Froissart Bound on Total Cross-section without Unknown Constants

We determine the scale of the logarithm in the Froissart bound on total cross-sections using absolute bounds on the D-wave below threshold for $ππ$ scattering. E.g. for $π^0 π^0$ scattering we show that for c.m. energy $\sqrt{s}\rightarrow \infty$, $\barσ_{tot}(s,\infty)\equiv s\int_{s} ^{\infty} ds'σ_{tot}(s')/s'^2 \leq π(m_π)^{-2} [\ln (s/s_0)+(1/2)\ln \ln (s/s_0) +1]^2$ where $m_π^2/s_0= 17π\sqrt{π/2}$ .

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