Unified description of diffractive deep inelastic scattering with saturation

Cyrille Marquet

Phys. Rev. D 76, 094017 – Published 15 November 2007

Abstract

We propose a new description of inclusive diffraction in deep inelastic scattering. The diffractive structure functions are expressed in the dipole picture and contain heavy-quark contributions. The dipole scattering amplitude, a saturation model fitted on inclusive deep inelastic scattering data, features a saturation scale $Q_{s} (x)$ larger than 1 GeV for $x = 10^{- 5}$ . The $q \bar{q} g$ contribution to the diffractive final state is modeled in such a way that both the large- $Q^{2}$ and small- $β$ limits are implemented. In the regime $x_{P} < 0.01$ in which saturation is expected to be relevant, we obtain a parameter-free description of the HERA data with $χ^{2} / points = 1.2$ .

Received 20 June 2007

DOI:https://doi.org/10.1103/PhysRevD.76.094017

Authors & Affiliations

Cyrille Marquet^*

RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA

^*marquet@quark.phy.bnl.gov

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Vol. 76, Iss. 9 — 1 November 2007

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Images

Figure 1
Representation of $γ^{*} - p$ deep inelastic scattering; inclusive (left) and diffractive (right) events are pictured with the relevant kinematic variables: the photon virtuality $Q^{2}$ , the energy squared of the $γ^{*} - p$ collision $W^{2}$ , and in the case of diffraction the momentum transfer $t$ and the invariant mass of the diffractive final state $M_{X}^{2}$ .Reuse & Permissions
Figure 2
The QCD dipole picture of deep inelastic scattering. The left diagram represents $γ^{*} - p$ elastic scattering and (via the optical theorem) corresponds to formula (7). The right diagram represents diffractive scattering (without possible final states containing gluons) and corresponds to formula (8). In this case, the final state (indicated by the vertical dashed line) is characterized by $t = - Δ^{2}$ and $M_{X}^{2} = (κ^{2} + m_{f}^{2}) / (z (1 - z))$ , with $Δ = q + q^{'}$ and $κ = (1 - z) q - z q^{'}$ in terms of the quark and antiquark momenta $q$ and $q^{'}$ . Via Fourier transformations, $q$ and $q^{'}$ impose different sizes and impact parameters for the dipole in the amplitude and the dipole in the complex conjugate amplitude.Reuse & Permissions
Figure 3
The contribution of the $X = q \bar{q} g$ final state in diffractive $γ^{*} p \to X p$ scattering. Left diagram: at large $Q^{2}$ ; the quark-antiquark transverse distance is much smaller than the quark-gluon transverse distance and an effective $g g$ dipole scatters off the proton. Right diagram: at small $β$ ; the quark-antiquark-gluon triplet scatters after the gluon emission and the quark-antiquark pair scatters before the gluon emission, with a relative minus sign. In both cases only the amplitude is shown, it has to be squared to obtain the cross section.Reuse & Permissions
Figure 4
The contribution of the $q \bar{q} g$ final state to the transverse diffractive structure function $F_{T}^{q \bar{q} g}$ at $β = 0$ as a function of $Q^{2}$ . The full lines show the exact result $F_{T}^{q \bar{q} g} |_{L L (1 / β)}$ while the dashed lines show the leading $\ln (Q^{2})$ result $F_{T}^{q \bar{q} g} |_{L L (Q^{2})}$ . Different sets of curves are for different values of $x_{P} = 0.01, 0.001, 0.0001, 0.000 01$ , from bottom to top. As $Q^{2}$ increases the two results get closer, but they coincide for only very large values of $Q^{2}$ .Reuse & Permissions
Figure 5
$x_{P} σ_{r}^{D, 3} (β, x_{P}, Q^{2})$ as a function of $x_{P}$ for different values of $β$ and $Q^{2}$ . The H1 (LRG) and ZEUS (FPC) diffractive data are compared to the predictions of our model, and the $x_{P}$ range is restricted to $x_{P} < 0.01$ . In this figure, the H1 data are unchanged and it is our predictions which are multiplied by the factor 1.23. The ZEUS data are multiplied by 0.85 in order to convert them to the H1 $M_{Y}$ range and the bin centers have been shifted to the H1 values using a parametrization given in 34. Only the statistical part of the uncertainty is shown for the data points on this plot. The shape of the curves in the $β = 0.9$ bins is due to the fact that the contribution of $F_{L}^{D, 3}$ to the reduced cross section is important for large values of $β$ .Reuse & Permissions
Figure 6
Predictions for the longitudinal diffractive structure function. $x_{P} F_{L}^{D, 3} (β, x_{P}, Q^{2})$ is plotted as a function of $β$ for $Q^{2} = 5 {GeV}^{2}$ and for different values of $x_{P} = 0.01, 0.001, 0.0001$ . With our parametrization, only the $q \bar{q}$ final state contributes.Reuse & Permissions

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