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<p>We propose a systematic method to block-diagonalize the finite volume effective Hamiltonian for two-particle systems with arbitrary spin in both the rest and moving frame. The framework is convenient and efficient for addressing the left-hand cut issue arising from long-range potential, which are challenging in the framework of standard Lüscher formula. Furthermore, the method provides a foundation for further extension to three-particle systems. We first benchmark our method by examining several toy models, demonstrating its consistency with standard Lüscher formula in the absence of long-range potential. In the presence of long-range potential, we investigate and resolve the effects and issues of left-hand cut. As a realistic application, we calculate the finite volume spectra of isoscalar <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25982_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi>D</mi> <msup> <mover accent="true"> <mi>D</mi> <mo stretchy="true">¯</mo> </mover> <mo>∗</mo> </msup> </math></EquationSource> <EquationSource Format="TEX">\( D{\overline{D}}^{\ast } \)</EquationSource> </InlineEquation> system, where the well-known exotic state <i>χ</i><sub><i>c</i>1</sub>(3872) is observed. The results are qualitatively consistent with the lattice QCD calculation, highlighting the reliability and potential application of our framework to the study of other exotic states in hadron physics.</p>

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Finite volume Hamiltonian method for two-particle systems containing long-range potential on the lattice

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月15日

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  • Kang Yu,
  • Guang-Juan Wang,
  • Jia-Jun Wu,
  • Zhi Yang

摘要

We propose a systematic method to block-diagonalize the finite volume effective Hamiltonian for two-particle systems with arbitrary spin in both the rest and moving frame. The framework is convenient and efficient for addressing the left-hand cut issue arising from long-range potential, which are challenging in the framework of standard Lüscher formula. Furthermore, the method provides a foundation for further extension to three-particle systems. We first benchmark our method by examining several toy models, demonstrating its consistency with standard Lüscher formula in the absence of long-range potential. In the presence of long-range potential, we investigate and resolve the effects and issues of left-hand cut. As a realistic application, we calculate the finite volume spectra of isoscalar D D ¯ ∗ \( D{\overline{D}}^{\ast } \) system, where the well-known exotic state χc1(3872) is observed. The results are qualitatively consistent with the lattice QCD calculation, highlighting the reliability and potential application of our framework to the study of other exotic states in hadron physics.