Traces of the new $$a_0(1780)$$ a 0 ( 1780 ) resonance in the $$J/\psi \rightarrow \phi K^+K^-(K^0\bar{K}^0)$$ J / ψ → ϕ K + K - ( K 0 K ¯ 0 ) reaction

Abstract

Abstract We study the $$J/\psi \rightarrow \phi K \bar{K}$$ J / ψ → ϕ K K ¯ decay, looking for differences in the production rates of $$K^+ K^-$$ K + K - or $$K^0 \bar{K}^0$$ K 0 K ¯ 0 in the region of 1700–1800 MeV, where two resonances appear dynamically generated from the vector-vector interaction. Two resonances are known experimentally in that region, the $$f_0(1710)$$ f 0 ( 1710 ) and a new resonance reported by the BABAR and BESIII collaborations. The $$K \bar{K}$$ K K ¯ should be produced with $$I=0$$ I = 0 in that reaction, but due to the different $$K^{*0}$$ K ∗ 0 and $$K^{*+}$$ K ∗ + masses some isospin violation appears. Yet, due to the large width of the $$K^*$$ K ∗ , the violation obtained is very small and the rates of $$K^+ K^-$$ K + K - or $$K^0 \bar{K}^0$$ K 0 K ¯ 0 production are equal within $$5\%$$ 5 % . However, we also find that due to the step needed to convert two vectors into $$K \bar{K}$$ K K ¯ , a shape can appear in the $$K \bar{K}$$ K K ¯ mass distribution that can mimic the $$a_0$$ a 0 production around the $$K^* \bar{K}^*$$ K ∗ K ¯ ∗ threshold, and is simply a threshold effect.