Measurement and QCD Analysis of the Diffractive Deep-Inelastic Scattering Cross Section at HERA

TL;DR

The paper analyzes diffractive deep-inelastic scattering at HERA using H1 data to measure the diffractive NC cross section across a wide $Q^2$ range and to extract diffractive parton distribution functions (DPDFs) via a NLO DGLAP fit. It tests proton-vertex factorisation, characterises the $x_{I\!P}$ dependence with an effective pomeron intercept $\alpha_{I\!P}(0)\approx1.118$, and finds that gluons carry about 70% of the exchanged momentum within the probed $z$ range. A first diffractive charged current measurement is found consistent with DPDF-based predictions, and the ratio of diffractive to inclusive DIS is largely independent of $Q^2$ in most of the kinematic plane, supporting a universal diffractive parton structure. The results provide precise DPDFs for predicting diffractive processes at HERA and, by extension, at the LHC and future colliders, and they illuminate the interplay between quark and gluon densities in diffraction.

Abstract

A detailed analysis is presented of the diffractive deep-inelastic scattering process $ep\to eXY$, where $Y$ is a proton or a low mass proton excitation carrying a fraction $1 - \xpom > 0.95$ of the incident proton longitudinal momentum and the squared four-momentum transfer at the proton vertex satisfies $|t|<1 {\rm GeV^2}$. Using data taken by the H1 experiment, the cross section is measured for photon virtualities in the range $3.5 \leq Q^2 \leq 1600 \rm GeV^2$, triple differentially in $\xpom$, $Q^2$ and $β= x / \xpom$, where $x$ is the Bjorken scaling variable. At low $\xpom$, the data are consistent with a factorisable $\xpom$ dependence, which can be described by the exchange of an effective pomeron trajectory with intercept $\alphapom(0)= 1.118 \pm 0.008 {\rm (exp.)} ^{+0.029}_{-0.010} {\rm (model)}$. Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis of the $Q^2$ and $β$ dependences of the cross section. The resulting gluon distribution carries an integrated fraction of around 70% of the exchanged momentum in the $Q^2$ range studied. Total and differential cross sections are also measured for the diffractive charged current process $e^+ p \to \barν_e XY$ and are found to be well described by predictions based on the diffractive parton distributions. The ratio of the diffractive to the inclusive neutral current $ep$ cross sections is studied. Over most of the kinematic range, this ratio shows no significant dependence on $Q^2$ at fixed $\xpom$ and $x$ or on $x$ at fixed $Q^2$ and $β$.

Figures (8)

• Figure 1: Schematic illustration of the neutral current diffractive DIS process $ep \rightarrow eXp$, proceeding via virtual photon exchange. The dotted lines in (a) and (b) show the points at which the diagram can be divided under the assumptions of QCD hard scattering collinear factorisation and proton vertex factorisation, respectively. The kinematic variables defined in section \ref{['sec:kine']} are also indicated in (a).
• Figure 2: The $\beta$ and $Q^2$ dependences of the diffractive reduced cross section, multiplied by $x_{_{I\!\!P}}$, at $x_{_{I\!\!P}} = 0.0003$. In (b) the data are multiplied by a further factor of $3^i$ for visibility, with $i$ as indicated. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. Normalisation uncertainties are not shown. The data are compared with the reduced cross section at $E_p = 820 \ {\rm GeV}$ derived from the results of 'H1 2006 DPDF Fit A', which is shown as a shaded error band (experimental uncertainties only) in kinematic regions which are included in the fit and as a pair of dashed lines in regions which are excluded from the fit.
• Figure 3: The $\beta$ and $Q^2$ dependences of the diffractive reduced cross section, multiplied by $x_{_{I\!\!P}}$, at $x_{_{I\!\!P}} = 0.001$. See the caption of figure \ref{['q2dep1']} for further details.
• Figure 4: The $\beta$ and $Q^2$ dependences of the diffractive reduced cross section, multiplied by $x_{_{I\!\!P}}$, at $x_{_{I\!\!P}} = 0.003$. In (a), the quantity $y^2 / Y_+ \cdot F_L^{D(3)}$ is also shown, as extracted from the 'H1 2006 DPDF Fit A'. Adding this quantity to the reduced cross section yields $F_2^{D(3)}$. See the caption of figure \ref{['q2dep1']} for further details.
• Figure 5: The $\beta$ and $Q^2$ dependences of the diffractive reduced cross section, multiplied by $x_{_{I\!\!P}}$, at $x_{_{I\!\!P}} = 0.01$. In (a), the contribution of the sub-leading exchange alone according to the 'H1 2006 DPDF Fit A' is also shown. The data with $Q^2 \leq 90 \ {\rm GeV^2}$ ($Q^2 \geq 200 \ {\rm GeV^2}$) were obtained with $E_p = 820 \ {\rm GeV}$ ($E_p = 920 \ {\rm GeV}$). The fit results are shown for $E_p = 820 \ {\rm GeV}$. See the caption of figure \ref{['q2dep1']} for further details.