Triangle singularity enhancing isospin violation in $D_s^{+}\to {\pi }^{+}{\pi }^0{f}_0(980)$ and ${\overline{B}}_s^0\to J/\psi {\pi }^0{f}_0(980)$ decays

¹ Department of Physics, Guangxi Normal University Guilin 541004, China
² Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia - CSIC, Institutos de Investigación de Paterna, Aptdo. 22085, 46071 Valencia, Spain
³ Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

^* e-mail: liangwh@gxnu.edu.cn

Published online: 1 February 2019

Abstract

We investigate isospin violation in the ${\overline{B}}_s^0\to J/\psi {\pi }^0{a}_0(980)(f_0(980))$ and $D_s^{+}\to {\pi }^{+}{\pi }^0{a}_0(980)(f_0(980))$ reactions, which proceed via a triangle mechanism. We show that the mechanism develops a singularity around the π⁰f₀(980) or π⁰a₀(980) invariant mass of 1420 MeV where the π⁰f₀ and π⁰a₀ decay modes are magnified and also the ratio of π⁰f₀ to π⁰a₀ production, stressing the role of the triangle singularities as a factor to enhance isospin violation. The measurement of these reactions would bring further information into the role of triangle singularities in isospin violation and the a₀ – f₀ mixing in particular and shed further light into the nature of the low lying scalar mesons.