# Getting to Higgs

Lifetime is the average time between creation and decay of a particle, which cannot be predicted for an individual particle, so we use the average time. The lifetime is the time when e-1 (or 37%) of them have survived. Derivation of equation

To simplify calculations, we will use only the information in a plane perpendicular (transverse) to the beams, that is, in the x-y plane.

The lifetime of B mesons is

t = d/v (since velocity = distance/time) The velocity can be determined from the momentum. However, we cannot use the usual equation p = mv These particles are moving at velocities close to the speed of light, c. Here the correct formula is
 (Do you find the usual formula for p if v is much smaller than c?)

You can solve this and find

 (You will need to use this form when you are using length measured in cm.)
When particle physicists use E, p and m, they hide the factors of c in the units. They write Relativity tells us that very fast particles appear to have lifetimes that are longer than they would be if they were at rest. We have to correct for this: (Did you calculate trest or tlab when you used t = d/v?) Remember the data from the 292 B events. Create an equation for the velocity, trest and tlab, in the first data cell and select the 292 cells and fill in the rest of the data.

 Run Event No. B MassGeV/c2 ptBGeV/c dt cm Velocityv/c Lab Lifetimesec Rest Lifetimesec Bin 65160 642324 5.277 7.966 0.388 66500 89978 5.274 20.508 0.940