Further remarks on $ππ$ scattering dispersion relations

Physics – High Energy Physics – High Energy Physics - Phenomenology

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replace with revised version to appear in Chinese Physics Letters. Numerical calculation improved. $M_\sigma\simeq 483 {\rm

Scientific paper

10.1088/0256-307X/20/3/308

The naive use of higher order perturbation theory leads the left--hand cut integrals in $\pi\pi$ dispersion relations~\cite{hjy,Xiao01} divergent. This problem is discussed and solved. Also we point out that the Adler zero condition imposes three constraints on the dispersion relations. The $\sigma $ pole position is determined using the improved method, $M_\sigma= 483\pm 13 {\rm MeV}$,$\Gamma_\sigma= 705 \pm 50{\rm MeV}$. The scattering length parameter is found to be in excellent agreement with the experimental result.

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