How to understand $ρ$ Resonance from the Quark Model and $ππ$ $P$-wave phase shift
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| Format: | Preprint |
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2026
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| _version_ | 1866915960800149504 |
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| author | Zhao, Wen-Ze Ni, Ru-Hui Wu, Jia-Jun |
| author_facet | Zhao, Wen-Ze Ni, Ru-Hui Wu, Jia-Jun |
| contents | As the lightest isovector vector meson, the $ρ$ meson is an important object for investigating the structure of resonant states in strong interactions. Owing to its strong coupling to the $ππ$ channel and its large decay width, the conventional constituent quark model treatment, in which it is simply regarded as a pure $q\bar q$ bound state while the hadronic-channel coupling effects are neglected, is insufficient to fully characterize its physical properties. To this end, in the present work we establish a unified framework for studying the structure and resonant properties of the $ρ$ meson by combining the quark-gluon and hadronic degrees of freedom. At the quark-gluon level, we first determine the parameters of the chiral quark model by refitting a set of narrow mesons for which open OZI-allowed strong-decay channels are absent or strongly suppressed. With these parameters fixed, the bare mass of the $ρ$ meson is obtained and used as the input for the subsequent hadronic-level analysis. At the hadronic level, based on inverse scattering theory, we construct a model including the coupling between the bare state and the $ππ$ continuum, extract the $ρ_0-ππ$ interaction using the $P$-wave $ππ$ scattering phase-shift data, and further calculate the width of the $ρ$ meson as well as the bare-state component in the physical state. The present work also provides a generalizable analytical framework for further studies of other hadronic resonances with significant channel-coupling effects. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_24270 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | How to understand $ρ$ Resonance from the Quark Model and $ππ$ $P$-wave phase shift Zhao, Wen-Ze Ni, Ru-Hui Wu, Jia-Jun High Energy Physics - Phenomenology High Energy Physics - Experiment As the lightest isovector vector meson, the $ρ$ meson is an important object for investigating the structure of resonant states in strong interactions. Owing to its strong coupling to the $ππ$ channel and its large decay width, the conventional constituent quark model treatment, in which it is simply regarded as a pure $q\bar q$ bound state while the hadronic-channel coupling effects are neglected, is insufficient to fully characterize its physical properties. To this end, in the present work we establish a unified framework for studying the structure and resonant properties of the $ρ$ meson by combining the quark-gluon and hadronic degrees of freedom. At the quark-gluon level, we first determine the parameters of the chiral quark model by refitting a set of narrow mesons for which open OZI-allowed strong-decay channels are absent or strongly suppressed. With these parameters fixed, the bare mass of the $ρ$ meson is obtained and used as the input for the subsequent hadronic-level analysis. At the hadronic level, based on inverse scattering theory, we construct a model including the coupling between the bare state and the $ππ$ continuum, extract the $ρ_0-ππ$ interaction using the $P$-wave $ππ$ scattering phase-shift data, and further calculate the width of the $ρ$ meson as well as the bare-state component in the physical state. The present work also provides a generalizable analytical framework for further studies of other hadronic resonances with significant channel-coupling effects. |
| title | How to understand $ρ$ Resonance from the Quark Model and $ππ$ $P$-wave phase shift |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2604.24270 |