Chiral order and fluctuations in multi-flavour QCD

Multi-flavour chiral perturbation theory (PT) may exhibit instabilities due to vacuum fluctuations of sea pairs. Keeping the fluctuations small would require a very precise fine tuning of the low-energy constants and to , . 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 N_f dependence of chiral symmetry breaking (SB) and a suppression of the multi-flavour chiral order parameters. A simple resummation is shown to cure the instability of PT, 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 pairs. Thanks to the latter, the standard two-flavour PT is protected from multi-flavour instabilities and could provide a well-defined expansion scheme in powers of non-strange quark masses. Received: 31 July 2002 / Revised version: 6 November 2002 / Published online: 15 January 2003 RID="a" ID="a" e-mail: sdg@hep.phys.soton.ac.uk RID="b" ID="b" e-mail: luca.girlanda@pd.infn.it ^* Present address: ECT^*, Villa Tambosi, Strada delle Tabarelle 286, 38050 Trento, Italy RID="c" ID="c" e-mail: stern@ipno.in2p3.fr