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arXiv · 0810.2423

Sigma-resonance and convergence of chiral perturbation theory

D. J. Cecile·Shailesh Chandrasekharan
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Abstract

The dimensionless parameter $ξ' = M^2/(16 π^2 F^2)$, where $F$ is the pion decay constant in the chiral limit and $M$ is the pion mass at leading order in the quark mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $σ$-resonance is different. Our model allows us to study efficiently the convergence of chiral perturbation theory as a function of $ξ'$. We first confirm that the leading low energy constants appearing in the chiral Lagrangian are the same when calculated from the $ε$-regime and the $p$-regime. However, $ξ' \lesssim 0.002$ is necessary before 1-loop chiral perturbation theory predicts the data within 1%. However, for $ξ' > 0.0035$ the data begin to deviate qualitatively from 1-loop chiral perturbation theory predictions. We argue that this qualitative change is due to the presence of a light $σ$-resonance in our model. Our findings may be useful for lattice QCD studies.

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D. J. Cecile, Shailesh Chandrasekharan. 2008-10-14. Sigma-resonance and convergence of chiral perturbation theory. https://arxiv.org/abs/0810.2423

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