Structure Function Measurements and Kinematic Reconstruction at HERA

TL;DR

This paper analyzes the methods for measuring the proton structure function F2 at HERA and how kinematic reconstruction affects DIS cross-section determinations. It introduces a detector-response based framework with bin quality metrics (stability and purity) and compares electron-based, hadronic-based, and mixed reconstruction approaches, including rescaled variants. It discusses error propagation, ISR considerations, and performance across low x and high Q2 and high x and low Q2 regions, highlighting the omega method for high Q2. The work provides practical guidance for optimizing measurements with future high-luminosity HERA data.

Abstract

The procedure used for structure function measurements at HERA is briefly described and related to the properties of kinematic reconstruction. The reconstruction methods of the inclusive deep inelastic scattering variables are reviewed and their sensitivity to the energy and angle miscalibrations are discussed in detail. New prescriptions are introduced and related to the standard methods in order to optimize the F_2 structure function measurement over the widest kinematic range, both in the low x, low Q^2 and in the high x, high Q^2 regions. The prospects for the future high Q^2 studies are briefly discussed.

Figures (8)

• Figure 1: Smearing Acceptance, Stability and Purity at $Q^2$=20 GeV$^2$ for the 3 kinematic reconstruction methods: e (open triangles), DA (open squares), $\Sigma$ (closed circles).
• Figure 2: Purity at $Q^2$=1, 5, 50, 500, 5000 and 25000 GeV$^2$ for the 3 kinematic reconstruction methods: e (open triangles), DA (open squares), $\Sigma$ (closed circles).
• Figure 3: Purity at $Q^2$=1, 50 and 5000 GeV$^2$ for the 3 kinematic reconstruction methods: A$\Sigma$ (open triangles), ADA (open squares), $e\Sigma$ (closed circles).
• Figure 4: Distribution of $x_{rec}/x_{gen}$ (a) and $Q^2_{rec}/Q^2_{gen}$ (b) for the $e$, DA, $\Sigma$ and D$\Sigma$ methods for $Q^2 > 7$ GeV$^2$ at high $y$ ($0.3<y<0.7$)
• Figure 5: Distribution of $x_{method}/x_{gen}$ (a) and $Q^2_{method}/Q^2_{gen}$ (b) for the $e$, $\Sigma$, $r\Sigma$ and $r$D$\Sigma$ ($\equiv$PT) methods for $Q^2 > 7$ GeV$^2$ at high $y$ ($0.3<y<0.7$).