Role of higher twist effects in diffractive DIS and determination of diffractive parton distribution functions

The current analysis aims to present the results of a QCD analysis of diffractive parton distribution functions (PDFs) at next-to-leading-order accuracy in perturbative QCD. In this new determination of diffractive PDFs, we use all available and up-to-date diffractive deep-inelastic scattering (DIS) datasets from H1 and ZEUS collaborations at HERA, including the most recent $\mathrm{H}1/\mathrm{ZEUS}$ combined measurements. In this analysis, we consider the heavy quark contributions to the diffractive DIS in the so-called framework of the fonll general mass variable flavor number scheme. The uncertainties on the diffractive PDFs are calculated using the standard “Hessian error propagation,” which served to provide a more realistic estimate of the uncertainties. This analysis is enriched, for the first time, by including the nonperturbative higher twist (HT) effects in the calculation of diffractive DIS cross sections, which are particularly important at $\mathrm{large}\text{−}x$ and low $Q^2$ regions. Then, the stability and reliability of the extracted diffractive PDFs are investigated upon the inclusion of HT effects. We discuss the novel aspects of the approach used in this QCD fit, namely, optimized and flexible parametrizations of diffractive PDFs, the inclusion of HT effects, and considering the recent $\mathrm{H}1/\mathrm{ZEUS}$ combined dataset. Finally, we present the extracted diffractive PDFs with and without the presence of HT effects and discuss the fit quality and the stability upon variations of the kinematic cuts and the fitted datasets. We show that the inclusion of HT effects in diffractive DIS can improve the description of the data, which leads, in general, to a very good agreement between data and theory predictions.

Figure 1

A schematic parton model diagram of inclusive diffractive DIS $ep\to epX$. Four-momenta are indicated in parentheses as well. The variable $\beta$ is the momentum fraction of the struck quark.

Figure 2

Different experiments of diffractive DIS datasets in the $\beta$ and $Q^2$ plane. The dashed lines represent the kinematic cuts applied on $Q^2$ and $\beta$ in this analysis. The data points lying outside these lines shown in the figure are only excluded in the present QCD fits.

Figure 3

The value of the total ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}$. vs the minimum ${\mathrm{GeV}}^2$ of data, ${\mathrm{Q}}_{\min }^2$, for all datasets entering in this study, which represents our specific choice of the kinematical cuts on the ${\mathrm{Q}}_{\min }^2$.

Figure 4

The diffractive PDFs as a function of momentum fraction $z$ obtained at the input scale of $Q_0^2=1.8{\mathrm{GeV}}^2$ for both of our analyses with and without the HT corrections. The error bands represent the uncertainty estimation coming from the experimental errors.

Figure 5

The extracted diffractive PDFs for gluon and quark densities in three photon virtuality of $Q^2=6$, 20 and $200{\mathrm{GeV}}^2$ compared to the results of h1-2006 fit B [16] and zeus-2010 fit SJ [17].

Figure 6

The extracted diffractive PDFs for gluon and quark densities at $Q^2=6{\mathrm{GeV}}^2$ compared to the most recent analysis by gkg18 [13].

Figure 7

Comparison between the experimental data on the diffractive reduced cross sections $x_{\mathbb{P}}{\sigma }_r^{D(3)}(\beta ,Q^2;x_{\mathbb{P}})$ from the recent H1 and ZEUS combined dataset [15] and the corresponding NLO theoretical predictions from our NLO QCD fits without (solid curves) and with (dashed curves) considering HT effects. The dots show the central values of the experimental data points, and the data errors are defined by adding in quadrature the systematical and statistical uncertainties.

Figure 8

Comparison between the experimental data on the diffractive reduced cross sections $x_{\mathbb{P}}{\sigma }_r^{D(3)}(\beta ,Q^2;x_{\mathbb{P}})$ from the H1-LRG-12 datasets [25] and the corresponding NLO theoretical predictions from our NLO QCD fits without (solid curves) and with (dashed curves) considering HT effects. The comparisons have been done for the fixed value of $x_{\mathbb{P}}=0.0003$ and different photon virtuality $Q^2$.

Figure 9

Same as Fig. 8 but for the fixed value of $x_{\mathbb{P}}=0.001$.

Figure 10

Same as Fig. 8 but for the fixed value of $x_{\mathbb{P}}=0.003$.

Figure 11

Same as Fig. 8 but for the fixed value of $x_{\mathbb{P}}=0.01$.

Figure 12

Same as Fig. 8 but for the fixed value of $x_{\mathbb{P}}=0.03$.

Figure 13

Comparison between the experimental data from the H1 and ZEUS combined dataset [15] at $Q^2=2.5{\mathrm{GeV}}^2$ and the corresponding theoretical predictions. The comparisons have been shown as theory to data ratios. Our results without HT effects are shown as a circle and the results including HT effects are presented as a triangle. The shaded bands correspond to the errors of experimental data points that are obtained by adding systematical and statistical uncertainties in quadrature.

Figure 14

Same as Fig. 13 but for $Q^2=5.09{\mathrm{GeV}}^2$.

Figure 15

Same as Fig. 13 but for $Q^2=8.8{\mathrm{GeV}}^2$.