physconomics
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- Homework Statement
- A D meson decays into a K and pi-meson. Calculate energy and velocity of pi meson
- Relevant Equations
- E^2 = p^2c^2 + m^2c^4
Four vectors
rest mass of D = 1.86GEV/C^2
K = 0.5GEV/C^2
PI = 0.13GEV/C^2
Right, so I thought I'd done this correctly but clearly not because my velocity is greater than the speed of light, where have I gone wrong?
P = (M, 0, 0, 0)
p1 = (E1, p1x, p1y, p1z)
p2 = (E2, p2x, p2y, p2z)
P = p1 + p2
p2 = P - p1
square each side
to get (p2)2 = P2 - 2Pp1 + p12
therefore
(m2)2 = M2 - 2ME1 + m12
So E1 = (M2 - m12 + m22) / (2M)
which gives 0.867GeV
then
p1 = sqrt(E12 - m12) = 1.372x10^-10
then because p1=ymv, v = 8.90x10^16
where y = 0.867/0.13
Thank you!
P = (M, 0, 0, 0)
p1 = (E1, p1x, p1y, p1z)
p2 = (E2, p2x, p2y, p2z)
P = p1 + p2
p2 = P - p1
square each side
to get (p2)2 = P2 - 2Pp1 + p12
therefore
(m2)2 = M2 - 2ME1 + m12
So E1 = (M2 - m12 + m22) / (2M)
which gives 0.867GeV
then
p1 = sqrt(E12 - m12) = 1.372x10^-10
then because p1=ymv, v = 8.90x10^16
where y = 0.867/0.13
Thank you!