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Eikonal fit to $p p$ and $\bar{p} p$ scattering and the edge in the scattering amplitude

Martin M. Block^*

Loyal Durand^†

Phuoc Ha^‡

Francis Halzen^§

Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA

Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA

Department of Physics, Astronomy and Geosciences, Towson University, Towson, Maryland 21252, USA

Wisconsin IceCube Particle Astrophysics Center and Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

^*mblock@northwestern.edu
^†Present address: 415 Pearl Court, Aspen, Colorado 81611, USA. ldurand@hep.wisc.edu
^‡pdha@towson.edu
^§francis.halzen@icecube.wisc.edu

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Phys. Rev. D 92, 014030 – Published 27 July, 2015

DOI: https://doi.org/10.1103/PhysRevD.92.014030

Abstract

We make a detailed eikonal fit to current data on the total and elastic scattering cross sections, the ratios $ρ$ of the real to the imaginary parts of the forward elastic scattering amplitudes, and the logarithmic slopes $B$ of the differential cross sections $d σ / d t$ at $t = 0$ , for proton-proton and antiproton-proton scattering at center-of-mass energies $W$ from 5 GeV to 57 TeV. The fit allows us to investigate the structure of the eikonal amplitudes in detail, including the impact-parameter structure of the energy-independent edge in the scattering amplitude shown to exist by Block et al., [Phys. Rev. D 91, 011501(R) (2015)]. We show that the edge region has an essentially fixed shape with a peak at approximately the “black disk” radius $R_{tot} = \sqrt{σ_{tot} / 2 π}$ of the scattering amplitude, a constant width $t_{edge} \approx 1 fm$ , and migrates to larger impact parameters with increasing energy proportionally to $R_{tot}$ . We comment on possible physical mechanisms which could lead to the edge. We show that the eikonal results for the cross sections and $ρ$ values are described to high accuracy by analytic expressions of the forms used in earlier analyses by Block and Halzen, and extend the result to the elastic-scattering slope parameter $B$ . These expressions provide simple extrapolations of the results to much higher energies where the cross sections approach the black disk limit with $σ_{elas}$ , $σ_{inel} \to σ_{tot} / 2$ and $B \to σ_{tot} / 8 π$ . Finally, we calculate the survival probabilities for large rapidity gaps in the scattering.

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References (33)

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Eikonal fit to $p p$ and $\bar{p} p$ scattering and the edge in the scattering amplitude

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Eikonal fit to $p p$ and $\bar{p} p$ scattering and the edge in the scattering amplitude