Analysis of combined HERA data in the Impact-Parameter dependent Saturation model

TL;DR

This work reanalyzes the IP-Sat dipole model against the high-precision HERA combined data at small x, extracting four IP-Sat parameters by fitting the reduced cross-section and then testing predictions for F2, F_L, F2^cc, and exclusive diffractive processes (vector mesons and DVCS). The study demonstrates excellent agreement across a wide kinematic range, supports universality of the IP-Sat dipole amplitude, and reveals a centrality-dependent saturation scale. It also highlights surprisingly small effective light-quark masses and shows the gluon distribution behavior differs from global NNLO fits at small x but remains stable. The results provide a solid benchmark for saturation physics at colliders and for initial-state modeling in heavy-ion collisions and future Electron-Ion Collider studies.

Abstract

The Impact-Parameter dependent Saturation Model (IP-Sat) is a simple dipole model that incorporates key features of the physics of gluon saturation and matches smoothly to the perturbative QCD dipole expression at large Q^2 for a given x. It was previously shown that the model gives a good description of HERA data suggesting evidence for gluon saturation effects at small x. The model has also been applied to proton-proton and proton-nucleus collisions and provides the basis for the IP-Glasma model of initial conditions in heavy ion collisions. Here we present a reanalysis of available data in electron-proton collisions at small Bjorken-x, including the recently released combined data from the ZEUS and H1 collaborations. We first confront the model to the high precision combined data for the reduced cross-section and obtain its parameters. With these parameters fixed, we compare model results to data for the structure function F_2, the longitudinal structure function F_L, the charm structure function F_2^{c\bar{c}}, exclusive vector meson (J/ψ, φand ρ) production and Deeply Virtual Compton Scattering (DVCS). Excellent agreement is obtained for the processes considered at small x in a wide range of Q^2. Our results strongly hint at universality of the IP-Sat dipole amplitude and the extracted impact-parameter distribution of the proton. They also provide a benchmark for further refinements in studies of QCD saturation at colliders.

Figures (13)

• Figure 1: The parameters of the IP-Sat model, $A_g, \lambda_g, \mu_0^2$ and the corresponding $\chi^2/d.o.f$ obtained from the fit as a function of lower virtuality cut $Q^2_{\text{min}}$ in the data bin selection.
• Figure 2: The $\chi^2/d.o.f$ of the fit as a function of quark masses. In the left panel, we take $m_c=1.27$ GeV and vary the light quark mass while in the right panel, we take $m_u=0$ and vary the charm quark mass.
• Figure 3: Left: The gluon structure function as a function of $x$ for various fixed values of virtuality $Q^2$ extracted in the dipole saturation model (IP-Sat), CT10 (NNLO) Lai:2010vv and MSTW 2008 (NNLO) mstw. The corresponding theoretical uncertainties are represented with bands between solid, dashed and dotted lines for IP-Sat, CT10 and MSTW, respectively. Right: The gluon structure function $xg\left(x, \mu^2(r)\right)$ as a function of dipole transverse size $r$ for various fixed values of $x$.
• Figure 4: Left: The saturation scale extracted from the IP-Sat model with the parameter sets given in table \ref{['t-1']} and the old parameterization set from Ref. watt2007 labeled by IP-Sat (old) as a function of $1/x$ at various impact-parameter $b$. Right: The saturation scale as a function of the impact-parameter $b$ for various fixed values of $x$. In both panels, the lower and upper curves in the band correspond to the results obtained with the parameter sets given in table \ref{['t-1']} with charm mass $m_c=1.27, 1.4$ GeV, respectively.
• Figure 5: Results for the structure function $F_2(x,Q^2)$ as a function of $x$ for various values of $Q^2$. In order to separate data for each $Q^2$ from the others, the data and model results represented by the lines are multiplied by a factor $2^i$, with $i$ given on plot. We used the parameters set of the IP-Sat model given in table \ref{['t-1']} with $m_c=1.27$ GeV. The experimental data are from combined H1 and ZEUS collaborations Aaron:2009aa.