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

S. Nussinov
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Abstract

In this short note we show that (I) in a QCD-like theory with four (rather than two) degenerate flavors $ud u'd'$, the $ππ'$ scattering length is positive (attractive); and (II) in QCD with only two (u,d) degenerate flavors the I=2 (say, $π^+π^+$ hadronic) scattering length is, in the large $N_C$ limit, repulsive. $π(π')$ are the lowest physical states coupling to $J^p = \bar{u}(x)γ_5d(x)$ and $J^{p'} = \bar{u}'(x)γ_5d'(x),$ respectively.

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S. Nussinov. 2000-10-26. QCD Inequalities, Large $N_C$ and $ππ$ Scattering Lengths. https://arxiv.org/abs/hep-th/0010250

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