the kinematics of the subtraction term is built as follows. Calling $k_{\oplus}$ the 4-momentum of the incoming $b$, and $k_b$, $k_g$ the 4-momenta of the final $b$ and $g$ partons, one defines the momentum of the $b$ quark in the underlying Born configuration as $$\bar{k}_b = k_b + k_g - k_{\oplus} \frac{(k_b + k_g)^2}{2 (k_b + k_g) \cdot
  k_{\oplus}},$$ in such a way that $\bar{k}_b^2 = 0$. Furthermore, the incoming $b$ quark momentum is redefined as $$\bar{k}_{\oplus} = k_{\oplus} - k_{\oplus} \frac{(k_b + k_g)^2}{2 (k_b +
  k_g) \cdot k_{\oplus}},$$ so that the total 4-momentum is conserved. We see that in this way the 4-momentum of the top quark has been altered, near the collinear limit, by an amount $$k_{\oplus} \frac{(k_b + k_g)^2}{2 (k_b + k_g) \cdot k_{\oplus}} \approx
  \frac{m_{b g}^2}{E_{b g}} .$$ Since the CS procedure does not impose that the top 4-momentum is the same in the real and subtraction terms[^2] it will turn out that the top virtualities will differ there by an amount of order $m_{b g}^2 / E_{b g}$. The collinear singularity in the real and subtraction terms will thus match only if $$m_{b g}^2 \ll \Gamma_t E_{b g}, \label{eq:collimgamma}$$ where $\Gamma_t$ is the top width. 