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How does one compute the Q^2 values for colliding beam processes?

If I have a high energy proton E_p incident on a positron E_e (head on) which scatters the positron at an angle to the proton direction with known scattering energy E', then is the Q^2 value given by

[itex]Q^2 = (\vec{p}_p + \vec{p}_e - p_e')^2 = (E_p - E_e)^2 + E'^2 - 2(E_p-E_e)E'\cos\theta[/itex]?

Consveration of momentum implies that

[itex]\vec{p}_p + \vec{p}_e = \vec{p}_p' + \vec{p}_e' [/itex] so I have defined Q as the momentum of the scattered proton. Is this the conventional definition of Q?