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a 0 (980)-f 0 (980) mixing in χ c1 → π 0 f 0 (980) → π 0 π + π - and χ c1 →π 0 a 0 (980) → π 0 π 0 η
2017-09-12  【 】【打印】【关闭

Institute of Theoretical Physics

Chinese Academy of Sciences

 Key Laboratory of Theoretical Physics

Seminar

Title

题目

a 0 (980) − f 0 (980) mixing in χ c1 → π 0 f 0 (980) → π 0 π + π − and χ c1 →π 0 a 0 (980) → π 0 π 0 η

Speaker

报告人

PhD. Vinicius Rodrigues Debastiani

Affiliation

所在单位

Departamento de Fisica Teorica and Instituto de Fisica Corpuscular (IFIC), Universidad de Valencia / CSIC

Date

日期

2017年9月12日(周二)下午3:00

Venue

地点

Room 322, ITP

Abstract

摘要

We study the isospin breaking in the reactions $\chi_{c1} \to \pi^0 \pi^+ \pi^-$ and $\chi_{c1} \to \pi^0 \pi^0 \eta$ and its relation to the $a_0(980) - f_0(980)$ mixing, which was measured by the BESIII Collaboration. We show that the same theoretical model previously developed to study the $\chi_{c1} \to \eta \pi^+ \pi^-$ reaction (also measured by BESIII), and further explored in the predictions to the $\eta_{c} \to \eta \pi^+ \pi^-$, can be successfully employed in the present study. We assume that the $\chi_{c1}$ behaves as an $SU(3)$ singlet to find the weight in which trios of pseudoscalars are created, followed by the final state interaction of pairs of mesons to describe how the $a_0(980)$ and $f_0(980)$ are dynamically generated, using the chiral unitary approach in coupled channels. The isospin violation is introduced through the use of different masses for the charged and neutral kaons, either in the propagators of the pairs of mesons created in the $\chi_{c1}$ decay, or in the propagators inside the $T$ matrix, constructed through the unitarization of the scattering and transition amplitudes of pairs of pseudoscalar mesons. We find that violating isospin inside the $T$ matrix makes the $\pi^0\eta \to \pi^+\pi^-$ amplitude nonzero, which gives an important contribution and also enhances the effect of the $K\bar{K}$ term. Also, we find that in the total amplitude the most important effect is the isospin breaking inside the $T$ matrix, due to the constructive sum of $\pi^0\eta \to \pi^+\pi^-$ and $K\bar{K} \to \pi^+ \pi^-$, which is essential to get a good agreement with the experimental measurement of the mixing.

Contact person

所内联系人

邹冰松
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