Singularities and accumulation of singularities of πN scattering amplitudes |
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Authors: | Qu-Zhi Li Han-Qing Zheng |
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Affiliation: | 1.Department of Physics Peking University, Beijing 100871, China;2.College of Physics, Sichuan University, Chengdu, Sichuan 610065, China;3.Collaborative Innovation Center of Quantum Matter, Beijing, China |
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Abstract: | It is demonstrated that for the isospin I = 1/2 πN scattering amplitude, TI=1/2(s, t), $s={left({m}_{N}^{2}-{m}_{pi }^{2}right)}^{2}/{m}_{N}^{2}$ and $s={m}_{N}^{2}+2{m}_{pi }^{2}$ are two accumulation points of poles on the second sheet of complex s plane, and are hence accumulation of singularities of TI=1/2(s, t). For TI=3/2(s, t), $s={left({m}_{N}^{2}-{m}_{pi }^{2}right)}^{2}/{m}_{N}^{2}$ is the accumulation point of poles on the second sheet of the complex s plane. The proof is valid up to all orders of chiral expansions. |
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Keywords: | dispersion relations partial wave analyticity |
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