120 research outputs found
Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility
The first two non-trivial moments of the distribution of the topological
charge (or gluonic winding number), i.e., the topological susceptibility and
the fourth cumulant, can be computed in lattice QCD simulations and exploited
to constrain the pattern of chiral symmetry breaking. We compute these two
topological observables at next-to-leading order in three-flavour Chiral
Perturbation Theory, and we discuss the role played by the eta propagation in
these expressions. For hierarchies of light-quark masses close to the physical
situation, we show that the fourth cumulant has a much better sensitivity than
the topological susceptibility to the three-flavour quark condensate, and thus
constitutes a relevant tool to determine the pattern of chiral symmetry
breaking in the limit of three massless flavours. We provide the complete
formulae for the two topological observables in the isospin limit, and predict
their values in the particular setting of the recent analysis of the RBC/UKQCD
collaboration. We show that a combination of the topological susceptibility and
the fourth cumulant is able to pin down the three-flavour condensate in a
particularly clean way in the case of three degenerate quarks.Comment: 31 pages, 7 figures. Accepted for publication in EPJ
Chiral dynamics with strange quarks in the light of recent lattice simulations
Several lattice collaborations performing simulations with 2+1 light
dynamical quarks have experienced difficulties in fitting their data with
standard Nf=3 chiral expansions at next-to-leading order, yielding low values
of the quark condensate and/or the decay constant in the Nf=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 Kl3} 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 Nf=2 and Nf=3 chiral limits. We discuss the
consequences for the ratio of decay constants F_K/F_pi and the Kl3 form factor
at vanishing momentum transfer.Comment: 31 pages. Published versio
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Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility
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