# 2nd (and last) probl. - threshold temperature for intermediate vector boson Z?

1. Aug 21, 2004

### Linda

Did that make any sense at all?

The problem goes, and I do my best to translate from Enlish from Swedish:

The mass of the intermediate vector boson Z is 97,1 times the mass of a protone, whos energy "at rest" is 938 MeV.
a) Calculate the threshold temperature of Z.
b) Calculate how long, after Big Bang, it took before this particle seazed to exist.

c = speed of light, and k = Boltzmanns constant = 1,38 * 10^-23 JL^-1

I hope this made some sense to someone. Please suggest a formula, I have no idea what to do!

Thanks a million,

Linda, Sweden

2. Aug 22, 2004

### zefram_c

a) Not too hard. Neglecting numerical factors, an order-of-magnitude estimate is
(mass of Z) * c^2 = (energy needed to produce a Z) = k * T
From where, you can get T. Caveat: by what mechanism do you want to produce the Z? You may have to pair produce, in which case the result doubles.
b) Once you have the temperature from (a) and some model of cooling after the BB, it shouldn't be too difficult. The Z is unstable by nature with a very small lifetime so as soon as the temperature drops below the Z threshold, the Z can be said to vanish.

3. Aug 22, 2004

### Linda

Thanks Zefram,
for helping me, I managed to solve it after!
Linda, Sweden