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arXiv · 1808.05057

Test of semi-local duality in a large $N_C$ framework

Ling-Yun Dai·Xian-Wei Kang·Ulf-G. Meißner
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Abstract

In this paper we test the semi-local duality based on the method of Ref.[1] for calculating final-state interactions at varying number of colors ($N_C$). We compute the amplitudes by dispersion relations that respect analyticity and coupled channel unitarity, as well as accurately describing experiment. The $N_C$ dependence of the $ππ\toππ$ scattering amplitudes is obtained by comparing these amplitudes to the one of chiral perturbation theory. The semi-local duality is investigated by varying $N_C$. Our results show that the semi-local duality is not violated when $N_C$ is large. At large $N_C$, the contributions of the $f_2(1270)$, the $f_0(980)$ and the $f_0(1370)$ cancel that of the $ρ(770)$ in the finite energy sum rules, while the $f_0(500)$ has almost no effect. This gives further credit to the method developed in Ref.[1] for investigating the $N_C$ dependence of hadron-hadron scattering with final-state interactions. This study is also helpful to understand the structure of the scalar mesons.

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Ling-Yun Dai, Xian-Wei Kang, Ulf-G. Meißner. 2018-10-22. Test of semi-local duality in a large $N_C$ framework. https://doi.org/10.1103/physrevd.98.074033

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