Abstract
A measurement of the total pp cross section at the LHC at s=7 TeV is presented. In a special run with high-β⋆ beam optics, an integrated luminosity of 80 μb−1 was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable t. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the |t| range from 0.01 GeV2 to 0.1 GeV2 to extrapolate to |t|→0, the total cross section, σtot(pp→X), is measured via the optical theorem to be:σtot(pp→X)=95.35±0.38(stat.)±1.25(exp.)±0.37(extr.)mb, where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to |t|→0. In addition, the slope of the elastic cross section at small |t| is determined to be B=19.73±0.14(stat.)±0.26(syst.) GeV−2.
Highlights
The total hadronic cross section is a fundamental parameter of strong interactions, setting the scale of the size of the interaction region at a given energy
Using a fit to the differential elastic cross section in the |t| range from 0.01 GeV2 to 0.1 GeV2 to extrapolate to |t| → 0, the total cross section, σtot(pp → X), is measured via the optical theorem to be: σtot(pp → X) = 95.35 ± 0.38 ± 1.25 ± 0.37 mb, where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to |t| → 0
B(s)=12 - 0.22 ln(ss0) + 0.037 ln2(ss0). Of this analysis is the determination of the effective beam optics, which takes into account measurements from ALFA that are sensitive to ratios of transport matrix elements and calibration uncertainties of the quadrupoles
Summary
The total hadronic cross section is a fundamental parameter of strong interactions, setting the scale of the size of the interaction region at a given energy. The optical theorem, which relates the imaginary part of the forward elastic-scattering amplitude to the total cross section, is a general theorem in quantum scattering theory. Dispersion relations, which connect the real part of the elastic-scattering amplitude to an integral of the total cross section over energy, are based upon the analyticity and crossing symmetry of the scattering amplitude. All of these relations lead to testable constraints on the total cross section. The background t-spectrum peaks strongly at small t and falls off steeply, distinguishably different from the distribution obtained for elastic events
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