Froissart Bound on Total Cross-section without Unknown Constants

Abstract

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 $\pi \pi$ scattering. E.g. for ${\pi }^0{\pi }^0$ scattering we show that for c.m. energy $\sqrt{s}\to \infty$, ${\bar{\sigma }}_{tot}(s,\infty )\equiv s{\int }_s^{\infty }d{s}^{\prime }{\sigma }_{tot}(s^{\prime })/s^{\prime 2}\le \pi (m_{\pi }{)}^{-2}[\ln (s/s_0)+(1/2)\ln \ln (s/s_0)+1{]}^2$ where $m_{\pi }^2/s_0=17\pi \sqrt{\pi /2}$ .

Comments: 6 pages