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 $m_{\pi }^2/s_0=17\pi \sqrt{\pi /2}$ .

6 pages

References in corpus (4)

• Hadronic forward scattering: Predictions for the Large Hadron Collider and cosmic rays
• The Froissart bound for inelastic cross-sections
• How Robust is the Froissart Bound?
• An upper bound on the total inelastic cross-section as a function of the total cross-section

Cited by in corpus (10)

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• Impact analysis of TOTEM data at the LHC: black disk limit exceeded
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• Analyticity Properties and Asymptotic Behavior of Scattering Amplitude in Higher Dimensional Theories
• Self-similarity and the Froissart bound
• Pomeron pole plus grey disk model: real parts, inelastic cross sections and LHC data
• Asymptotic Behaviour of Pion--Pion Total Cross-Sections
• Secondary dips and the asymptotics
• Froissart Bound, Diffraction Scattering of Hadrons and Scaling at Asymptotic Energies
• An investigation on the leading and subleading high-energy behavior of hadron-hadron total cross sections using a best-fit analysis of hadronic scattering data