Heavy-meson molecules with dynamical pions
Abstract
We investigate heavy-meson molecules by treating the pion as a dynamical degree of freedom. We construct an energy-independent Hamiltonian that couples the two- and three-body Fock spaces. The two-body sector contains a pseudoscalar meson and a vector meson H1H2*, while the three-body sector consists of two pseudoscalar mesons and a pion H1H2 π. The H* self-energy, the H1H2* pion-exchange interaction, and the H1H2π three-body propagation are consistently generated through the coupling between the two Fock sectors. We use the Gaussian expansion and complex scaling methods to solve the coupled Schrödinger equation. Previous approaches usually reduce three-body effects to energy-dependent two-body kernels and solve the equations iteratively. Our approach obtains the poles by solving a single linear generalized eigenvalue problem. The eigenvectors also provide explicit wave functions in both Fock sectors, allowing a qualitative analysis of channel weights and spatial structure. We benchmark the framework in Tcc+ and X(3872). The benchmark results are consistent with the current experimental pole determinations. We then apply this formalism to the BBπ, BB̅π, DBπ and DB̅π systems. We predict one isoscalar bound state in each of these systems. The DBπ and DB̅π systems also contain resonances lying below and above their three-body threshold, respectively. We propose complementary searches for these resonances through DB*→ DBγ and DB̅π. This coupled Fock-space framework can be readily extended to other few-body systems in which unstable constituents can decay and change the particle number.
Related
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- Probing Saturation Effect in Heavy Meson Pair Correlation in Forward pA Collisions
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BibTeX
@misc{chen2026heavymeson,
title = {{Heavy-meson molecules with dynamical pions}},
author = {Yan-Ke Chen and Liang-Zhen Wen and Lu Meng and Shi-Lin Zhu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01768},
eprint = {2611.01768},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01768},
}
RIS
TY - UNPB
TI - Heavy-meson molecules with dynamical pions
AU - Yan-Ke Chen
AU - Liang-Zhen Wen
AU - Lu Meng
AU - Shi-Lin Zhu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01768
UR - https://arxiv.org/abs/2611.01768
AB - We investigate heavy-meson molecules by treating the pion as a dynamical degree of freedom. We construct an energy-independent Hamiltonian that couples the two- and three-body Fock spaces. The two-body sector contains a pseudoscalar meson and a vector meson H_1H_2^*, while the three-body sector consists of two pseudoscalar mesons and a pion H_1H_2 π. The H^* self-energy, the H_1H_2^* pion-exchange interaction, and the H_1H_2π three-body propagation are consistently generated through the coupling between the two Fock sectors. We use the Gaussian expansion and complex scaling methods to solve the coupled Schrödinger equation. Previous approaches usually reduce three-body effects to energy-dependent two-body kernels and solve the equations iteratively. Our approach obtains the poles by solving a single linear generalized eigenvalue problem. The eigenvectors also provide explicit wave functions in both Fock sectors, allowing a qualitative analysis of channel weights and spatial structure. We benchmark the framework in T_cc^+ and X(3872). The benchmark results are consistent with the current experimental pole determinations. We then apply this formalism to the BBπ, BB̅π, DBπ and DB̅π systems. We predict one isoscalar bound state in each of these systems. The DBπ and DB̅π systems also contain resonances lying below and above their three-body threshold, respectively. We propose complementary searches for these resonances through DB^*→ DBγ and DB̅π. This coupled Fock-space framework can be readily extended to other few-body systems in which unstable constituents can decay and change the particle number.
ER -