{aligned}$$

$$\begin{aligned}
A_{\Sigma2}\to&
-\sqrt3A_{\Sigma\frac12}+2A_{\Sigma\frac32}
+\frac23(\sqrt3A_{\Sigma\frac12}+A_{\Sigma\frac32}){\vec{\tau}_1}\cdot{\vec{\tau}_2}\\
B_{\Sigma2}\to&
-\sqrt3B_{\Sigma\frac12}+2B_{\Sigma\frac32}
+\frac23(\sqrt3B_{\Sigma\frac12}+B_{\Sigma\frac32}){\vec{\tau}_1}\cdot{\vec{\tau}_2}\,.\end{aligned}$$

$$\begin{aligned}
A_{\Sigma3}\to&
-\sqrt3A_{\Sigma\frac12}+2A_{\Sigma\frac32}
-\frac23(\sqrt3A_{\Sigma\frac12}+2A_{\Sigma\frac32}){\vec{\tau}_1}\cdot{\vec{\tau}_2}\\
B_{\Sigma3}\to&
-\sqrt3B_{\Sigma\frac12}+2B_{\Sigma\frac32}
-\frac23(\sqrt3B_{\Sigma\frac12}+2B_{\Sigma\frac32}){\vec{\tau}_1}\cdot{\vec{\tau}_2}\,.\end{aligned}$$

Note that Eqs. (\[eq:va\]) and (\[eq:vc\]) only have physical meaning away from the SU(3) limit.

Brief comparison of LO and NLO contributions {#sec:bc}
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  ![(UP) Medium-Long range part of the potentials for the one-pion-exchange, one-kaon-exchange, ball diagram and triangle diagrams. (DOWN) Medium-Long range part of the potentials for the one-pion-exchange, one-kaon-exchange, box and crossed box diagrams. \[fig:pot\]](pottriangles "fig:")![(UP) Medium-Long range part of the potentials for the one-pion-exchange, one-kaon-exchange, ball diagram and triangle diagrams. (DOWN) Medium-Long range part of the potentials for the one-pion-exchange, one-kaon-exchange, box and crossed box diagrams. \[fig:pot\]](potboxes "fig:")
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