The light-front wave function of a proton composed of three quarks and a perturbative gluon is computed. This is then used to derive expressions for the color charge density correlator $⟨{\rho }^a({\overrightarrow{q}}_1){\rho }^b({\overrightarrow{q}}_2)⟩$ at $\mathcal{O}(g^4)$ due to the emission of a gluon by one of the quarks in the light-cone gauge. The correlator exhibits the soft and collinear singularities. Albeit, we employ exact gluon emission and absorption vertices, and hence the gluon is not required to carry very small light-cone momentum, or to be collinear to the emitting quark. We verify that the correlator satisfies the Ward identity and that it is independent of the renormalization scale, i.e., that ultraviolet divergences cancel. Our expressions provide $x$-dependent initial conditions for Balitsky-Kovchegov evolution of the $C$-even part of the dipole scattering matrix to higher energies. That is, we determine the first nontrivial moment of the color charge fluctuations which act as sources for soft color fields in the proton with wavelengths greater than approximately $1/x\sim 10–100$.

中文翻译：

---

亚飞克刻度在由三个夸克和胶子构成的质子中的彩色电荷波动

计算了由三个夸克和微扰胶子组成的质子的光前波函数。然后将其用于导出色电荷密度相关器的表达式$⟨{\rho }^{\mathrm{一种}}（{\overrightarrow{q}}_{\mathrm{1个}}）{\rho }^b（{\overrightarrow{q}}_{\mathrm{2个}}）⟩$ 在 $\mathcal{Ø}（G^4）$由于光锥计中的一个夸克发出了胶子。相关器表现出柔和的共线性奇点。尽管我们采用了精确的胶子发射和吸收顶点，因此不需要胶子携带很小的圆锥形动量或与发射夸克共线。我们验证了相关器满足Ward身份，并且独立于重新规范化尺度，即紫外线发散消除了。我们的表达提供$X$的Balitsky-Kovchegov演化的依赖初始条件 $C$-偶极子散射矩阵的偶数部分具有更高的能量。也就是说，我们确定色带波动的第一个非平凡矩，这些波动充当质子中波长大于约3的质子的柔和色场的来源。$\mathrm{1个}/X〜10–100$。