Resumming QCD vacuum fluctuations in three-flavor Chiral Perturbation Theory

Abstract

Due to its light mass of order Λ QCD , the strange quark can play a special role in Chiral Symmetry Breaking (χSB): differences in the pattern of χSB in the limits N f = 2 (m u , m d → 0, m s physical) and N f = 3 (m u , m d , m s → 0) may arise due to vacuum fluctuations of ss pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p 4 ) low-energy constants L 4 and L 6 . In case of large fluctuations, we show that the customary treatment of SU(3) × SU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of ss pairs, in order to extract information about χSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavour analysis of the low-energy ππ scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2m s /(m u + m d ) ≥ 14 at 95% confidence level. We outline how additional information may be incorporated to further constrain the pattern of χSB in the N f = 3 chiral limit.

Chiral extrapolation of the strangeness changing scalar Kπ form factor

“…Indeed, if large values for L r 4 and L r 6 as expected from a large violation of the OZI rule were confirmed in the future then the use of standard ChPT as done here would not really be appropriate. A way of solving the problem could be for example to work within resummed ChPT [72,73]. A study along this line is in progress [74].…”

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.…”

“…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.…”

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

“…Up to now, we have considered the masses and decay constants of Goldstone bosons [28,31,40] and observables derived from ππ scattering [35,40] in this framework. Exploiting the fact that some quantities describing the dynamics of pseudoscalar mesons are well measured and inverting the relationships between these observables and LECs, we can express the O(p 4 ) LECs in terms of…”