Dependence of hadronic properties on Quark Masses and Constraints on their Cosmological Variation

We follow our previous paper on possible cosmological variation of weak scale (quark masses) and strong scale, inspired by data on cosmological variation of the electromagnetic fine structure constant from distant quasar (QSO) absorption spectra. In this work we identify the {\em strange quark mass} $m_s$ as the most important quantity, and the {\em sigma meson mass} as the ingredient of the nuclear forces most sensitive to it. As a result, we claim significantly stronger limits on ratio of weak/strong scale ($W=m_s/\Lambda_{QCD}$) variation following from our previous discussion of primordial Big-Bang Nucleosynthesis ($|\delta W/W|<0.006$) and Oklo natural nuclear reactor ($|\delta W/W|<1.2 \cdot 10^{-10}$; there is also a non-zero solution $\delta W/W=(-0.56 \pm 0.05) \cdot 10^{-9}$) .