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  • Open Access

Low-Energy Constants of Chiral Perturbation Theory from Pion Scalar Form Factors in Nf=2+1-Flavor Lattice QCD with Controlled Errors

Georg von Hippel* and Konstantin Ottnad†

  • *Contact author: hippel@uni-mainz.de
  • †Contact author: kottnad@uni-mainz.de
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Phys. Rev. Lett. 135, 071904 – Published 13 August, 2025

DOI: https://doi.org/10.1103/f4x5-frx1

Abstract

We determine the low-energy constants f0, L4r and L5r of SU(3) chiral perturbation theory from a lattice QCD calculation of the scalar form factors of the pion with fully controlled systematics. Lattice results are computed on a large set of Nf=2+1 gauge ensembles covering four lattice spacings a∈[0.049,0.086]  fm, pion masses Mπ∈[130,350]  MeV, and various large physical volumes. By determining the notorious quark-disconnected contributions with unprecedented precision and using a large range of source-sink separations tsep∈[1.0,3.25]  fm, we are able for the first time to obtain the scalar radii from a z-expansion parametrization of the form factors rather than a simple linear approximation at small momentum transfer. The low-energy constants are obtained from the physical extrapolation of the radii using next-to-leading-order SU(3) next-to-leading-order chiral perturbation theory to parametrize the quark mass dependence. Systematic uncertainties are estimated via model averages based on the Akaike information criterion. Our determination of L4r is the first lattice determination to obtain a result not compatible with zero.

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See Also

Scalar size of the pion from lattice QCD

Konstantin Ottnad and Georg von Hippel
Phys. Rev. D 112, 034504 (2025)

Article Text

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Outline

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Phys. Rev. Lett. 135, 071904– Published 13 August, 2025
  • Received 2 April 2025
  • Accepted 2 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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