Probing gluon saturation through dihadron correlations at an electron-ion collider

Two-particle azimuthal angle correlations have been proposed to be one of the most direct and sensitive probes to access the underlying gluon dynamics involved in hard scatterings. In anticipation of an electron-ion collider (EIC), detailed studies of dihadron correlation measurements in electron-proton and electron-ion collisions at an EIC have been performed. The impact of such measurements on the understanding of the different gluon distribution functions, as a clean signature for gluon saturation and to constrain saturation models further, has been explored. It is shown that dihadron correlation measurements will be one of the key methods to probe gluon saturation phenomena at a future EIC.

Figure 1

${\pi }^0$-correlation curves calculated in the saturation formalism at $10\mathrm{GeV}\times 100\mathrm{GeV}$ for $e+p$ (thick line) and $e+\mathrm{Au}$ (thin line) with (dashed curve) and without (solid curve) the Sudakov factor. The kinematics chosen are $y=0.7$, $Q^2=1{\mathrm{GeV}}^2$, $z_{h1}=z_{h2}=0.3$, $p_{h1\perp }>2\mathrm{GeV}/c$, $1\mathrm{GeV}/c<p_{h2\perp }<p_{h1\perp }$.

Figure 2

The eRHIC kinematics coverage compared to $p+\mathrm{A}$ at RHIC. The dash-dotted and dashed lines show the eRHIC kinematics for the beam energies of $10\mathrm{GeV}\times 100\mathrm{GeV}$ and $20\mathrm{GeV}\times 100\mathrm{GeV}$, respectively. The solid lines represent the RHIC coverage at $\sqrt{s}=200\mathrm{GeV}$ for $\eta =0$ and $\eta =4$, where $\eta =-\ln \tan (\theta /2)$ is the pseudorapidity of the particles.

Figure 3

Expected yields of charged particle pairs at transverse momentum $p_T>1\mathrm{GeV}/c$ in bins of ($Q^2$, $x_{Bj}$) for an integrated luminosity of $1{\text{fb}}^{-1}$ for $e+p$ $10\mathrm{GeV}\times 100\mathrm{GeV}$ (left) and $20\mathrm{GeV}\times 100\mathrm{GeV}$ (right) in the kinematic range of $1{\mathrm{GeV}}^2<Q^2<20{\mathrm{GeV}}^2$, and $0.01<y<0.95$.

Figure 4

Particle $p_T$ distributions for $e+p$ $10\mathrm{GeV}\times 100\mathrm{GeV}$ collisions with $1{\mathrm{GeV}}^2<Q^2<20{\text{GeV}}^2$, $0.01<y<0.95$. Left: charged particle production from LO DIS, gluon dijets (PGF and resolved gluon channel) and quark dijets (QCDC and resolved quark channel). Right: ${\pi }^{\pm },K^{\pm },p^{\pm }$ and ${\pi }^0$ production for all processes.

Figure 5

Feynman diagrams for different pythia subprocesses contributing to the hard interaction: (a) direct, (b) VMD, (c) anomalous. The dotted lines indicate the presence of a spectator. Bubbles stand for a hadron or hadronic structure.

Figure 6

Feynman diagrams for the hard processes based on pointlike photons: (a) $\mathcal{O}({\alpha }_s^0)$ LO DIS, (b) PGF and (c) QCDC.

Figure 7

Comparison of dihadron correlation due to different physical inputs, such as intrinsic $k_T$, initial state parton shower (IS), final state parton shower plus resonance decay (FS) and $p_T$ broadening in fragmentation processes. The $e+p$ data are for charged hadrons with a beam energy of $20\mathrm{GeV}\times 100\mathrm{GeV}$ with $1.0{\mathrm{GeV}}^2<Q^2<1.5{\mathrm{GeV}}^2$, $0.65<y<0.75$, $p_T^{\text{trig}}>2\text{GeV/}c$, $1\text{GeV/}c<p_T^{\text{assoc}}<p_T^{\text{trig}}$, $0.2<z_h^{\text{trig}}$, $z_h^{\text{assoc}}<0.4$.

Figure 8

Simulated data points for particle correlations for charged hadrons in $e+p$ and $e+\mathrm{Au}$ collisions with beam energies of $20\mathrm{GeV}\times 100\mathrm{GeV}$ and $1.0{\mathrm{GeV}}^2<Q^2<1.5{\mathrm{GeV}}^2$, $0.65<y<0.75$, $p_T^{\text{trig}}>2\text{GeV}/c$, $1\text{GeV}/c<p_T^{\text{assoc}}<p_T^{\text{trig}}$, $0.25<z_h^{\text{trig}}$, $z_h^{\text{assoc}}<0.35$. Lines are the fit for $e+p$ or $e+\mathrm{A}$ points. The shaded band shows the uncertainty due to the EPS09 nuclear PDFs.

Figure 9

${\pi }^0$ $\mathrm{\Delta }\varphi$ correlation comparing pythia and theoretical saturation calculations for $e+p$ $10\mathrm{GeV}\times 100\mathrm{GeV}$ for events from PGF and resolved gluon channel subprocesses at $1.0{\mathrm{GeV}}^2<Q^2<2.0{\mathrm{GeV}}^2$, $0.65<y<0.75$, $p_T^{\text{trig}}>2\text{GeV}/c$, $1\text{GeV}/c<p_T^{\text{assoc}}<p_T^{\text{trig}}$, $0.25<z_h^{\text{trig}}$, $z_h^{\text{assoc}}<0.35$. The solid and dashed curves show theoretical predictions including saturation effects for $e+p$ without and with the Sudakov factor, respectively. The filled and empty circles illustrate pythia simulations for $e+p$ without and with parton showers.

Figure 10

The correlation of $x_{Bj}$ vs $x_g$ for the PGF process for $e+p$ at $10\mathrm{GeV}\times 100\mathrm{GeV}$ with $0.01<y<0.95$, $1{\mathrm{GeV}}^2<Q^2<20{\text{GeV}}^2$. A relatively broad correlation between these two variables is observed.

Figure 11

$x_g$ distributions in various kinematics bins probed by the correlated hadron pairs in the PGF process for $e+p$ $10\mathrm{GeV}\times 100\mathrm{GeV}$.

Figure 12

The contours show the $\eta$ regions covered by the correlated dihadron pairs for $10\mathrm{GeV}\times 100\mathrm{GeV}$ and $20\mathrm{GeV}\times 100\mathrm{GeV}$. Thick lines mark out the region for $0.6<y<0.8$ while thin lines for $0.25<y<0.35$.

Figure 13

The correlation function at $1{\mathrm{GeV}}^2<Q^2<2{\mathrm{GeV}}^2$, $0.6<y<0.8$ for an integrated luminosity of $1{\text{fb}}^{-1}$. The $e+p$ result comes from pythia simulations. The $e+\mathrm{Au}$ results are a combination of simulations from a saturation-based model plus modified pythia simulations. The suppression factor uncertainty was estimated by varying $Q_s^2$ by a factor of 0.5 and 2. Sudakov resummation has also been incorporated for $e+\mathrm{Au}$. The solid lines represent a fit for the simulated pseudodata including detector effects; the dashed line excludes detector effects.