Abstract
The three point correlation function of color charge densities is evaluated explicitly in light cone gauge for a proton on the light cone. This includes both $C$-conjugation even and odd contributions. We account for perturbative corrections to the three-quark light cone wave function due to the emission of an internal gluon which is not required to be soft. We verify the Ward identity as well as the cancellation of UV divergences in the sum of all diagrams so that the correlator is independent of the renormalization scale. It does, however, exhibit the well known soft and collinear singularities. The expressions derived here provide the $C$-odd contribution to the initial conditions for high-energy evolution of the dipole scattering amplitude to small $x$. Finally, we also present a numerical model estimate of the impact parameter dependence of quantum color charge three-point correlations in the proton at moderately small $x$.
Highlights
In this paper we present explicit expressions for all diagrams which determine the cubic light-cone gauge color charge correlator hρaðq⃗ 1Þρbðq⃗ 2Þρcðq⃗ 3Þi in a proton
We label them as Fig:1ðq3q2gÞ, for example, corresponding to a diagram of the type shown in Fig. 1 where the first probe gluon couples to the internal gluon, the second probe gluon couples to the second quark, and the third probe couples to the third quark
We have computed the diagrams for the light-cone gauge color charge correlator hρaðq⃗ 1Þρbðq⃗ 2Þρcðq⃗ 3Þi in a proton made of three quarks and a perturbative gluon which is not required to carry a small light-cone momentum
Summary
In this paper we present explicit expressions for all diagrams which determine the cubic light-cone gauge color charge correlator hρaðq⃗ 1Þρbðq⃗ 2Þρcðq⃗ 3Þi in a proton. The odderon is related to cubic color charge density fluctuations hρaðq⃗ 1Þρbðq⃗ 2Þρcðq⃗ 3Þi (see below) and provides insight into three-body correlations in the proton This may guide phenomenological models of correlated “hot spots” which have been applied to proton-proton scattering at high energies [39,40,41,42]. We compute the correlator of three color charge operators hρaðq⃗ 1Þρbðq⃗ 2Þρcðq⃗ 3Þi where ρaðq⃗ Þ 1⁄4 ρaglðq⃗ Þ þ ρaquðq⃗ Þ This expectation value is defined as the matrix element of the product of three color charge operators between the incoming (jPi) and outgoing (hKj) proton states, stripped of the delta functions expressing conservation of plus and transverse momenta: X. We label them as Fig:1ðq3q2gÞ, for example, corresponding to a diagram of the type shown in Fig. 1 (i.e., a gluon exchange across the operator insertion by a quark with itself, with at least one of the probes attached to that internal gluon) where the first probe gluon (momentum q⃗ 1, color a) couples to the internal gluon, the second probe gluon (momentum q⃗ 2, color b) couples to the second quark, and the third probe (momentum q⃗ 3, color c) couples to the third quark
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