$S^+$ is a diagonal matrix in color space, and is given as : $S^+ = S_{rg} ^+ \hat{P_{rg}} + S_b ^+ \hat{P_b}, where, \hat{P_b} = 1_c - \hat{P_{rg}}$ is the projector on blue quarks, $\hat{P_{rg}}$ projects onto the "red" and "green" color components, and, $S_b ^+ = (\require{cancel}{p_+})^{-1} = \frac{\cancel{p_+}}{p_+ ^2}$. Now, $T^+$ is a component of the Nambu-Gorkov propagator given as $T^+ = \frac{\triangle ^* \gamma _5 \tau _2 \lambda _2 (\cancel{p_-}\cancel{p_+})}{D(p)} - \frac{\triangle ^* \gamma _5 \tau _2 \lambda _2 |\triangle|^2}{D(p)} \rightarrow T^+ = \bigg[(-) \frac{(\cancel{p_-}\cancel{p_+})\triangle ^* \gamma _5 \tau _2 \lambda _2}{D(p)} -(-) \frac{|\triangle|^2 \triangle ^* \gamma _5 \tau _2 \lambda _2}{D(p)}\bigg]; \\ $ $\overrightarrow{\tau} and \lambda$'s are the Pauli and Gell-Mann matrices respectively, $\triangle ^* and \triangle$ are scalars, $\cancel{p_\pm}\equiv\cancel{p} \pm \mu \gamma ^0$. Question: Are the extra negative signs (shown in round brackets) in the last expression for $T^+$ due to the anticommuting nature of $(\triangle ^* \gamma _5 \tau _2 \lambda _2)$ with $(\cancel{p_-}\cancel{p_+})$, or, beacuse $(\cancel{p_-}\cancel{p_+})$ 'lives' in color space while "$\triangle ^* \gamma _5 \tau _2 \lambda _2$" do not (but, as per the definitions of $\cancel{p_\pm}$ which include the Dirac matrix $\gamma _0$, shouldn't it 'be living' in Dirac space)? For further refernce, [please refer to Problem 4 in this paper].1


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