Chiral order and fluctuations in multi-flavour QCD

Multi-flavour (Nf greater than or equal to 3) chiral perturbation theory (chiPT) 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 L-4(mu) and L-6(mu) to L-4(crit)(M-rho) = -0.51*10^(-3), L-6(crit)(M-rho) = -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 (chiSB) and a suppression of the multi-flavour chiral order parameters. A simple resummation is shown to cure the instability of N-f greater than or equal to 3 chiPT, but it modifies the standard expressions of some O(p(2)) and O(p(4)) low-energy parameters in terms of observables. On the other hand, for r = m(s)/m > 15, the two-flavour condensate is not suppressed, due to the contribution induced by massive vacuum ss pairs. Thanks to the latter, the standard two-flavour chiPT is protected from multi-flavour instabilities and could provide a well-defined expansion scheme in powers of non-strange quark masses