# Difference between revisions of "Limits based on Mandelstam Variables"

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− | The domain of the arccos function is from −1 to +1 inclusive and the range is from 0 to π radians inclusive (or from 0° to 180°). | + | The domain of the arccos function is from −1 to +1 inclusive and the range is from 0 to π radians inclusive (or from 0° to 180°). We find as expected for u=0 at <math>\theta=180^{\circ}</math> |

<center><math>\theta_{t=max}=180^{\circ}</math></center> | <center><math>\theta_{t=max}=180^{\circ}</math></center> |

## Revision as of 21:40, 12 June 2017

# 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

The domain of the arccos function is from −1 to +1 inclusive and the range is from 0 to π radians inclusive (or from 0° to 180°). We find as expected for u=0 at