Two-body decay
MB and MC have equal and opposite momenta, so Eq. (3.12) tells us that
And conservation of energy gives (dropping the c’s)
Eqs. (3.114) and (3.115) are two equations in the two unknowns, EB and EC. Solving the equations gives (using
the shorthand a ≡ MA, etc.)
From Eq. (3.114), the magnitude of the (equal and opposite) momentum p of the particles in then
REMARK: It turns out that the quantity under the radical in Eq. (3.117) can be factored into
This makes it clear that if a = b + c then p = 0, because there is no energy left over for the particles to be able to
move. Interestingly, the form of p in Eq. (3.117) looks very much like the area of a triangle with sides a, b, c, which is
given by Heron’s formula as
In the given decay, we must have a ≥ b + c; whereas in a triangle, we must have a ≤ b + c.