Constraining the $DDD^*$ three-body bound state via the $Z_c(3900)$ pole
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2024
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| _version_ | 1866912376412962816 |
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| author | Zhu, Hai-Xiang Meng, Lu Ma, Yao Li, Ning Chen, Wei Zhu, Shi-Lin |
| author_facet | Zhu, Hai-Xiang Meng, Lu Ma, Yao Li, Ning Chen, Wei Zhu, Shi-Lin |
| contents | In this study, we propose using the $Z_c(3900)$ pole position to constrain the existence of the $DDD^*$ three-body bound state within the one-boson-exchange (OBE) model. The existence of the $DDD^*$ bound state remains uncertain due to significant variations in the OBE interaction, particularly in the strength of scalar-meson-exchange interactions, which can differ by a factor about 20 between two commonly used OBE models. This discrepancy renders the $DDD^*$ system highly model-dependent. To address this issue, we constrain the scalar-meson-exchange interaction using the $Z_c(3900)$ pole position, where the pseudoscalar-meson coupling is well-determined, and the $ρ$- and $ω$-exchange interactions nearly cancel each other out, leaving the coupling constant of the $σ$-exchange as the only unknown parameter. Our results indicate that the isospin-$\frac{1}{2}$ $DDD^*$ bound states exist when $Z_c(3900)$ is a virtual state of $D\bar{D}^*/\bar{D}D^*$ located within approximately $-15$ MeV of the threshold. However, the three-body bound state is gone when the $Z_c(3900)$ virtual state pole is more than $20$ MeV away from the threshold. Each experimental progress, either on the $DDD^*$ state or the $Z_c(3900)$, can shed light on the nature of the other state. Another significant outcome is a refined set of OBE model parameters calibrated using the pole positions of $X(3872)$, $T_{cc}(3875)$, and $Z_c(3900)$, rigorously addressing the cutoff dependence. These parameters provide a valuable resource for more accurate calculations of systems involving few-body $D$, $D^*$ and their antiparticles. Additionally, we find no evidence of the $DDD^*$ three-body resonances after extensive search using a combination of the Gaussian expansion method and the complex scaling method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_12816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constraining the $DDD^*$ three-body bound state via the $Z_c(3900)$ pole Zhu, Hai-Xiang Meng, Lu Ma, Yao Li, Ning Chen, Wei Zhu, Shi-Lin High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Theory In this study, we propose using the $Z_c(3900)$ pole position to constrain the existence of the $DDD^*$ three-body bound state within the one-boson-exchange (OBE) model. The existence of the $DDD^*$ bound state remains uncertain due to significant variations in the OBE interaction, particularly in the strength of scalar-meson-exchange interactions, which can differ by a factor about 20 between two commonly used OBE models. This discrepancy renders the $DDD^*$ system highly model-dependent. To address this issue, we constrain the scalar-meson-exchange interaction using the $Z_c(3900)$ pole position, where the pseudoscalar-meson coupling is well-determined, and the $ρ$- and $ω$-exchange interactions nearly cancel each other out, leaving the coupling constant of the $σ$-exchange as the only unknown parameter. Our results indicate that the isospin-$\frac{1}{2}$ $DDD^*$ bound states exist when $Z_c(3900)$ is a virtual state of $D\bar{D}^*/\bar{D}D^*$ located within approximately $-15$ MeV of the threshold. However, the three-body bound state is gone when the $Z_c(3900)$ virtual state pole is more than $20$ MeV away from the threshold. Each experimental progress, either on the $DDD^*$ state or the $Z_c(3900)$, can shed light on the nature of the other state. Another significant outcome is a refined set of OBE model parameters calibrated using the pole positions of $X(3872)$, $T_{cc}(3875)$, and $Z_c(3900)$, rigorously addressing the cutoff dependence. These parameters provide a valuable resource for more accurate calculations of systems involving few-body $D$, $D^*$ and their antiparticles. Additionally, we find no evidence of the $DDD^*$ three-body resonances after extensive search using a combination of the Gaussian expansion method and the complex scaling method. |
| title | Constraining the $DDD^*$ three-body bound state via the $Z_c(3900)$ pole |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Theory |
| url | https://arxiv.org/abs/2412.12816 |