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The impact parameter dependence of color charge correlators in the proton is obtained from the light front formalism in light cone gauge. We include NLO corrections due to the $|qqqgrangle$ Fock state via light-cone perturbation theory. Near the center of the proton, the $b$-dependence of the correlations is very different from a transverse profile function. The resulting $t$-dependence of exclusive $J/Psi$ photoproduction transitions from exponential to power law at $|t| approx 1$ GeV$^2$. This prediction could be tested at upcoming DIS facilities or in nucleus-proton ultraperipheral collisions (UPCs).
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Color charge correlations in the proton at moderately small $xsim 0.1$ are extracted from its light-cone wave function. The charge fluctuations are far from Gaussian and they exhibit interesting dependence on impact parameter and on the relative transverse momentum (or distance) of the gluon probes. We provide initial conditions for small-$x$ Balitsky-Kovchegov evolution of the dipole scattering amplitude with impact parameter and $hat r cdot hat b$ dependence, and with non-zero $C$-odd component due to three-gluon exchange. Lastly, we compute the (forward) Weizsaecker-Williams gluon distributions, including the distribution of linearly polarized gluons, up to fourth order in $A^+$. The correction due to the quartic correlator provides a transverse momentum scale, $q > 0.5$ GeV, for nearly maximal polarization.
Color charge correlators provide fundamental information about the proton structure. In this Letter, we evaluate numerically two-point color charge correlations in a proton on the light cone including the next-to-leading order corrections due to emission or exchange of a perturbative gluon. The non-perturbative valence quark structure of the proton is modelled in a way consistent with high-$x$ proton structure data. Our results show that the correlator exhibits startlingly non-trivial behavior at large momentum transfer or central impact parameters, and that the color charge correlation depends not only on the impact parameter but also on the relative transverse momentum of the two gluon probes and their relative angle. Furthermore, from the two-point color charge correlator, we compute the dipole scattering amplitude. Its azimuthal dependence differs significantly from a impact parameter dependent McLerran-Venugopalan model based on geometry. Our results also provide initial conditions for Balitsky-Kovchegov evolution of the dipole scattering amplitude. These initial conditions depend not only on the impact parameter and dipole size vectors, but also on their relative angle and on the light-cone momentum fraction $x$ in the target.
We construct a general QCD light front formalism to compute many-body color charge correlators in the proton. These form factors can be extracted from deeply inelastic scattering measurements of exclusive final states in analogy to electromagnetic form factors extracted in elastic electron scattering experiments. Particularly noteworthy is the potential to extract a novel Odderon form factor, either indirectly from exclusive $J/Psi$ measurements, or directly from exclusive measurements of the $eta_c$ or tensor mesons at large Bjorken x. Besides the intrinsic information conveyed by these color charge correlators on the spatio-temporal tomography at the sub-femtoscopic scale at large x, the corresponding cumulants extend the domain of validity of McLerran-Venugopalan type weight functionals from small x and large nuclei to nucleons and light nuclei at large $x$, as well as to non-zero momentum transfer. This may significantly reduce nonperturbative systematic uncertainties in the initial conditions for QCD evolution equations at small $x$ and could be of strong relevance for the phenomenology of present and future collider experiments.
We derive an analytical expression for the two-gluon production in the pA (light-heavy) collisions, and focus specifically on the rapidity dependent part. We approximate the gauge field from the heavy target as the Color Glass Condensate which interacts with the light projectile whose source density allows for a perturbative expansion. We discuss the longitudinal correlations of produced particles. Our calculation goes in part beyond the eikonal limit for the emitted gluons so that we can retain the exponential terms with respect to the rapidity difference. Our expression can thus describe the short-range correlations as well as the long-range ones for which our formula is reduced to the known expression. In a special case of two high-pt gluons in the back-to-back kinematics we find that dependence on the rapidity separation is only moderate even in the diagrammatically connected part.
The McLerran-Venugopalan (MV) model is a Gaussian effective theory of color charge fluctuations at small-$x$ in the limit of large valence charge density, {it i}.{it e}., a large nucleus made of uncorrelated color charges. In this work, we explore the effects of the first non-trivial (even C-parity) non-Gaussian correction on the color charge density to the MV model (quartic term) in SU(2) and SU(3) color group in the non-perturbative regime. We compare our (numerical) non-perturbative results to (analytical) perturbative ones in the limit of small or large non-Gaussian fluctuations. The couplings in the non-Gaussian action, $barmu$ for the quadratic and $kappa_4$ for the quartic term, need to be renormalized in order to match the two-point function in the Gaussian theory. We investigate three different choices for the renormalization of these couplings: i) $kappa_{4}$ is proportional to a power of $barmu$; ii) $kappa_4$ is kept constant and iii) $barmu$ is kept constant. We find that the first two choices lead to a scenario where the small-$x$ action evolves towards a theory dominated by large non-Gaussian fluctuations, regardless of the system size, while the last one allows for controlling the deviations from the MV model.
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