Internal particle width effects on the triangle singularity mechanism in the study of the η(1405) and η(1475) puzzle

Abstract

In this article, the analyticity of triangle loop integral with complex masses of internal particles is discussed in a new perspective, based on which we obtain the explicit width dependence of the absorptive part of the triangle amplitude. We reanalyze the decay pattern of ηð1405=1475Þ with the width effects included in the triangle singularity (TS) mechanism. Based on the present experimental information, we provide a selfconsistent description of the KKπ, ηππ, and 3π decay channels for ηð1405=1475Þ. Our results confirm the claim that the TS mechanism plays a decisive role in the understanding of the ηð1405Þ and ηð1475Þ puzzle. Namely, the observed differences of η resonances within the mass region of 1.40-1.48 GeV are originated from the same state. For the isospin violated process J=ψ → γηð1405=1475Þ → f 0 ð980Þπ → 3π, we identify an additional contribution to the a 0 ð980Þ − f 0 ð980Þ mixing via the TS mechanism.

Triangle singularities in J/ψ→ηπ0ϕ and π0π0Jing1, Sakai2, Guo3 et al. 2019Phys. Rev. D18210View full textAdd to dashboardCite

“…[13] or the isoscalar h 1 ð1380Þ whose mass is about 1.41 GeV [3,14,15]. 1 From the second point of view, because this is an isospin-breaking process and that peak position about 1.4 GeV is near the threshold of K ÃK , similar to the enhancement of the isospin violation by triangle singularity as seen in the ηð1405=1475Þ → π 0 f 0 ð980Þ [19][20][21][22][23], triangle diagrams involving K ÃK K intermediate states can also lead to a peak and a significant isospin-breaking enhancement here [see also Sec. VI.A.4 in Ref.…”

“…1), and the K Ã decays into πK subsequently; then the K moves in the same direction with theK and catches up with it, and the KK pair finally forms the ϕ. Triangle singularity effects of the K Ã KK loops have been studied for processes with the KK pair forming an f 0 ð980Þ or a 0 ð980Þ instead of a ϕ in Refs. [19][20][21][22][23][29][30][31][32][33][34].…”

Role of the triangle mechanism in the $Λ_b\rightarrow Λ_cπ^-f_0(980)$ reaction

“…The τ − → ν τ K * 0 K − decay amplitude without a 1 (1260) is given by replacing G µν a1 with g µν in Eq. (11). The π − f 0 (980) invariant mass distributions with and without a 1 (1260) are compared in Fig.…”

The $$D_s^+ \rightarrow a_0(980) e^+ \nu _e$$ reaction and the $$a_0(980)-f_0(980)$$ mixing

“…This was explained in Refs. [37,38,[49][50][51] by means of a triangle mechanism for the decay which develops a triangle singularity [52,53]. The idea of enhancing the isospin violation, and hence the mixing of a 0 (980) − f 0 (980) has been exploited later and several reactions have been proposed: in Ref.…”