Direct extraction of the chiral quark condensate and bounds on the light quark masses

We select sum rules from which one can extract directly reliable limits on the size of the chiral symmetry breaking light quark condensate (<(psi)over bar>psi). Combined results from the nucleon and B*-B mass-splitting sum rules give a result compatible with the standard value: (<(psi)over bar>psi)(1 GeV) similar or equal to (-229 MeV)(3), through the determinations of the quark-gluon mixed condensate. The vector form factor of the D --> K*lv semi-leptonic decay leads to the range 0.6 less than or equal to (<(psi)over bar>psi)/(-229 MeV)(3) less than or equal to 1.5. The upper limit combined with the Gell-Mann-Oakes-Renner (GMOR) relation implies the interesting lower bound on the sum of light quark masses:(m(u) + M-d)(1 GeV) greater than or equal to 9.4 MeV, which combined with the ratio of light quark masses from chiral perturbation theory leads to m(s)(1 GeV) greater than or equal to (121 +/- 12) MeV. The lower limit combined with the positivity of the m(q)(2) contribution to the GMOR relation leads to the upper bound : (m(u) + m(d))(1 GeV) less than or equal to 15.7 MeV, which is independent on the nature of chiral symmetry breaking. (C) 1998 Elsevier Science B.V.