# Mandelstam variable

1. Feb 14, 2010

### EmmaK

1. The problem statement, all variables and given/known data
In a scattering experiment the square-root of

(i)Consider a proton of (relativistic) energy,E, incident on another proton in a stationary target. Show that in this case, s= 2m_p(m_p+E/c^2) where m_p is the proton mass.
(ii)Now consider 2 protons travelling with equal and opposite momenta, each of energy E which collide head-on. Calculate the value of s.
(iii)Using the answers to parts (i) and (ii) consider experiments with highly relativistic proton beams, and comment on the relative advantage of two colliding beams over a single beam incident on a fixed target, in searches for new undiscovered types of elementary particles
(iv)In what important way does the comparison in part (iii)differ here compared to the case of classical Galilean kinematics?

2. Relevant equations

s=(p1+p2)^2
E=pc
E=mc^2 (stationary proton)
E^2=p^2c^2+m_p ^2c^4 (moving proton)

3. The attempt at a solution
I've tried rearranging the formulae to get value of p for each proton, then subbing it into the first equation, but i just can seem to get it to work

2. Feb 14, 2010

### Ant1508

Lol, came across this looking for help with it!
I managed to get to the first answer by using the equation for s which we were given in lectures:
s=((Total Relativistic Energy)^2-(Total Momentum)^2)/c^2
Just sub in E and p and it should work, repeat for question 2.
I believe question 2 is sorted by assuming that in high energy, the mass of the particles is irrelevant, and the latter gives more energy.

3. Feb 14, 2010

### EmmaK

Still not working lol! must be doing something really stupid

4. Feb 14, 2010

### vela

Staff Emeritus
What do you have for p1 and p2?

5. Feb 14, 2010

got it :)