Three-body unitary determination of the f1(1285) and f1(1420) pole positions
Abstract
We study the IG(JPC)=0+(1++) KK̅π system in an infinite-volume three-body unitary framework, focusing on the pole content of the region of the f1(1285) and f1(1420) resonances. The coupled πa0-KK̅* amplitude is constructed in the spectator-isobar representation, where the one-particle-exchange interaction required by three-body unitarity automatically incorporates the triangle-singularity mechanism. The short-range three-body interaction is constrained by fitting the 0+(1++) component of the BESIII K0SK0Sπ0 invariant-mass distribution in the J/ψ→γ(K0SK0Sπ0) decay. Analytically continuing the fitted amplitude to the relevant unphysical Riemann sheets, we find two robust poles: √(sf1(1285))&= (1277±2±1) −i(12±1±0)MeV ,notag √(sf1(1420))&= (1435±2±7) −i(40±2±1)MeV .notag The pole trajectories indicate that the f1(1285) originates from dressing a bare state introduced in the potential. In contrast, the f1(1420) is predominantly dynamically generated, and a single-channel analysis traces it to an S-wave KK̅* quasi-bound state mixed with the nearby bare state, supporting its hadronic-molecule interpretation. We also find an additional pole deeper in the complex plane in the best-fit amplitude on the same Riemann sheet as the f1(1285). This additional pole is generated by the P-wave πa0 contact interaction alone. It has a sizable cutoff and two-body-input dependence, and leaves little visible imprint on the physical lineshape. Finally, we provide a detailed and pedagogical appendix on how three-body cuts affect the solution of the integral equation.
Versions
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BibTeX
@misc{hu2026threebody,
title = {{Three-body unitary determination of the $f_1(1285)$ and $f_1(1420)$ pole positions}},
author = {Tao-Ran Hu and Hai-Long Fu and Feng-Kun Guo and Ulf-G. Meißner and Xu Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.19040},
eprint = {2606.19040},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.19040},
}
RIS
TY - UNPB
TI - Three-body unitary determination of the f_1(1285) and f_1(1420) pole positions
AU - Tao-Ran Hu
AU - Hai-Long Fu
AU - Feng-Kun Guo
AU - Ulf-G. Meißner
AU - Xu Zhang
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2606.19040
UR - https://arxiv.org/abs/2606.19040
AB - We study the I^G(J^PC)=0^+(1^++) KK̅π system in an infinite-volume three-body unitary framework, focusing on the pole content of the region of the f_1(1285) and f_1(1420) resonances. The coupled πa_0-KK̅^* amplitude is constructed in the spectator-isobar representation, where the one-particle-exchange interaction required by three-body unitarity automatically incorporates the triangle-singularity mechanism. The short-range three-body interaction is constrained by fitting the 0^+(1^++) component of the BESIII K^0_SK^0_Sπ^0 invariant-mass distribution in the J/ψ→γ(K^0_SK^0_Sπ^0) decay. Analytically continuing the fitted amplitude to the relevant unphysical Riemann sheets, we find two robust poles: √(s_f_1(1285))&= (1277±2±1) −i(12±1±0)MeV ,notag √(s_f_1(1420))&= (1435±2±7) −i(40±2±1)MeV .notag The pole trajectories indicate that the f_1(1285) originates from dressing a bare state introduced in the potential. In contrast, the f_1(1420) is predominantly dynamically generated, and a single-channel analysis traces it to an S-wave KK̅^* quasi-bound state mixed with the nearby bare state, supporting its hadronic-molecule interpretation. We also find an additional pole deeper in the complex plane in the best-fit amplitude on the same Riemann sheet as the f_1(1285). This additional pole is generated by the P-wave πa_0 contact interaction alone. It has a sizable cutoff and two-body-input dependence, and leaves little visible imprint on the physical lineshape. Finally, we provide a detailed and pedagogical appendix on how three-body cuts affect the solution of the integral equation.
ER -