Chiral effective theory with a light scalar and lattice QCD

Abstract

We extend the usual chiral perturbation theory framework ($\chi$PT) to allow the inclusion of a light dynamical isosinglet scalar. Using lattice QCD results, and a few phenomenological inputs, we explore the parameter space of the effective theory. We discuss the S-wave pion-pion scattering lengths, extract the average value of the two light quark masses and evaluate the impact of the dynamical singlet field in the low--energy constants ${\bar{l}}_1$, ${\bar{l}}_3$ and ${\bar{l}}_4$ of $\chi$PT. We also show how to extract the mass and width of the sigma resonance from chiral extrapolations of lattice QCD data.

Journal version. Added the study of the scalar two-point function and a discussion of the analytical properties of the sigma pole and its dependence on the quark masses. We clarified the relation of $chi$PT${}_S$ with unitarized $chi$PT. Figures 6 and 8 have been improved. 28 pages, 2 tables, 8 figures

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• I=2 $\pi$-$\pi$ scattering length with dynamical overlap fermion
• Precise determination of the sigma pole location from a dispersive analysis

Cited by in corpus (17)

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• Hazma: A Python Toolkit for Studying Indirect Detection of Sub-GeV Dark Matter
• Extending Chiral Perturbation Theory with an Isosinglet Scalar
• Strong dynamics, composite Higgs and the conformal window
• Chiral effective theories with a light scalar at one loop
• The twelve-flavor $\mathbf{\beta }$-function and dilaton tests of the sextet scalar
• Linear Sigma EFT for Nearly Conformal Gauge Theories
• Resonance effects in pion and kaon decay constants
• The lowest resonance in QCD from low--energy data
• On pion and kaon decay constants and chiral SU(3) extrapolations
• Tantalizing dilaton tests from a near-conformal EFT
• Photoproduction of the scalar mesons $f_0(500)$ and $f_0(980)$ off the nucleon
• Beyond the Standard Model: Charting Fundamental Interactions via Lattice Simulations
• The reactions $\pi \pi \to \pi \pi$ and $\gamma \gamma \to \pi \pi$ in $\chi$PT with an isosinglet scalar resonance
• Insights into $Q^2{\bar{Q}}^2$ states from an effective perspective