Lattice determination of the QCD low-energy constant ℓ7

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 & times; 103 = 2.79(58)stat(19)syst = 2.79(61)tot agrees with and substantially improves on previous determinations.