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Lattice determination of the QCD low-energy constant ℓ7

Claudio Bonanno1,*, Gilberto Colangelo2,†, Francesco D’Angelo3,‡, Massimo D’Elia4,§, Roberto Dionisio4,∥, Roberto Frezzotti5,¶, Giuseppe Gagliardi6,**, Vittorio Lubicz6,††, Guido Martinelli7,‡‡ et al.

Francesco Sanfilippo3,§§ and Silvano Simula3,∥∥

  • *Contact author: claudio.bonanno@csic.es
  • †Contact author: gilberto@itp.unibe.ch
  • ‡Contact author: francesco.dangelo@roma3.infn.it
  • §Contact author: massimo.delia@unipi.it
  • ∥Contact author: roberto.dionisio@phd.unipi.it
  • Contact author: roberto.frezzotti@roma2.infn.it
  • **Contact author: giuseppe.gagliardi@roma3.infn.it
  • ††Contact author: vittorio.lubicz@uniroma3.it
  • ‡‡Contact author: guido.martinelli@roma1.infn.it
  • §§Contact author: francesco.sanfilippo@roma3.infn.it
  • ∥∥Contact author: simula@roma3.infn.it
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Phys. Rev. D 113, 074510 – Published 15 April, 2026

DOI: https://doi.org/10.1103/8sy5-f78d

Abstract

We provide a nonperturbative determination of the scheme- and scale-independent low-energy constant ℓ7, appearing in the QCD effective chiral Lagrangian at next-to-leading order, by means of lattice QCD simulations with Nf=2+1 quark flavors. We adopt staggered fermions and extract ℓ7 from the pion mass splitting by suitably generalizing the method introduced by Frezzotti et al. [Phys. Rev. D 104, 074513 (2021)] for the Wilson discretization. Adopting 12 gauge ensembles with three different values of the pion mass, and four different values of the lattice spacing, we are able to achieve controlled extrapolations toward the continuum, infinite volume, and chiral limits. Our final result ℓ7×103=2.79(58)stat(19)syst=2.79(61)tot agrees with and substantially improves on previous determinations.

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Phys. Rev. D 113, 074510– Published 15 April, 2026
  • Received 17 December 2025
  • Accepted 26 February 2026
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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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