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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
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| 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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