self-energy.

These considerations lead to the full RG equations as follows. $$\begin{aligned}
&&\frac{d}{d l} (\frac{1}{m}) =\left(z-2 + u  f_1(\frac{m}{M_c})\right) (\frac{1}{m}) \ , \nonumber \\
&& \frac{d}{d l}(\frac{m}{M_0}) = -u f_1(\frac{m}{M_c}) \frac{m}{M_0} \ , \nonumber \\
&& \frac{d}{d l}(\frac{m}{M_c}) = -u F_2(\frac{m}{M_c}) \ , \nonumber \\
&&\frac{d }{d l} (u) = \varepsilon \, u - N_f F_1(\frac{m}{M_c}) u^2 \ . \nonumber  \label{beta}\end{aligned}$$ Here the following functions of anisotropy are introduced. $$\begin{aligned}
&&f_1 (x) = \frac{2}{ \pi} \int d \Omega_{k} \frac{\hat{k}_x^2\hat{k}_y^2}{\sqrt{1+x(2+x) p_c(\hat{k})} } \ , \nonumber \\
&&f_2 (x) = \frac{1}{2 \pi}  \int d \Omega_k\frac{(\hat{k}_x^2-\hat{k}_y^2)^2 }{\sqrt{1+x(2+x)p_c(\hat{k})} } \ ,\nonumber \\
&&f_3 (x) = \frac{3}{8 \pi} \int d \Omega_k   \frac{x^4 k_x^2 (\hat{k}_y^2-\hat{k}_z^2)^2 }{\Big(\sqrt{1+x(2+x)p_c(\hat{k})}\Big)^5} + O(\frac{1}{x}) \ , \nonumber \\
&&F_1 (x) = 2 f_3 (x)+  \frac{1}{N_f} f_1 (x) \ , \nonumber \\
&&F_2 (x)=   ( 1+x)\left(f_1 (x) -f_2 (x)\right) \ , \nonumber \end{aligned}$$ where $p_c(k)  = \sum_{i=1}^3 k_i^4 -\sum_{i \neq j} k_i^2 k_j^2$ is used. The first two functions, $f_1$ and $f_2$, are from the fermion self energy and the third function, $f_3$, is from the boson self-energy calculation. The asymptotic form of $f_3$ is shown above while its complete form can be obtained by evaluating the bosonic self energy function directly. Numerical 