(Estimating integrands I) For $|y_{1}|+|y_{2}|\gtrsim 1$ and $|x_{1}|,|x_{2}|\leq\frac{1}{2}$, we have the estimate

$$|\gamma_{p3}-\gamma_{p4}|\leq\frac{CA^{-1/4}|\mu|}{|y|_{a}\varrho}.$$

Morever there are improved estimates for $\gamma_{p3},\gamma_{p4}$ depending on the sign of $\mu$:

$$\begin{cases}|\gamma_{p3}|\leq\frac{CA^{-3/4}|y|_{a}}{\varrho^{2}}\max(1,\log(\frac{A\mu^{2}}{|y|_{a}^{2}})),\quad&\mu\geq 0,\\ |\gamma_{p4}|\leq\frac{CA^{-3/4}|y|_{a}}{\varrho^{2}}\max(1,\log(\frac{A\mu^{2}}{|y|_{a}^{2}})),\quad&\mu\leq 0.\end{cases}$$