QCD Inequalities, Large $N_C$ and $ππ$ Scattering Lengths

Details QCD Inequalities, Large $N_C$ and $ππ$ Scattering Lengths QCD Inequalities, Large $N_C$ and $ππ$ Scattering Lengths

2000-10-26

arxiv.org/abs/hep-th/0010250v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, latex with one postscript figure

Scientific paper

In this short note we show that (I) in a QCD-like theory with four (rather than two) degenerate flavors $ud u'd'$, the $\pi\pi'$ scattering length is positive (attractive); and (II) in QCD with only two (u,d) degenerate flavors the I=2 (say, $\pi^+\pi^+$ hadronic) scattering length is, in the large $N_C$ limit, repulsive. $\pi(\pi')$ are the lowest physical states coupling to $J^p = \bar{u}(x)\gamma_5d(x)$ and $J^{p'} = \bar{u}'(x)\gamma_5d'(x),$ respectively.

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