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  • Open Access

How to understand the ρ resonance from the quark model and ππ P-wave phase shift

Wen-Ze Zhao1, Ru-Hui Ni1,*, and Jia-Jun Wu1,2,†

  • *Contact author: niruhui@ucas.ac.cn
  • †Contact author: wujiajun@ucas.ac.cn
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Phys. Rev. D 114, 014020 – Published 8 July, 2026

DOI: https://doi.org/10.1103/rn1z-fdh7

Abstract

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 qq¯ 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 Okubo-Zweig-Iizuka-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 ρ0−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 coupled-channel effects.

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Phys. Rev. D 114, 014020– Published 8 July, 2026
  • Received 29 April 2026
  • Accepted 10 June 2026
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