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Determination of the Longitudinal Proton Structure Function F_L(x,Q^2) at Low x

C. Adloff

TL;DR

This work demonstrates the first determination of the longitudinal proton structure function $F_L(x,Q^2)$ in the DIS regime at very low $x$ by exploiting high inelasticity data from HERA and subtracting the $F_2$ contribution predicted by an NLO QCD fit. The method relies on precise cross-section measurements at $y\approx0.7$, detailed detector calibration, and robust radiative corrections, using a DGLAP-based framework to constrain $F_2$ and then extract $F_L$. The measured $F_L$ value at $Q^2=15.4$ GeV$^2$ and $x=2.43\times10^{-4}$ is $0.52^{+0.25}_{-0.22}$ (syst) $\pm 0.03$ (stat), with a derivative $dF_L/d\ln(x) = -0.085 \pm 0.080$ (stat) $^{+0.082}_{-0.083}$ (syst), and is compatible with QCD predictions based on the gluon distribution inferred from $F_2$. This result validates the presence of significant gluon effects in the proton at low $x$ and demonstrates the feasibility of isolating $F_L$ in the HERA kinematic domain, providing a crucial test of perturbative QCD and parton dynamics in a previously inaccessible region.

Abstract

A measurement of the inclusive cross section for the deep-inelastic scattering of positrons off protons at HERA is presented at momentum transfers $8.5 \leq Q^2 \leq 35 GeV^2$ and large inelasticity $y = 0.7$, i.e. for the Bjorken-x range $0.00013 \leq x \leq 0.00055$. Using a next-to-leading order QCD fit to the structure function F_2 at lower y values, the contribution of F_2 to the measured cross section at high y is calculated and, by subtraction, the longitudinal structure function F_{L} is determined for the first time with an average value of $F_L=0.52 \pm 0.03 (stat)$^ {+0.25}_{-0.22}$ (syst) at $Q^2=15.4 GeV^2$ and $x=0.000243$.

Determination of the Longitudinal Proton Structure Function F_L(x,Q^2) at Low x

TL;DR

This work demonstrates the first determination of the longitudinal proton structure function in the DIS regime at very low by exploiting high inelasticity data from HERA and subtracting the contribution predicted by an NLO QCD fit. The method relies on precise cross-section measurements at , detailed detector calibration, and robust radiative corrections, using a DGLAP-based framework to constrain and then extract . The measured value at GeV and is (syst) (stat), with a derivative (stat) (syst), and is compatible with QCD predictions based on the gluon distribution inferred from . This result validates the presence of significant gluon effects in the proton at low and demonstrates the feasibility of isolating in the HERA kinematic domain, providing a crucial test of perturbative QCD and parton dynamics in a previously inaccessible region.

Abstract

A measurement of the inclusive cross section for the deep-inelastic scattering of positrons off protons at HERA is presented at momentum transfers and large inelasticity , i.e. for the Bjorken-x range . Using a next-to-leading order QCD fit to the structure function F_2 at lower y values, the contribution of F_2 to the measured cross section at high y is calculated and, by subtraction, the longitudinal structure function F_{L} is determined for the first time with an average value of ^ {+0.25}_{-0.22}Q^2=15.4 GeV^2x=0.000243$.

Paper Structure

This paper contains 12 sections, 6 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Cross Section Measurement
  3. Kinematics
  4. The H1 Detector
  5. Trigger
  6. Event Selection
  7. Photoproduction Background
  8. Cross Section Determination
  9. Determination of $F_L$
  10. QCD Fit
  11. Results
  12. Summary

Figures (4)

  • Figure 1: Energy distributions of a) the highest energy and b) the next highest energy BEMC clusters for the final data sample. The simulated spectra are normalized to the luminosity of the data.
  • Figure 2: Energy distributions of the highest energy cluster in the BEMC a) for photoproduction events in which the scattered positron was tagged and b) for the events rejected by the CIP requirement. The simulated spectra are normalized to the luminosity of the data.
  • Figure 3: Double differential cross section $\kappa d\sigma /dxdQ^2 = F_2 -\frac{y^2}{Y_+} F_L$ with $\kappa = Q^4x/(2 \pi \alpha^2 \cdot Y_+)$ in six $Q^2$ bins as a function of $x$. For $y > 0.6$ this analysis (open points) extends the previously published measurement [6] (closed points) towards lower $x$ and is drawn here with full errors. The open points at larger $x$ are given without errors for ease of comparison with the data of [6]. The three lines represent calculated cross sections using for $F_2$ the QCD fit, as described in sect. 3.1, and three different assumptions for $F_L$. These are the two extremes, $F_L=0$ (dashed-dotted line) and $F_L=F_2$ using $F_2$ from the QCD fit (dashed line), and $F_L$ as calculated in NLO from the quark and gluon distributions determined by the QCD fit (solid line).
  • Figure 4: Longitudinal structure function $F_L$ as function of $Q^2$ or $x=Q^2/sy$ for $y=0.7$. The inner error bars are the statistical errors. The full error bars represent the statistical and systematic errors added in quadrature. The error band represents the uncertainty of the calculation of $F_L$ using the gluon and quark distributions, as determined from the NLO QCD analysis of the H1 data [6] for $y \leq 0.35$ and the BCDMS data [8]. The dashed lines define the allowed range of $F_L$ values from $F_L=0$ to $F_L=F_2$ where $F_2$ is given by the QCD fit.