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

Abstract

We reanalyse the topological susceptibility assuming the possibility of a significant paramagnetic suppression of the three-flavour quark condensate and a correlated enhancement of vacuum fluctuations of ss pairs. Using the framework of resummed χPT, we point out that simulations performed near the physical point, with a significant mass hierarchy between u, d and s dynamical quarks, are not able to disentangle the contributions from the quark condensate and sea ss-pair fluctuations, and that simulations with three light quark masses of the same order are better suited for this purpose. We perform a combined fit of recent RBC/UKQCD data on pseudoscalar masses and decay constants as well as the topological susceptibility, and we reconsider the determination of lattice spacings in our framework, working out the consequences on the parameters of the chiral Lagrangian. We obtain (Σ(3; 2 GeV)) 1/3 = 243 ± 12 MeV for the three-flavour quark condensate in the chiral limit. We notice a significant suppression compared to the twoflavour quark condensate Σ(2; 2 GeV)/Σ(3; 2 GeV) = 1.51 ± 0.11 and we confirm previous findings of a competition between leading order and next-to-leading order contributions in three-flavour chiral series.

Isospin breaking in the phases of the K e4 form factors

“…General arguments based on the paramagnetic behaviour of the spectrum of the Dirac operator [13,58] indicate that it should be smaller than its counterpart F in N f = 2 χPT, which is evaluated around 85 MeV by lattice simulations. On the other hand, recent fits of data to next-tonext-to-leading-order χPT suggest values of F 0 as low as 65 MeV [61], in agreement with results obtained by considering lattice data in the framework of resummed χPT designed to cope with such low N f = 3 chiral order parameters [10][11][12]. In order to cover the span of possible values, we take…”

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Constraints on low energy QCD parameters from $$\eta \rightarrow 3\pi $$ η → 3 π and $$\pi \pi $$ π π scattering

“…For the two flavor order parameters, we use the lattice QCD values [8]. In addition, similarly to [24], we implement constraints following from…”

First determination of f +(0)|V us | from a combined analysis of τ → Kπν τ decay and πK scattering with constraints from K ℓ3 decays

“…Usually F (3) is traded with F π , the difference being of higher orders and thus a 0 = 1.16 GeV −2 . However there are some indications from several studies that possibly significative differences of patterns exist between the N f = 2 and N f = 3 chiral limits [63,64]- [68][69][70]. Such differences can be interpreted as a paramagnetic suppression of chiral order parameters when the number of massless flavors in the theory increases, in relation with the role ofss vacuum pairs in chiral dynamics.…”