# Limits based on Mandelstam Variables

Since the Mandelstam variables are the scalar product of 4-momenta, which are invariants, they are invariants as well. The sum of these invariant variables must also be invariant as well. Find the sum of the 3 Mandelstam variables when the two particles have equal mass in the center of mass frame gives:

Since

This implies

In turn, this implies

At the condition both t and u are equal to zero, we find

Holding u constant at zero we can find the maximum of t
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