D}_s^{\ast}\overline{K} \)</EquationSource> </InlineEquation> scattering amplitudes are computed, along with interactions in several other <i>I</i> = 1/2 <i>J</i><sup><i>P</i></sup> channels. Using lattice QCD, we work at a light-quark mass corresponding to <i>m</i><sub><i>π</i></sub> ≈ 391 MeV, where the lowest three-hadron threshold (<i>Dππ</i>) lies high enough to enable a rigorous treatment of this system considering only two-hadron scattering channels. At this light-quark mass, an axial-vector <i>D</i><sub>1</sub> bound state is observed just below <i>D</i><sup>∗</sup><i>π</i> threshold, that is strongly coupled to <i>D</i><sup>∗</sup><i>π</i> in a relative <i>S</i>-wave and influences a wide energy region up to the <i>D</i><sup>∗</sup><i>η</i> threshold. An axial-vector <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>D</mi> <mn>1</mn> <mo>′</mo> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {D}_1^{\prime } \)</EquationSource> </InlineEquation> resonance is observed in the elastic <i>D</i><sup>∗</sup><i>π</i> energy-region, which is coupled more strongly to <i>D</i>-wave <i>D</i><sup>∗</sup><i>π</i>. A single narrow tensor state is seen in <i>J</i><sup><i>P</i></sup> = 2<sup>+</sup> coupled to both <i>Dπ</i> and <i>D</i><sup>∗</sup><i>π</i>. In the region where <i>D</i><sup>∗</sup><i>η</i> and <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∗</mo> </msubsup> <mover accent="true"> <mi>K</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( {D}_s^{\ast}\overline{K} \)</EquationSource> </InlineEquation> are kinematically open, the available energy levels indicate significant <i>S</i>-wave interactions. Upon searching this region for poles, several possibilities exist with large uncertainties. One additional state consistently arises, predominantly coupled to the <i>S</i>-wave <i>D</i><sup>∗</sup><i>π</i> − <i>D</i><sup>∗</sup><i>η</i> − <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∗</mo> </msubsup> <mover accent="true"> <mi>K</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( {D}_s^{\ast}\overline{K} \)</EquationSource> </InlineEquation> amplitudes around the upper energy limit of this analysis.</p>

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D1 and D2 resonances in coupled-channel scattering amplitudes from lattice QCD

  • Nicolas Lang,
  • David J. Wilson

摘要

Isospin-1/2 charmed axial-vector DπDη D s K ¯ \( {D}_s^{\ast}\overline{K} \) scattering amplitudes are computed, along with interactions in several other I = 1/2 JP channels. Using lattice QCD, we work at a light-quark mass corresponding to mπ ≈ 391 MeV, where the lowest three-hadron threshold (Dππ) lies high enough to enable a rigorous treatment of this system considering only two-hadron scattering channels. At this light-quark mass, an axial-vector D1 bound state is observed just below Dπ threshold, that is strongly coupled to Dπ in a relative S-wave and influences a wide energy region up to the Dη threshold. An axial-vector D 1 \( {D}_1^{\prime } \) resonance is observed in the elastic Dπ energy-region, which is coupled more strongly to D-wave Dπ. A single narrow tensor state is seen in JP = 2+ coupled to both and Dπ. In the region where Dη and D s K ¯ \( {D}_s^{\ast}\overline{K} \) are kinematically open, the available energy levels indicate significant S-wave interactions. Upon searching this region for poles, several possibilities exist with large uncertainties. One additional state consistently arises, predominantly coupled to the S-wave DπDη D s K ¯ \( {D}_s^{\ast}\overline{K} \) amplitudes around the upper energy limit of this analysis.