ρ→ ππ Hadronic Decay in the Nambu-Jona-Lasinio Model: Mass-Width Interplay and Beyond-RPA Corrections

A novel framework for analyzing unstable composite particles using Green's functions and dispersion relations is presented. As an illustrative example, we explore the ρ vector meson decay process ρ→ππ within the Nambu -- Jona - Lasinio (NJL) model. This approach addresses a key limitation of the four-quark interaction description, which adequately describes two-quark bound states but fails to describe decay processes. The Bethe-Salpeter(BS) wave function of the ρ meson exhibits time evolution that leads to the physical mass M incorporating a correction Δ M. This correction depends on the decay width Γ(M). This work provides crucial insights into the dynamical relationship between resonance masses and their decay properties, addressing a long-standing challenge in hadron physics. The calculated mass and width are in good agreement with the experimental values, demonstrating the effectiveness of this approach for studying unstable hadronic systems beyond conventional bound-state approximations. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.