Light and heavy quark masses, Flavour breaking of chiral condensates, Meson weak leptonic decay constants in QCD

Abstract

We review the present status for the determinations of the light and heavy quark masses, the light quark chiral condensate and the decay constants of light and heavy-light (pseudo)scalar mesons from QCD spectral sum rules (QSSR). Bounds on the light quark running masses at 2 GeV are found to be: 6 MeV<(m_d+m_u)(2)<11 MeV and 71 MeV<m_s(2)<148 MeV. The agreement of the ratio m_s/(m_u+m_d)=24.2 from pseudoscalar sum rules with the one (24.4\pm 1.5) from ChPT indicates the consistency of the pseudoscalar sum rule approach. QSSR predictions from different channels for the light quark running masses leads: m_s(2)=(117.4\pm 23.4) MeV, (m_d+m_u)(2)=(10.1\pm 1.8) MeV, (m_d-m_u)(2)=(2.8\pm 0.6) MeV with the corresponding values of the RG invariant masses. The different QSSR predictions for the heavy quark masses lead to the running masss values: m_c(m_c)=(1.23\pm 0.05) GeV and m_b(m_b)=(4.24\pm 0.06) GeV, from which one can extract the scale independent ratio m_b/m_s=48.8\pm 9.8. Runned until M_Z, the b-quark mass becomes: m_b(M_Z)=(2.83\pm 0.04) GeV in good agreement with the average of direct measurements (2.82\pm 0.63) GeV from three-jet heavy quark production at LEP, and then supports the QCD running predictions based on the renormalization group equation. As a result, we have updated our old predictions of the weak decay constants f_{π&#39;(1.3)}, f_{K&#39;(1.46)}, f_{a_0(0.98)}, f_{K^*_0(1.43)}. We obtain from a global fit of the light (pseudo)scalar and B_s mesons, the flavour breakings of the normal ordered chiral condensate ratio: <ss>/<uu>=0.66\pm 0.10. The last section is dedicated to the QSSR determinations of f_{D_{(s)}} and f_{B_{(s)}}.