Chiral order and fluctuations in multi-flavour QCD

• Published in: The European physical journal. C, Particles and fields Vol. 27; no. 1; pp. 115 - 134
• Main Authors: Descotes-Genon, S., Girlanda, L., Stern, J.
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.03.2003
• Subjects: Broken symmetry; Chiral dynamics; Dependence; Flavor (particle physics); Order parameters; Perturbation theory; Phenomenology; Variation
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s2002-01098-9

Multi-flavour \((N_f \ge 3)\) chiral perturbation theory (\(\chi\)PT) may exhibit instabilities due to vacuum fluctuations of sea \(\bar q q\) 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 \(L_4^{\mathrm {crit}}(M_\rho) = - 0.51 \cdot 10^{-3}\), \(L_6^{\mathrm {crit}}(M_\rho) = - 0.26 \cdot 10^{-3}\). 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 (\(\chi\)SB) and a suppression of the multi-flavour chiral order parameters. A simple resummation is shown to cure the instability of \(N_f\ge 3\)\(\chi\)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 \(\bar ss\) pairs. Thanks to the latter, the standard two-flavour \(\chi\)PT is protected from multi-flavour instabilities and could provide a well-defined expansion scheme in powers of non-strange quark masses.