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Register a new userNon-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-$x$ action
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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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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 discuss application of formalism of small-$x$ effective action for reggeized gluons, cite{Gribov,LipatovEff,BFKL}, for the calculation of classical gluon field of relativistic color charge, similarly to that done in CGC approach of cite{Venug,Kovner}. The equations of motion with the reggeon fields are solved in LO and NLO approximations and new solutions are found. The results are compared to the calculations performed in the CGC framework and it is demonstrated that the LO CGC results for the classical field are reproduced in our calculations. Possible applications of the NLO solution in the effective action and CGC frameworks are discussed as well.
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).
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.
In dense quark matter, the response of the color superconducting gaps to a small variation, $deltamu$, in the chemical potential of the strange quark was studied. The approximation of three massless flavors of quarks and a general ansatz for the color flavor structure of the gap matrix was used. The general pole structure of the quasi-particle propagator in this ansatz is presented. The gap equation was solved using both an NJL interaction model and perturbative single gluon exchange at moderate densities and results are presented for varying values of $deltamu$. Quantitative and qualitative differences in the dependence of the gaps on $deltamu$ were found.
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