Eikonal fit to $pp$ and $\bar{p}p$ scattering and the edge in the scattering amplitude
| Autor: | Block, Martin M., Durand, Loyal, Ha, Phuoc, Halzen, Francis |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | We make a detailed eikonal fit to current data on the total and elastic scattering cross sections, the ratios $\rho$ of the real to the imaginary parts of the forward elastic scattering amplitudes, and the logarithmic slopes $B$ of the differential cross sections $d\sigma/dt$ 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 {\em et al.} \cite{edge}. We show that the edge region has an essentially fixed shape with a peak at approximately the "black disk" radius $R_{\rm tot}=\sqrt{\sigma_{\rm tot}/2\pi}$ of the scattering amplitude, a constant width $t_{\rm edge}\approx 1$ fm, and migrates to larger impact parameters with increasing energy proportionally to $R_{\rm tot}$. We comment on possible physical mechanisms which could lead to the edge. We show that the eikonal results for the cross sections and $\rho$ 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. Finally, we calculate the survival probabilities for large rapidity gaps in the scattering. Comment: 19 pages, 11 figures, accepted for publication in Physical Review D |
| Databáze: | arXiv |
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