in the derivation of  , Kovchegov used  , which does not contain the fusion process of dipoles. We will come back to dipole fusion processes on section 5.

(400,300)(0,0) (0,200)(50,200)[3]{}[5]{} (175,200)(75,125)(360) (300,200)(350,200)[3]{}[5]{} (100,250)(250,250) (100,245)(250,245) (95,225)(255,225) (95,220)(255,220) (90,200)(260,200) (90,195)(260,195) (95,180)(255,180) (95,175)(255,175) (100,160)(250,160) (100,155)(250,155) (150,230)(150,50)[3]{}[15]{} (155,230)(155,50)[3]{}[15]{} (115,215)(115,50)[3]{}[15]{} (120,215)(120,50)[3]{}[15]{} (200,190)(200,50)[3]{}[14]{} (205,190)(205,50)[3]{}[14]{} (230,165)(230,50)[3]{}[11]{} (235,165)(235,50)[3]{}[11]{} (145,40)(3,10)(90) (160,40)(3,10)(90) (110,40)(3,10)(90) (125,40)(3,10)(90) (195,40)(3,10)(90) (210,40)(3,10)(90) (225,40)(3,10)(90) (240,40)(3,10)(90) (145,50)(160,50) (145,30)(160,30) (110,50)(125,50) (110,30)(125,30) (195,50)(210,50) (195,30)(210,30) (225,50)(240,50) (225,30)(240,30)

MC Simulation of Onium Evolution With Energy Conservation
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The Main Idea
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As we mentioned earlier, the probability to emit small dipoles becomes infinitely large as the dipole size approaches zero. To deal with this we introduced a cutoff, $\rho$. This cutoff is an ultraviolet cutoff since a small dipole corresponds to two hard gluons. This follows from the relation $\frac{1}{r}\sim p_\perp$, where $r$ is the transverse size of the dipole and $p_\perp$ is the transerverse momentum. We will now develop an onium state using an ordering in rapidity, $y$, such that the rapidity increases for each emission. We find it convenient to define $y=$ln$\frac{p_\perp}{p_+}$, hence $p_+=p_\perp e^{-y}$. We see that, for fixed $y$, $p_+\rightarrow \infty$ as $r\rightarrow 0$. This means that, if we allow very small $r$ we will violate energy conservation 