Chiral dynamics with strange quarks in the light of recent lattice simulations

Abstract

Several lattice collaborations performing simulations with 2+1 light dynamical quarks have experienced difficulties in fitting their data with standard N f = 3 chiral expansions at next-to-leading order, yielding low values of the quark condensate and/or the decay constant in the N f = 3 chiral limit. A reordering of these expansions seems required to analyse these data in a consistent way. We discuss such a reordering, known as Resummed Chiral Perturbation Theory, in the case of pseudoscalar masses and decay constants, pion and kaon electromagnetic form factors and K ℓ3 form factors. We show that it provides a good fit of the recent results of two lattice collaborations (PACS-CS and RBC/UKQCD). We describe the emerging picture for the pattern of chiral symmetry breaking, marked by a strong dependence of the observables on the strange quark mass and thus a significant difference between chiral symmetry breaking in the N f = 2 and N f = 3 chiral limits. We discuss the consequences for the ratio of decay constants F K /F π and the K ℓ3 form factor at vanishing momentum transfer.

Topological susceptibility on the lattice and the three-flavour quark condensate

“…In refs. [16][17][18][43][44][45][46][47], we have argued that the pattern of N f = 3 chiral symmetry breaking could be affected significantly by vacuum fluctuations of ss pairs, leading to the suppression of the quark condensate, the enhancement of L 6 (and L 4 ) and finally a numerical competition between LO and NLO contributions in N f = 3 chiral expansions. Such a problem would occur for eq.…”

“…A scenario where such features could occur was discussed in a series of articles [16][17][18][43][44][45][46][47]: significant vacuum fluctuations of ss pairs, hinted at by the violation of the Zweig rule in the scalar sector, could lead to a paramagnetic suppression of LO chiral order parameters (quark condensate and pseudoscalar decay constant). In the N f = 3 chiral expansions of observables such as decay constants, masses, form factors.…”

“…We have already discussed the salient features of the resummed χPT framework [47]. Let us briefly recall the basic ideas keeping in mind that no specific hypothesis is made upon the relative size of LO and NLO.…”

“…We will thus include a further element that was not discussed in detail in ref. [47], but presented in ref. [44], i.e., the decay constant and mass of the η-meson which features as a propagating mode of the correlator χ.…”

“…Indeed, in refs. [16][17][18][43][44][45][46][47], we have considered the decay constants and masses as they could be obtained from the NLO expression of A µ A ν where the propagators are explicitly expressed in terms of the physical masses, considering either the correlator at 0 (for F 2 π ) or its residue at the pseudoscalar pole (for F 2 π M 2 π ). Thanks to our diagrammatical analysis of the two-point correlator χ in χPT, we can easily identify the contribution from the propagation of the η meson in eq.…”