<p>We perform a lattice QCD calculation of the <i>S</i>-wave interactions between the ground-state spin-1<i>/</i>2 doubly charmed baryons and Goldstone bosons. The lattice QCD simulations are carried out on four 2 + 1 flavor Wilson-Clover ensembles generated by the CLQCD collaboration, with a lattice spacing <i>a</i> = 0<i>.</i>07746 fm and two different pion masses, <i>M</i><sub><i>π</i></sub> ~ 210 and ~ 300 MeV. Energy levels are extracted for four single channels, <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="normal">Ω</mi> <mi mathvariant="italic">cc</mi> </msub> <msup> <mover accent="true"> <mi>K</mi> <mo stretchy="true">¯</mo> </mover> <mfenced close=")" open="(" separators=","> <mrow> <mo>−</mo> <mn>2</mn> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </mfenced> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {\varOmega}_{cc}{\overline{K}}^{\left(-2,1/2\right)} \)</EquationSource> </InlineEquation>, Ξ<sub><i>cc</i></sub><i>K</i><sup>(1,1)</sup>, Ξ<sub><i>cc</i></sub><i>K</i><sup>(1<i>,</i>0)</sup>, and Ξ<sub><i>cc</i></sub><i>π</i><sup>(0<i>,</i>3<i>/</i>2)</sup>, where the superscripts (<i>S, I</i>) denote strangeness <i>S</i> and isospin <i>I</i>. Our results indicate that the Ξ<sub><i>cc</i></sub><i>K</i><sup>(1<i>,</i>0)</sup> channel is attractive, exhibiting negative energy shifts relative to the non-interacting two-hadron thresholds, while the other three channels are repulsive. Using Lüscher’s finite-volume formula, we extract the near-threshold phase shifts and determine the <i>S</i>-wave scattering lengths. Furthermore, a virtual state pole is found in the Ξ<sub><i>cc</i></sub><i>K</i><sup>(1<i>,</i>0)</sup> scattering amplitude. These results provide <i>ab initio</i> input to enable high-precision studies of the properties and spectroscopy of doubly heavy baryons.</p>

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Low-energy interactions between doubly charmed baryons and Goldstone bosons from lattice QCD

  • Jing-Yu Yi,
  • Ze-Rui Liang,
  • Liuming Liu,
  • De-Liang Yao

摘要

We perform a lattice QCD calculation of the S-wave interactions between the ground-state spin-1/2 doubly charmed baryons and Goldstone bosons. The lattice QCD simulations are carried out on four 2 + 1 flavor Wilson-Clover ensembles generated by the CLQCD collaboration, with a lattice spacing a = 0.07746 fm and two different pion masses, Mπ ~ 210 and ~ 300 MeV. Energy levels are extracted for four single channels, Ω cc K ¯ 2 1 / 2 \( {\varOmega}_{cc}{\overline{K}}^{\left(-2,1/2\right)} \) , ΞccK(1,1), ΞccK(1,0), and Ξccπ(0,3/2), where the superscripts (S, I) denote strangeness S and isospin I. Our results indicate that the ΞccK(1,0) channel is attractive, exhibiting negative energy shifts relative to the non-interacting two-hadron thresholds, while the other three channels are repulsive. Using Lüscher’s finite-volume formula, we extract the near-threshold phase shifts and determine the S-wave scattering lengths. Furthermore, a virtual state pole is found in the ΞccK(1,0) scattering amplitude. These results provide ab initio input to enable high-precision studies of the properties and spectroscopy of doubly heavy baryons.