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

AI Thread Summary
The discussion revolves around calculating the threshold temperature for the intermediate vector boson Z, which has a mass 97.1 times that of a proton. To find the threshold temperature, the relationship between mass, energy, and temperature is utilized, specifically using the formula (mass of Z) * c^2 = k * T. Additionally, the time after the Big Bang until the Z boson ceases to exist is linked to the cooling model post-Big Bang and the Z boson's inherent instability. Participants in the discussion provide insights and formulas to assist in solving these calculations. The conversation highlights the complexities of particle physics and the importance of understanding the mechanisms involved in particle production.
Linda
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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
 
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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
 

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