Six particle amplitudes from scattering equations

Six-gluon amplitude:

(1)   \begin{align*}   \mathcal{A}_6({-}{-}{-}{+}{+}{+}) \,=\, A_{11} + A_{12} + A_{13} + A_{14} + A_{15}  \end{align*}

with

(2)   \begin{align*}    A_{11} \,&=\, -{{\langle{1 2}\rangle}^4 [4 5]^3 \over    s_{345} {\langle{1 6}\rangle} {\langle{2 6}\rangle} [3 4] \langle{1}| 4{+}5 |3] \langle{2}| 3{+}4 |5]}    \\[0.5em]    %%  A_{12} \,&=\, -{{\langle{2 5}\rangle} \langle{2}| 5{+}6 |4]^3 \over    {\langle{2 6}\rangle} {\langle{5 6}\rangle} [3 4] {\langle{2}| 3{+}4 |1]} {\langle{5}| 3{+}4 |1]} {\langle{5}| 2{+}6 |3]}}    \\[0.5em]    %%    A_{13} \,&=\, -{[3 6]\, {\langle{1}| 4{+}5 |6]}^3 \over    {\langle{4 5}\rangle} [2 6]\, [2 3]\, {\langle{1}| 4{+}5 |3]} {\langle{4}| 2{+}3 |6]} {\langle{5}| 2{+}6 |3]}}    \\[0.5em]    %%    A_{14} \,&=\, {{\langle{2 3}\rangle}^3 [5 6]^3 {\langle{2}| 3{+}4 |6]} \over    s_{561} {\langle{3 4}\rangle} [1 6]\, {\langle{2}| 3{+}4 |1]} {\langle{2}| 3{+}4 |5]} {\langle{4}| 2{+}3 |6]}}    \\[0.5em]    %%    A_{15} \,&=\, {{\langle{3}| 4{+}5 |6]}^3 \over    s_{345} {\langle{3 4}\rangle} {\langle{4 5}\rangle} [1 2]\, [2 6]\, {\langle{5}| 3{+}4 |1]}} \end{align*}

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