Difference between 2to2 interactions

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SUMMARY

The discussion centers on the differences between two interactions represented by the equations a+b → c+d and b+a → d+c, as outlined in Ken-Ichi Hikasa's "State-of-the-art formulas for helicity amplitude calculation and all that" version 2.4. The inquiry specifically addresses whether the only distinction lies in the ordering of terms or if there are underlying differences in helicity indices or diagram representations, such as s and t channels. The participant seeks clarification on the implications of these notations in the context of helicity amplitudes.

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ChrisVer
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What is the difference between these interactions?
a+b \rightarrow c+d
and
b+a \rightarrow d+c
?

I was reading the "State-of-the-art formulas for helicity amplitude calculation and all that" ver 2.4, part Ia. - Spherical-vector method for helicity amplitudes (Formalism), by Ken-Ichi Hikasa.
In the discrete symmetry and helicity amplitudes sector (pg 5) he gives different invariant matrices M forms for these two above.
 
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Are you SURE there is no difference between the notation in the two equations, ONLY the ordering? (such as a helicity index change?) He doesn't reference two different diagrams? (s and t channel?)
 

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