We argue that light quark loops produce a paramagnetic suppression of infrared-sensitive order parameters such as qq , as the number N f of light fermions increases. The possibly strong dependence of qq on N f is related to the observed Zweig rule violation in the scalar channel. Presuming the existence of a chiral phase transition for not too large N f , we discuss the phenomenological possibilities of separately determining the two-flavour and three-flavour condensates and the quark mass ratio r = 2m s /(m u + m d ). The issue is closely related to the interpretation of new forthcoming precise ππ data at low energy.
Abstract. The recently published E865 data on charged Ke4 decays and ππ phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters α and β, of the lowenergy constantsl3 andl4 as well as of the main two-flavour order parameters: ūu and Fπ in the limit mu = m d = 0 taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information on ππ phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the theoretical prediction relating 2a 0 0 − 5a 2 0 and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1-σ level is found and commented upon.
We discuss the influence of the vacuum fluctuations ofqq pairs on low-energy constants and condensates. 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 L 6 , which measures the Zweig-rule violation in the scalar channel. A chiral sum rule based on experimental data in this channel is used to constrain L 6 , confirming a significant decrease between the two-and the three-flavor condensates.
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.
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