Inclusive neutral current ep cross sections with HERA II and two-dimensional unfolding

In this thesis, the inclusive neutral current ep → eX cross section at small e- scattering angles has been measured using the electromagnetic SpaCal calorimeter in the backward region of the H1 detector. This calorimeter constructed of lead and scintillating fiber was designed to measure the scattered electron with high resolution in both energy and polar angle. The analysis comprises the kinematic range of 0.06 < ye < 0.6 for the inelasticity and 14 GeV2 < Qe2 < 110 GeV2 for the squared momentum exchange. The data sample consists of positron proton collisions of the years 2006 and 2007, adding up to an integrated luminosity of ∝141 pb-1. Due to the high luminosity of the HERA II run phase the accuracy is no longer limited by the data statistics but rather by the detector resolution and systematics. The migration becomes increasingly influential; an effect which leads to distortions of the measured distribution as well as to statistical correlations between adjacent data points. At this stage, the correction of detector effects as well as the precise determination of statistical correlations become important features of a rigorous error treatment. In this analysis two-dimensional unfolding has been applied. This is a novel approach to H1 inclusive cross section measurements, which are usually based on a bin-by-bin efficiency correction (bin-by-bin method). With unfolding, the detector effect to the measurements is modelled by a linear transformation (''response matrix'') which is used to correct any distortion of the data. The inclusion of off-diagonal elements results in a coherent assessment of the statistical uncertainties and correlations. The model dependence can be optimally evaluated. In this context, the bin-by-bin method can be viewed as an approximation based on a diagonal response matrix. In a scenario of limited detector resolution, the unfolded data distributions will typically exhibit strong fluctuations and correlations between the data points. This issue can be addressed by smoothing procedures (regularization). Different methods have been tested in the analysis. Among those are an algebraic method, a method exploiting the notion of global correlation and the standard L curve method. All three methods give similar results, which are consistent with the result from the standard bin-by-bin efficiency correction. However, the statistical uncertainties from unfolding are larger than those from the standard bin-by-bin method for all tested regularization prescriptions. For the algebraic method, the statistical uncertainty is of the order of 1-2% and the total error of the order of 2-3% throughout the kinematic range of this analysis. The statistical uncertainties from unfolding and from the bin-by-bin method has been compared. This is done by choosing a rather strong smoothing prescription for the unfolding, which leads to a minimum of correlations between the data points. A difference of the order of 20-30% in the error is found. This reflects the additional effect of migration on the statistical error, a contribution that has not been accounted for by the bin-by-bin method. To summarize, the propagation from the standard bin-by-bin efficiency correction to a full two dimensional unfolding treatment does not result in an observable change of the measured cross sections, thus establishing trust in previous measurements. However, a significant impact on the statistical uncertainties is observed, which seem to be clearly underestimated by the traditional (bin-by-bin) error treatment. (orig.)