Chiral order and fluctuations in multi-flavour QCD
Abstract
Multi-flavour (Nf>=3) Chiral Perturbation Theory (ChPT) may exhibit instabilities due to vacuum fluctuations of sea q-bar q pairs. Keeping the fluctuations small would require a very precise fine-tuning of the low-energy constants L4 and L6 to L4[crit](Mrho) = - 0.51 * 10(-3), and L6[crit](Mrho) = - 0.26 * 10(-3). A small deviation from these critical values -- like the one suggested by the phenomenology of OZI-rule violation in the scalar channel -- is amplified by huge numerical factors inducing large effects of vacuum fluctuations. This would lead in particular to a strong Nf-dependence of chiral symmetry breaking and a suppression of multi-flavour chiral order parameters. A simple resummation is shown to cure the instability of Nf>=3 ChPT, but it modifies the standard expressions of some O(p2) and O(p4) low-energy parameters in terms of observables. On the other hand, for r=ms/m > 15, the two-flavour condensate is not suppressed, due to the contribution induced by massive vacuum s-bar s pairs. Thanks to the latter, the standard two-flavour ChPT is protected from multi-flavour instabilities and could provide a well-defined expansion scheme in powers of non-strange quark masses.
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