Towards the quark mass dependence of $T_{cc}^+$ from lattice QCD
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912127439077376 |
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| author | Collins, Sara Nefediev, Alexey Padmanath, M. Prelovsek, Sasa |
| author_facet | Collins, Sara Nefediev, Alexey Padmanath, M. Prelovsek, Sasa |
| contents | The $DD^*$ scattering phase shifts in the $T_{cc}^+=cc\bar{u}\bar{d}$ channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to $m_π\simeq 280$~MeV. The phase shifts are analysed employing two approaches: effective range expansion and Lippmann--Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrised by contact terms and a slight repulsion at long range mediated by one-pion exchange with $m_π>m_{D^*}-m_D$. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for $m_c$ close to the physical value. They turn into a pair of virtual states at the largest $m_c$ studied. With further increasing $m_c$, one virtual pole representing $T_{cc}^+$ is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the $T_{cc}^+$ pole is briefly discussed using the data on $DD^*$ scattering from other lattice collaborations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards the quark mass dependence of $T_{cc}^+$ from lattice QCD Collins, Sara Nefediev, Alexey Padmanath, M. Prelovsek, Sasa High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory The $DD^*$ scattering phase shifts in the $T_{cc}^+=cc\bar{u}\bar{d}$ channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to $m_π\simeq 280$~MeV. The phase shifts are analysed employing two approaches: effective range expansion and Lippmann--Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrised by contact terms and a slight repulsion at long range mediated by one-pion exchange with $m_π>m_{D^*}-m_D$. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for $m_c$ close to the physical value. They turn into a pair of virtual states at the largest $m_c$ studied. With further increasing $m_c$, one virtual pole representing $T_{cc}^+$ is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the $T_{cc}^+$ pole is briefly discussed using the data on $DD^*$ scattering from other lattice collaborations. |
| title | Towards the quark mass dependence of $T_{cc}^+$ from lattice QCD |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2402.14715 |