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A unified description of diffractive deep inelastic scattering with saturation

Cyrille Marquet

TL;DR

The paper develops a unified dipole-framework for diffractive deep inelastic scattering with saturation, incorporating heavy-quark effects and a BK-inspired dipole amplitude. It introduces a heavy-quark–modified IIM model for the dipole amplitude, with a Gaussian impact-parameter profile and a consistent treatment of the $q\bar{q}$ and $q\bar{q}g$ final states across large-$Q^2$ and small-$\beta$ regimes. By constructing a parameter-free description (aside from $\alpha_s$) of HERA diffractive data at xpom<0.01, it demonstrates that saturation dynamics and geometric scaling can account for the observed cross sections without additional tuning. The work provides explicit expressions for diffractive structure functions and shows how to merge different kinematic limits within a single framework, highlighting the role of the saturation scale and nonlinear QCD evolution in diffraction.

Abstract

We propose a new description of inclusive diffraction in deep inelastic scattering (DIS). 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 DIS 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-beta limits are implemented. In the regime xpom<0.01 in which saturation is expected to be relevant, we obtain a parameter-free description of the HERA data with chi^2/points=1.2.

A unified description of diffractive deep inelastic scattering with saturation

TL;DR

The paper develops a unified dipole-framework for diffractive deep inelastic scattering with saturation, incorporating heavy-quark effects and a BK-inspired dipole amplitude. It introduces a heavy-quark–modified IIM model for the dipole amplitude, with a Gaussian impact-parameter profile and a consistent treatment of the and final states across large- and small- regimes. By constructing a parameter-free description (aside from ) of HERA diffractive data at xpom<0.01, it demonstrates that saturation dynamics and geometric scaling can account for the observed cross sections without additional tuning. The work provides explicit expressions for diffractive structure functions and shows how to merge different kinematic limits within a single framework, highlighting the role of the saturation scale and nonlinear QCD evolution in diffraction.

Abstract

We propose a new description of inclusive diffraction in deep inelastic scattering (DIS). 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 DIS 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-beta limits are implemented. In the regime xpom<0.01 in which saturation is expected to be relevant, we obtain a parameter-free description of the HERA data with chi^2/points=1.2.

Paper Structure

This paper contains 14 sections, 29 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The QCD dipole picture of deep inelastic scattering
  3. The $\gamma^*\to q\bar{q}$ wavefunctions
  4. The total cross-section $\sigma^{\gamma^*p\rightarrow X}_{tot}$
  5. The diffractive cross-section $d\sigma^{\gamma^*p\rightarrow Xp}_{diff}/d\beta dt$
  6. The saturation model for the dipole amplitude $T_{q\bar{q}}$
  7. The impact-parameter profile $S(\textbf{b})$
  8. The heavy-quark improved IIM saturation model for $N(|\textbf{r}|Q_s,x)$
  9. The $q\bar{q}$ components of the diffractive structure functions
  10. The $q\bar{q}g$ contribution to the diffractive final state
  11. The large$-Q^2$ limit
  12. The small$-\beta$ limit
  13. The model for $x_{\mathbb P} F_T^{q\bar{q}g}$
  14. Description of the HERA data

Figures (5)

  • Figure 1: Representation of $\gamma^*\!-\!p$ 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 $\gamma^*\!-\!p$ collision $W^2,$ and in the case of diffraction the momentum transfer $t$ and the invariant mass of the diffractive final state $M_X^2.$
  • Figure 2: The QCD dipole picture of deep inelastic scattering. The left diagram represents $\gamma^*\!-\!p$ elastic scattering and (via the optical theorem) corresponds to formula \ref{['tot']}. The right diagram represents diffractive scattering (without possible final states containing gluons) and corresponds to formula \ref{['diff']}. In this case, the final state (indicated by the vertical dashed line) is characterized by $t\!=\!-\boldsymbol{\Delta}^2$ and $M_X^2\!=\!(\boldsymbol{\kappa}^2\!+\!m_f^2)/(z(1-z)),$ with $\boldsymbol{\Delta}\!=\!\textbf{q}\!+\!\textbf{q}'$ and $\boldsymbol{\kappa}\!=\!(1\!-\!z)\textbf{q}\!-\!z\textbf{q}'$ in terms of the quark and antiquark momenta $\textbf{q}$ and $\textbf{q}'.$ Via Fourier transformations, $\textbf{q}$ and $\textbf{q}'$ impose different sizes and impact parameters for the dipole in the amplitude and the dipole in the complex conjugate amplitude.
  • Figure 3: The contribution of the $X\!=\!q\bar{q}g$ final state in diffractive $\gamma^*p\rightarrow Xp$ scattering. Left diagram: at large $Q^2;$ the quark-antiquark transverse distance is much smaller than the quark-gluon transverse distance and an effective $gg$ dipole scatters off the proton. Right diagram: at small $\beta;$ 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.
  • 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 $\beta\!=\!0$ as a function of $Q^2.$ The full lines show the exact result $F_T^{q\bar{q}g}|_{LL(1/\beta)}$ while the dashed lines show the leading $\ln(Q^2)$ result $F_T^{q\bar{q}g}|_{LL(Q^2)}.$ Different sets of curves are for different values of $x_{\mathbb P}=0.01,\ 0.001,\ 0.0001,\ 0.00001,$ from bottom to top. As $Q^2$ increases the two results get closer, but they coincide for only very large values of $Q^2.$
  • Figure :