Zweig rule violation in the scalar sector and values of low-energy constants

Abstract

We discuss the role of the Zweig rule (ZR) violation in the scalar channel for the determination of low-energy constants and condensates arising in the effective chiral Lagrangian of QCD. The analysis of the Goldstone boson masses and decay constants shows that the three-flavor condensate and some low-energy constants are very sensitive to the value of the ZR violating constant L 6 . A similar study is performed in the case of the decay constants. A chiral sum rule based on experimental data in the 0 ++ channel is used to constrain L 6 , indicating a significant decrease between the two-and the three-flavor condensates. The analysis of the scalar form factors of the pion at zero momentum suggests that the pseudoscalar decay constant could also be suppressed from N f = 2 to 3.

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

“…Indeed, the χ 2 min obtained from fit B5 gets similar contributions from F π , F π M π , F K M K and M Ω , whereas the contribution from the topological susceptibility is small. The rest of the analysis is unchanged, with a competition between LO and NLO contributions for the observables of interest: [17,18]. Our fit B5 features a fairly good χ 2 min /N compared to the results in ref.…”

“…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.…”

“…This suppression is expected to be more and more pronounced as more and more light quark masses are sent to zero due to a paramagnetic suppression from the vacuum fluctuations of sea-quark pairs [16]. This effect is hinted at by the significant violation of the Zweig rule in the scalar sector, and should affect three-flavour dynamics involving kaons and eta mostly, but not (or only mildly) the two-flavour dynamics of pions alone [17,18]. Such a suppression would lead to a decrease of the condensate in the N f = 3 case compared to its value in the N f = 2 limit.…”