Question

The tau lepton has a mass of ~ 2 GeV/c2 and lives on average for 3x10-13s. If you try to measure its mass (i.e. rest energy), what is the best precision that you can obtain?

The Z boson has a mass of ~ 90 GeV/c2 and lives on average for 3x10-25s. If you try to measure its mass, what is the best precision that you can obtain?

Answer 1

To measure the uncertainity in the measure of mass( or rest energy since, E = Mc2) we can use the time enegy uncertainity relation;

where Del E is uncertainity in the energy and del t is the average time elapsed during which a state changed.

so best precision that one can get in Del E = h/4.Pi.t.

Now, for tau lepton its average age is 3 * 10e-13. so using above equation Del E = 0.00329 eV/c2 and this the the minimum error that we can get to.

For z boson Del E = 3.29 GeV/c2 and this will be the minimum error that we can get.