The Constraints of Unitary on $ππ$ Scattering Dispersion Relations

Details The Constraints of Unitary on $ππ$ Scattering Dispersion Relations The Constraints of Unitary on $ππ$ Scattering Dispersion Relations

2002-01-28

arxiv.org/abs/hep-ph/0201257v2

Phys.Lett.B536:59-66,2002; Erratum-ibid.B549:362-363,2002

Physics

High Energy Physics

High Energy Physics - Phenomenology

10 pages with 4 figures, revised version to appear in Phys. Lett. B

Scientific paper

10.1016/S0370-2693(02)01811-7

A new dispersion relation for the partial wave $\pi\pi$ 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 $\sigma$ resonance and the $f_0(980)$ resonance are estimated based on the theoretical relations we obtained. The central value of the $\sigma$ pole position is $M_\sigma\simeq 410$MeV, $\Gamma_\sigma\simeq 550$MeV, obtained after including the the constraint of the Adler zero condition.

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