Abstract
The TOTEM experiment at the CERN LHC has measured elastic proton-proton scattering at the centre-of-mass energy $\sqrt{s}$ = 8 TeV and four-momentum transfers squared, |t|, from 6 x $10^{-4}$ GeV$^2$ to 0.2 GeV$^2$. Near the lower end of the |t|-interval the differential cross-section is sensitive to the interference between the hadronic and the electromagnetic scattering amplitudes. This article presents the elastic cross-section measurement and the constraints it imposes on the functional forms of the modulus and phase of the hadronic elastic amplitude. The data exclude the traditional Simplified West and Yennie interference formula that requires a constant phase and a purely exponential modulus of the hadronic amplitude. For parametrisations of the hadronic modulus with second- or third-order polynomials in the exponent, the data are compatible with hadronic phase functions giving either central or peripheral behaviour in the impact parameter picture of elastic scattering. In both cases, the $\rho$-parameter is found to be 0.12 $\pm$ 0.03. The results for the total hadronic cross-section are $\sigma_{tot}$ = (102.9 $\pm$ 2.3) mb and (103.0 $\pm$ 2.3) mb for central and peripheral phase formulations, respectively. Both are consistent with previous TOTEM measurements.
Highlights
Elastic scattering of protons is a process mediated by the strong and the electromagnetic interactions – the weak interaction is commonly neglected since its carriers are heavy compared to the small momentum transfers, |t|, typical of elastic scattering
The data for the analysis presented here have been taken with a new, special optics, conventionally labelled by the value of the β-function at the interaction point, β∗ = 1000 m, and developed for measuring low-|t| elastic scattering
The nuclear modulus was parametrised as an exponential function with a polynomial of degree Nb = 1 or 3 in the exponent
Summary
Elastic scattering of protons is a process mediated by the strong and the electromagnetic interactions – the weak interaction is commonly neglected since its carriers are heavy compared to the small momentum transfers, |t|, typical of elastic scattering. The combined scattering amplitude receives a third contribution reflecting Feynman diagrams with both strong and electromagnetic exchanges This term, together with the complex character of the scattering amplitudes, describes the effects of Coulomb–nuclear interference (CNI) in the differential cross-section. The form of the interpolation is inferred from non-diagonal RP track configurations (45 bottom–56 bottom or 45 top–56 top), artificially treated like diagonal signatures by inverting the coordinate signs in the arm 45; see the dashed distributions in the figure These non-diagonal configurations cannot contain any elastic signal and consist purely of background which is expected to be similar in the diagonal and non-diagonal configurations. Since the non-diagonal distributions are flat, the comparison of the signal-peak size to the amount of interpolated background yields the estimate 1 − B < 10−4
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