A Proton, m_{1} with Kinetic energy T = 200MeV strikes a stationary proton in the lab frame.

p + p -> p + p + X

what is the maximum mass of X, which can be produced.

I think I need to make use of E^2 - P^2 c^2 is invariant.

and

In S: E = (m_{1} + m_{0}c^2 , p = p_{1]

In S ' :

E^2 - P^2 c^2 = E^2_{1} + 2m_{0}E_{1}c^2 + m^2_{0}c^4 - T^2 (1)

where E_{1} = T + m_{0}c^2

I'm not sure what is happening in the centre of mass frame, I thought that the particle would have maximum mass when there was zero K.E i.e E' = (2m_{0} + m_{x})c^2, p' = 0 in the lab frame but I got lost when I tried to equate this with (1). This violates conservation of momentum so its pretty clearly wrong, but I'm not sure where to go any help would be appreciated.