# No mixing in light cone perturbation theory

In hep-ph/0609090, Triumvirate of Running Couplings in Small-x Evolution, Kovchegov et. al. calculated the running coupling correction to the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (JIMWLK) equation using light cone perturbation methods.

The diagrams he was calculated are of two types:

1. Bubbles which comes from (regular) gluon and goes to (regular) gluon.

2. Bubbles which comes from instanteneous gluon and goes to instanteneous gluon.

However, he didn't look in the more involved case when we have some mixing between interactions.

The question I would like to ask doesn't requires to read Kovchegov's paper and in terms of LCPT I can phrase it also in the following way - is there an arument why the matrix elements involving both regular and instanteneous interactions (such as $\left\langle g\left|H\right|qq\right\rangle \left\langle qq\left|H\right|0\right\rangle$ or $\left\langle qq\left|H\right|qq\right\rangle \left\langle qq\left|H\right|g\right\rangle \left\langle g\left|H\right|0\right\rangle$ for example, where $H$ denotes the interaction part of the QCD Hamiltonian) should not taken into account when calculating the wave function or any higher order corrections?

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I finaly got the answer - a careful calculation shows that these are identially vanishing. –  Yair Apr 28 '13 at 22:11