Abstract
The Froissart bound on the total cross section is subjected to test against very high energy data. We have found no clear evidence for its violation. The scaling property of differential cross section in the diffraction region is investigated. It exhibits scaling in the ISR, SPS, Tevatron and LHC energy domain which had hitherto remained unexplored. The slope of the diffraction peak is fitted and the data are tested against the rigorous bounds.
Highlights
The high energy scattering of hadrons is of great interest
The structure rests on certain fundamental axioms to be respected by relativistic quantum field theories (QFT)
II A, we propose a formula to fit the combined total cross section data, σpp and σpt p, from ISR energies all the way up to the cosmic rays
Summary
The high energy scattering of hadrons is of great interest. The total cross sections σpt p and σpt p , from ISR to LHC energies, are rising and the cosmic ray data continues to follow the trend. The first important point to note is that the total cross section cannot have arbitrary energy dependence This bound is not obtained from any model in a perturbative framework, rather, it is a consequence of general axioms. Remarks: (i) The analyticity of the 4-point scattering amplitudes is the cornerstone of the bound (1) The rigorous results such as analyticity and crossing symmetry are proved from axiomatic field theories [10,11,12,13]; either in the framework of Lehmann-Symanzyk-Zimmermann (LSZ) formulation [14] or from Wightman’s axioms [15]. The third section contains the summary of our results and conclusions
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