the center of mass energy, $Y\sim$ln$s/M^2$, $M$ being the mass of the onium. We also define $\bold{x}_{10}=\bold{x}_1-\bold{x}_0$, which means that the transverse size of the initial dipole is, $x_{10} \equiv \vert \bold{x}_{10}\vert$. The reason we choose to work with transverse coordinates instead of transverse momenta is that one can assume the partons to be frozen during emissions and the evolution process, which makes the analysis much easier. This is justified since the time scales for the processes that we consider are very short. Denoting the square of the wave function with $\phi$, Mueller showed that $$\phi^{(1)}(\bold{x}_1,Y)=\frac{\bar{\alpha}}{2\pi}\int d^2\bold{x}_2
\int_{0}^{Y}
dy\frac{x_{10}^2}{x_{20}^2x_{12}^2}\phi^{(0)}(\bold{x}_1,Y)
\label{eq:mueller2}$$ where $\bold{x_2}$ is the transverse position of the emitted gluon and $\phi^{(0)}$ and $\phi^{(1)}$ are the squared wave functions for the onia state without and with a gluon respectively. The factor $d^2\bold{x}_2\frac{x_{10}^2}{x_{20}^2x_{12}^2}$ plays the same role as the splitting functions we hade earlier. Observe that the $\bold{x}_2$ integral diverges for small $x_{20}$ or $x_{12}$. This means that the probability to emit a dipole goes to infinity as the dipole size approaches zero. To deal with this a cutoff, $\rho$, is introduced, which later can be sent to zero and will not appear in any physical quantities. Generally, if we have 