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arXiv · hep-ph/9709215

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

H. G. Dosch·S. Narison
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Abstract

We select sum rules from which one can extract directly reliable limits on the size of the chiral symmetry breaking light quark condensate $<\barψψ>$. Combined results from the nucleon and $B^*-B$ mass-splitting sum rules give a result compatible with the standard value: $<\barψψ> (1 GeV) \simeq (-229 MeV)^3$, through the determinations of the quark-gluon mixed condensate. The vector form factor of the $D\rar K^*lν$ semi-leptonic decay leads to the range $0.6\leq <\barψψ> (-229 MeV)^3 \leq 1.5$. The upper limit combined with the Gell-Mann-Oakes-Renner (GMOR) relation implies the interesting lower bound on the sum of light quark masses:$(m_u+m_d) (1 GeV) \geq$ 9.4 MeV, which combined with the ratio of light quark masses from chiral perturbation theory leads to $m_s (1 GeV) \geq (121\pm 12)$ MeV. The lower limit combined with the positivity of the $m_q^2$ contribution to the GMOR relation leads to the upper bound : $(m_u+m_d) (1 GeV) \leq$ 15.7 MeV, which is independent on the nature of chiral symmetry breaking.

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H. G. Dosch, S. Narison. 1997-11-12. Direct extraction of the chiral quark condensate and bounds on the light quark masses. https://doi.org/10.1016/s0370-2693(97)01370-1

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