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arXiv · hep-ph/0201257

The Constraints of Unitary on $ππ$ Scattering Dispersion Relations

Jianyang He·Z. G. Xiao·H. Q. Zheng
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Abstract

A new dispersion relation for the partial wave $ππ$ scattering $S$ matrix is set up. Using the dispersion relation we generalize the single channel unitarity condition, $SS^+=1$, to the entire complex $s$ plane, which is equivalent to the generalized unitarity condition in quantum mechanics. The pole positions of the $σ$ resonance and the $f_0(980)$ resonance are estimated based on the theoretical relations we obtained. The central value of the $σ$ pole position is $M_σ\simeq 410$MeV, $Γ_σ\simeq 550$MeV, obtained after including the the constraint of the Adler zero condition.

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Jianyang He, Z. G. Xiao, H. Q. Zheng. 2002-04-25. The Constraints of Unitary on $ππ$ Scattering Dispersion Relations. https://doi.org/10.1016/s0370-2693(02)01811-7

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