Abstract
Color charge correlations in the proton at moderately small $x\sim 0.1$ 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.
Highlights
The planned high luminosity Electron Ion Collider (EIC) is designed to perform “imaging” of the proton with unprecedented accuracy [1]
We use a model light-front wave function (LFWF) to show that interesting, nontrivial transverse momentum and impact parameter dependent color charge correlations in the proton should be expected
These initial conditions include a nonzero C-odd “odderon” contribution to the dipole scattering amplitude which may be evolved to smaller x [7] in order to address high-energy exclusive processes involving Codd exchanges or some spin dependent transverse momentum dependent (TMD) distributions such as the gluon Sivers function of a transversely polarized proton [8]
Summary
The planned high luminosity Electron Ion Collider (EIC) is designed to perform “imaging” of the proton (and of heavy ions) with unprecedented accuracy [1]. We use a model LFWF to show that interesting, nontrivial transverse momentum and impact parameter dependent color charge correlations in the proton should be expected These initial conditions include a nonzero C-odd “odderon” contribution to the dipole scattering amplitude which may be evolved to smaller x [7] in order to address high-energy exclusive processes involving Codd exchanges or some spin dependent transverse momentum dependent (TMD) distributions such as the (dipole) gluon Sivers function of a transversely polarized proton [8]. We have restricted our discussion to the valence quark Fock state, assuming that the process probes parton momentum fractions of order x ∼ 0.1, and moderately high transverse momenta In this regime, the above should be a reasonable first approximation. For numerical estimates we employ a model wave function ψðx; k⃗ 1; x2; k⃗ 2; x3; k⃗ 3Þ described in the Appendix A
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