Two-particle collision

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1. Jan 19, 2017

Guaicai

1. The problem statement, all variables and given/known data
In a two-particle collision the square of the invariant mass is.
M is total mass of the system (M2 is the square of the total mass)
m is the mass of each particles
E is the energy of each particles
p is momentum vector of eache particles

2. Relevant equations
M2 = (E1+E2)2 - (p1+p2)2 = m12+m22+2(E1E2 - p1 ⋅ p2)

now know the each energy E = mc2, here set the c =1 (Speed of Light),

3. The attempt at a solution
But how the momentum have dot product in this equation ? How the dot product p1 ⋅ p2 can derive from (p1+p2)2 ?

2. Jan 19, 2017

Simon Bridge

Try doing the algebra... hint: expand the brackets.

3. Jan 20, 2017

Guaicai

Yeah , i was tried to deriving (p1+p2)2 to the single dot product as above ,but always have the extra term.
(p1+p2)2
=p12+p22+2p1p2
=p12+p22+( p1 ⋅ p2 )

4. Jan 20, 2017

haruspex

What is the relationship between E1 and m1?