Sub-femtometer scale color charge fluctuations in a proton made of three quarks and a gluon

The light-front wave function of a proton composed three quarks and perturbative gluon is computed. This then used to derive expressions for the color charge density correlator $?{\ensuremath{\rho}}^{a}({\stackrel{\ensuremath{\rightarrow}}{q}}_{1}){\ensuremath{\rho}}^{b}({\stackrel{\ensuremath{\rightarrow}}{q}}_{2})?$ at $\mathcal{O}({g}^{4})$ due emission by one in light-cone gauge. exhibits soft collinear singularities. Albeit, we employ exact absorption vertices, hence not required carry very small momentum, or be emitting quark. We verify that satisfies Ward identity it independent renormalization scale, i.e., ultraviolet divergences cancel. Our provide $x$-dependent initial conditions Balitsky-Kovchegov evolution $C$-even part dipole scattering matrix higher energies. That is, determine first nontrivial moment fluctuations which act as sources fields with wavelengths greater than approximately $1/x\ensuremath{\sim}10--100$.