How many Higgs bosons have ever existed?

[Eel13]

If the Higgs boson is an excitation in the Higgs field, does that mean that it is exceedingly rare? Do they exist only on earth, or are they also created in high energy places such as quasars? Are the number of Higgs bosons that have existed in the universe on the order of hundreds, billions, or much much larger? I could also ask this question about other unstable particles suck as top quarks and large atoms. Thanks.

 

[Orodruin]

Given that nature does particle collisions spontaneously all the time by colliding cosmic rays with differents stuff, the number should be huge. However, it is not really a question that has a meaningful answer, there is no way of checking the answer experimentally.

 

[ChrisVer]

they dong exist at earth... even if cosmic rays were to collide with the upper atmosphere and produce higgs particles they wouldn't live long enough to reach the earth...

 

[Orodruin]

they dong exist at earth... even if cosmic rays were to collide with the upper atmosphere and produce higgs particles they wouldn't live long enough to reach the earth...

I never said they reached the Earth surface nor was that part of the question. I did not even specify the Earth as cosmic rays can collide with anything in its path. I would also consider the atmosphere a part of the Earth.

 

[ChrisVer]

my answer was not to you though... hahaha but to the 1st post...
There is no meaning to count the number of unstable particles of the universe. Because it won't be a fixed number but will change from region to region and with time.
The upper parts of the Earth atmosphere can't be considered "earth". For example pions are created by the CR but they never reach earth- only muons do. it's a part of definition, but the outer atmosphere is pretty much faraway.

 

[mfb]

For the atmosphere of earth: let's use the approximation that all high-energetic particles are protons, and that they always hit protons (those approximations are quite good at the relevant energy scales). The center-of-mass energy is then given by $\sqrt{2 m_p E}$ with the incoming particle energy E.
While the cross-section increases a bit with increasing energy, the flux decreases significantly, so most Higgs bosons come from the lower end of the available energy range. The Tevatron was the first collider to get a reasonable Higgs cross-section, at roughly 2 TeV CMS energy. This requires about 2000 TeV for the incoming particle, which corresponds to a flux of about 10 particles per square meter and year. The Higgs cross-section is about 1pb, compared to the total cross-section of about 100mb this gives 1 Higgs in 10¹¹ collisions. Putting everything together, the cosmic rays hitting Earth produce Higgs bosons at a rate of approximately 50000 per year or 6 per hour (+- one order of magnitude). Not so bad, but the LHC is much better with 15,000 per day (peak rate) or 600,000 in 2012.

 

[Orodruin]

Same computation for the Sun gives 69000 per hour. With the mean life of the Higgs being of the order of 1e-22 s, the number of Higgs bosons in the solar system at any given time should be significantly smaller than one.

 

[ohwilleke]

Given that nature does particle collisions spontaneously all the time by colliding cosmic rays with differents stuff, the number should be huge. However, it is not really a question that has a meaningful answer, there is no way of checking the answer experimentally.

Yea of little faith and creativity. We know that the number is greater than zero, and that it is finite because the age and expanse of the universe is finite. From there, it is simply a matter of improving precision.

We may not have a way of directly checking the answer experimentally, but we can check any of the assumptions that went into our answer experimentally.

For example, inputs in the calculation would include the age of the universe, the size of the universe, the amount of Standard Model particles in the universe (all of which are known to one or two significant digits at least), the mean lifetime of the Higgs boson, and a few key assumptions about Higgs boson production in stellar matter which can be estimated from the very solid ground of Standard Model physics and mainstream theory on stellar structure.

The biggest uncertainties would probably involve questions regarding GUT scale physics, inflation, dark matter interactions with the Higgs, and dark energy interactions with the Higgs. You could get much more accurate if you truncated the first 2% of the age of the universe after the Big Bang, because that is where it is hardest to estimate. If you wanted to estimate the average number of Higgs bosons in existence in the universe over a one year period at any time in the last 13.5 billion years, you could greatly increase your precision. For many purposes, knowing the current average number of Higgs bosons per year per sky radius of 1 degree, for example, might be a more useful number anyway.

Also, for many purposes, the reason you would want to know would be to set thresholds, for example, on the maximum flux of cosmic rays produced by Higgs boson decays in a particular detector so that this background could be compared to the signal of choice and ruled out (or not). In this case, one need only set an order of magnitude upper limit to be useful and don't have to worry about a lower bound, so you could cheat and make gross approximations in cases when your threshold isn't very sensitive to one or more of your assumptions (usually just a few assumptions will dominate the overall calculation).

 

[mfb]

Same computation for the Sun gives 69000 per hour. With the mean life of the Higgs being of the order of 1e-22 s, the number of Higgs bosons in the solar system at any given time should be significantly smaller than one.

With estimated 10²² to 10²⁴ stars in the observable universe, the expected number of currently existing Higgs bosons from cosmic rays is somewhere around one.