The decay of the

R. Molina; M. Döring; W. H. Liang; E. Oset

doi:10.1140/epjc/s10052-021-09574-y

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 782
https://doi.org/10.1140/epjc/s10052-021-09574-y

Regular Article - Theoretical Physics

The $π f_{0} (500)$ $\pi f_0(500)$ decay of the $a_{1} (1260)$

R. Molina¹^a, M. Döring²^,3, W. H. Liang⁴^,5 and E. Oset¹^,4

¹ Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC Institutos de Investigación de Paterna, Aptdo.22085, 46071, Valencia, Spain
² Department of Physics, The George Washington University, 20052, Washington, DC, USA
³ Theory Center, Thomas Jefferson National Accelerator Facility, 23606, Newport News, VA, USA
⁴ Department of Physics, Guangxi Normal University, 541004, Guilin, China
⁵ Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University, 541004, Guilin, China

^a Raquel.Molina@ific.uv.es

Received: 27 July 2021
Accepted: 23 August 2021
Published online: 2 September 2021

Abstract

We evaluate the $a_{1} (1260) \to π σ (f_{0} (500))$ $a_1(1260) \rightarrow \pi \sigma (f_0(500))$ decay width from the perspective that the $a_{1} (1260)$ $$a_1(1260)$$ resonance is dynamically generated from the pseudoscalar–vector interaction and the $σ$ $\sigma$ arises from the pseudoscalar–pseudoscalar interaction. A triangle mechanism with $a_{1} (1260) \to ρ π$ $a_1(1260) \rightarrow \rho \pi$ followed by $ρ \to π π$ $\rho \rightarrow \pi \pi$ and a fusion of two pions within the loop to produce the $σ$ $\sigma$ provides the mechanism for this decay under these assumptions for the nature of the two resonances. We obtain widths of the order of 13–22 MeV. Present experimental results differ substantially from each other, suggesting that extra efforts should be devoted to the precise extraction of this important partial decay width, which should provide valuable information on the nature of the axial vector and scalar meson resonances and help clarify the role of the $π σ$ $\pi \sigma$ channel in recent lattice QCD calculations of the $a_{1}$ $$a_1$$ .

© The Author(s) 2021

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