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  • First direct lattice calcul...
    Frezzotti, R; Gagliardi, G; Lubicz, V; Martinelli, G; Sanfilippo, F; Simula, S

    Physical review. D, 10/2021, Letnik: 104, Številka: 7
    Journal Article

    We evaluate by means of lattice QCD calculations the low-energy constant ℓ7 which parametrizes strong isospin effects at next-to-leading order (NLO) in SU(2) chiral perturbation theory. Among all low-energy constants at NLO, ℓ7 is the one known less precisely, and its uncertainty is currently larger than 50%. Our strategy is based on the RM123 approach in which the lattice path-integral is expanded in powers of the isospin breaking parameter Δm = (md − mu)/2. In order to evaluate the relevant lattice correlators we make use of the recently proposed rotated twisted-mass (RTM) scheme. Within the RM123 approach, it is possible to cleanly extract the value of ℓ7 from either the pion mass splitting Mπ+ − Mπ0 induced by strong isospin breaking at order O((Δm)2) (mass method), or from the coupling of the neutral pion π 0 to the isoscalar operator .../... at order O ( Δ m ) (matrix element method). In this pilot study we limit the analysis to a single ensemble generated by the Extended Twisted Mass Collaboration (ETMC) with Nf = 2 + 1 + 1 dynamical quark flavors, which corresponds to a lattice spacing a ≃ 0.095 fm and to a pion mass Mπ ≃ 260 MeV. We find that the matrix element method outperforms the mass method in terms of resulting statistical accuracy. Our determination, ℓ7 = 2.5 (1.4) × 10−3, is in agreement and improves previous calculations.(ProQuest: … denotes formulae omitted.)