Dependence of hadronic properties on quark masses and constraints on their cosmological variation

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