Chiral order and fluctuations in multi-flavour QCDS. Descotes-Genon1, L. Girlanda2 and J. Stern3
1 Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
2 Dipartimento di Fisica, Università di Padova and INFN, Via Marzolo 8, 35131 Padova, Italy
3 Groupe de Physique Théorique, Institut de Physique Nucléaire, 91406 Orsay-Cedex, France
(Received: 31 July 2002 / Revised version: 6 November 2002 / Published online: 15 January 2003 )
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 Nf 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(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 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.
© Società Italiana di Fisica, Springer-Verlag 2003