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

Click For Summary
SUMMARY

The discussion focuses on calculating the threshold temperature for the intermediate vector boson Z, which has a mass of 97.1 times that of a proton (938 MeV). The formula derived for threshold temperature is based on the relationship between mass-energy equivalence and Boltzmann's constant, expressed as (mass of Z) * c^2 = k * T. Additionally, the discussion addresses the time after the Big Bang when the Z boson ceased to exist, emphasizing its instability and short lifetime.

PREREQUISITES
  • Understanding of mass-energy equivalence (E=mc²)
  • Familiarity with Boltzmann's constant (k = 1.38 x 10^-23 J/K)
  • Basic knowledge of particle physics, specifically the properties of the Z boson
  • Concept of cosmic cooling post-Big Bang
NEXT STEPS
  • Calculate the threshold temperature for other particles using similar mass-energy relationships
  • Research the properties and decay mechanisms of the Z boson
  • Study the cooling models of the universe after the Big Bang
  • Explore advanced topics in particle physics, including pair production and its implications
USEFUL FOR

Physicists, students of particle physics, and anyone interested in cosmology and the early universe's conditions.

Linda
Messages
13
Reaction score
0
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
 
Physics news on Phys.org
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.
 
Thanks Zefram,
for helping me, I managed to solve it after! :smile:
Linda, Sweden