Role of the $σ$-resonance in determining the convergence of chiral perturbation theory

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dc.creatorCecile, D. J.
dc.creatorChandrasekharan, Shailesh
dc.date2008-01-24
dc.date.accessioned2026-07-07T11:55:32Z
dc.date.available2026-07-07T11:55:32Z
dc.descriptionThe dimensionless parameter $ξ= M_π^2/(16 π^2 F_π^2)$, where $F_π$ is the pion decay constant and $M_π$ is the pion 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 $p$-regime and the $ε$-regime as expected. However, $ξ\lesssim 0.002$ is necessary before 1-loop chiral perturbation theory predicts the data within 1%. For $ξ> 0.0035$ the data begin to deviate dramatically 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.
dc.description5 pages, 6 figures, revtex format
dc.identifierhttps://arxiv.org/abs/0801.3823
dc.identifierhttp://arxiv.org/abs/0801.3823
dc.identifierPhys.Rev.D77:091501,2008
dc.identifierdoi:10.1103/PhysRevD.77.091501
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/205276
dc.subjectHigh Energy Physics - Lattice
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectNuclear Theory
dc.titleRole of the $σ$-resonance in determining the convergence of chiral perturbation theory
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