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Register a new userExtracting many-body color charge correlators in the proton from exclusive DIS at large Bjorken x
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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.
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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.
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.
We highlight the principal results of a computation in the Color Glass Condensate effective field theory (CGC EFT) of the next-to-leading order (NLO) impact factor for inclusive photon+dijet production at Bjorken $x_{rm Bj} ll 1$ in deeply inelastic electron-nucleus (e+A DIS) collisions. When combined with extant results for next-to-leading log $x_{rm Bj}$ JIMWLK renormalization group (RG) evolution of gauge invariant two-point (dipole) and four-point (quadrupole) correlators of light-like Wilson lines, the inclusive photon+dijet e+A DIS cross-section can be determined to $sim 10$% accuracy. Our computation simultaneously provides the ingredients to compute fully inclusive DIS, inclusive photon, inclusive dijet and inclusive photon+jet channels to the same accuracy. This makes feasible quantitative extraction of many-body correlators of saturated gluons and precise determination of the saturation scale $Q_{S,A}(x_{rm Bj})$ at a future Electron-Ion Collider. An interesting feature of our NLO result is the structure of the violation of the soft gluon theorem in the Regge limit. Another is the appearance in gluon emission of time-like non-global logs which also satisfy JIMWLK RG evolution.
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).
Third-order results for the structure functions of charged-current deep-inelastic scattering are discussed. New results for 11th Mellin moment for F_2,L^(nu P - nubar P) structure functions and 12th moment for F_3^(nu P - nubar P) are presented as well as corresponding higher Mellin moments of differences between the respective crossing-even and -odd coefficient functions. Approximations in Bjorken-x space for these differences obtained with lowest five moments as well as consistency of new results with these approximations are discussed. The 1/N_c suppression of the differences is shown and the correction to the Paschos-Wolfenstein relation is discussed.
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