Measurement of D* Meson Cross Sections at HERA and Determination of the Gluon Density in the Proton using NLO QCD

TL;DR

This work measures D* meson production cross sections in deep inelastic scattering and photoproduction at HERA, then employs NLO QCD calculations to extract the gluon density in the proton, x_g g(x_g), across a low-x range. The analysis combines direct comparisons to HVQDIS and FMNR predictions with a data-driven unfolding procedure to map observed cross sections to the true gluon momentum fraction, yielding results at mu^2 ≈ 25–50 GeV^2. The extracted gluon densities from DIS and gamma-p collisions are consistent with each other and with the gluon density inferred from F2 scaling violations, validating the universality of the proton's gluon distribution in NLO QCD. Overall, the study demonstrates that heavy-quark production in ep scattering provides a direct, perturbatively reliable probe of the proton’s gluon content. It also confirms the applicability of the Three Flavour Number Scheme for DIS and massive charm calculations for photoproduction in describing charm production at HERA.

Abstract

With the H1 detector at the ep collider HERA, D* meson production cross sections have been measured in deep inelastic scattering with four-momentum transfers Q^2>2 GeV2 and in photoproduction at energies around W(gamma p)~ 88 GeV and 194 GeV. Next-to-Leading Order QCD calculations are found to describe the differential cross sections within theoretical and experimental uncertainties. Using these calculations, the NLO gluon momentum distribution in the proton, x_g g(x_g), has been extracted in the momentum fraction range 7.5x10^{-4}< x_g <4x10^{-2} at average scales mu^2 =25 to 50 GeV2. The gluon momentum fraction x_g has been obtained from the measured kinematics of the scattered electron and the D* meson in the final state. The results compare well with the gluon distribution obtained from the analysis of scaling violations of the proton structure function F_2.

Figures (9)

• Figure 1: (a) Mass difference $\Delta M = M (K^-\pi^+ \pi^+ _{slow}) - M (K^-\pi^+)$ distribution of $D^{\ast}$ candidates in DIS. The solid line represents the result of a fit as described in the text, which is used to extract the $D^{\ast}$ cross section. For the photoproduction samples ETAG33 (b) and ETAG44 (c) the unweighted $\Delta M$ distributions are shown.
• Figure 2: Differential DIS cross sections in the kinematic range of experimental acceptance (see Tab. \ref{['tab:sigranges']}). The H1 data are shown as points with error bars (inner: statistical, outer: total); the NLO QCD prediction using the CTEQ4F3 parton distribution set and a charm mass $m_c=1.5$ GeV is shown as a histogram. The shaded band represents the variation of the theoretical cross sections due to different choices of $m_c$ between 1.3 and 1.7 GeV. (a) Transverse $D^{\ast}$ momentum in the laboratory frame, (b) Transverse $D^{\ast}$ momentum in the hadronic centre-of-mass frame, (c) $D^{\ast}$ pseudo-rapidity, (d) four-momentum transfer squared, $Q^2$.
• Figure 3: Differential photoproduction cross sections in the kinematic range of experimental acceptance (see Tab. \ref{['tab:sigranges']}). The data are shown as solid dots with statistical error bars for the ETAG33 sample (a,b) and for the ETAG44 sample (c,d). A common systematic error of 15% is not shown. The histograms show the NLO QCD predictions based on the FMNR program, using the MRST1 parton density parameterization for the proton and the GRV-HO set for the photon. The width of the shaded band represents the variation of the theoretical cross sections due to different choices of $m_c$ between 1.3 and 1.7 GeV.
• Figure 4: Double-differential cross section $d^2\sigma_{\gamma p} /d\hat{y} dp_{\perp}$ for three different ranges of transverse momentum at an average $W_{\gamma p} = 194$ GeV, shown as data points with statistical error bars. A common systematic error of 15% is not shown. The histograms represent the NLO QCD predictions in the massive scheme based on the FMNR program (using the parton density sets MRST1 (proton) and GRV-HO (photon)); the shaded bands show their variations due to different choices of the charm quark mass between 1.3 and 1.7 GeV. The curve shows the result of a NLO QCD calculation in the massless scheme using the CTEQ4M parton density set for the proton and GRV-HO for the photon, and a charm fragmentation function extracted from $e^+e^-$ in the same framework.
• Figure 5: (a) Differential DIS cross section as a function of $x_g^{OBS}$ in the kinematic range of experimental acceptance (see Tab. \ref{['tab:sigranges']}). Figures (b-d) show the corresponding photoproduction cross sections, separately for $W_{\gamma P}=223$, 185 and 88 GeV, respectively. The meaning of the data points, histograms and their errors is the same as in Fig. \ref{['fig:difxsect']} (for DIS) and Fig. \ref{['fig:si8384']} (for $\gamma p$).