# Higgs boson in space!

Given the fact that the Higgs-like boson has an invariant mass of about 125GeV, could we detect Higgses from Outer Space as we detect photons, neutrinos, protons or cosmic rays? As the Space is the final frontier...Is there any program searching for Higgs resonances from The Outer Space?

• I think I once saw it estimated that at any time there should be about one naturally created Higgs boson in the entire observable universe. If that's true, the rate at which cosmic rays hitting our atmosphere create a Higgs boson would be so low as to never happen. But we need an actual calculation... – Mitchell Porter Jan 21 '18 at 3:09

First off, any Higgs resonances we saw would be created in our atmosphere, as the Higgs boson only "lives" for $10^{-22}~\rm s$. So you're really asking about Higgs production due to a primary cosmic ray interacting with our atmosphere.

In order to produce a Higgs boson, cosmic rays of fairly high energies are required. The production of a Higgs boson requires a center of mass energy of at least $m_H$. Since nucleons in the earth's atmosphere are approximately at rest, the center of mass energy of a cosmic ray interacting with a nucleon is given by $$E_{\rm COM}=\sqrt{s}=\sqrt{2mE}$$

where $m\approx 938~\rm GeV$ is the mass of the nucleon and $E$ is the energy of the cosmic ray. For $\sqrt{s}=m_H$, this comes out to about $8.3~\rm TeV$. Even that energy is not enough, because a proton's momentum is spread out among its partons, only one of which is involved in producing a Higgs boson. So you need a proton that is significantly greater than that in energy to have an appreciable chance of producing a Higgs boson. On order $100~\rm TeV$.

Now, at any given place on the earth, cosmic rays of that energy are fairly rare. Looking at the graph for the wikipedia page on cosmic rays suggests that it's on order one per day per square meter.

Furthermore, producing a Higgs boson is a rare event. The Higgs production cross section at the LHC at $\sqrt{s}=7~\rm TeV$ is approximately $10~\rm pb$ and the total proton-proton cross section about $100~\rm mb$. Put together, this means that, when two protons collide with that center of mass energy, the odds of them producing a Higgs boson are roughly $\frac{10~\rm pb}{100~\rm mb}\approx 10^{-10}$. This changes with energy, but it never gets much larger than that, and it's generally smaller for the energy of cosmic rays. So, this gives us on order one Higgs boson per $10^{10}~\rm m^2$ per day.

The surface of the earth is $5\times 10^{14}~\rm m^2$. So, putting all this together, there are optimistically on order $10^4$ Higgs bosons created in the atmosphere every day. Now, this leads to the final problem. Even if we could survey the entire sky for Higgs bosons, the decay of an average Higgs boson is not all that distinctive. The largest decays we could hope to really get much from are $\rm H\rightarrow\gamma\gamma$ (about $10^{-3}$ branching ratio) and $\rm H\rightarrow\mu\mu$ (a few times $10^{-4}$ branching ratio). So if we built an observatory to view the entire sky, we would only get about 10 usable Higgs bosons per day. Keep in mind this was using some rather optimistic rounding. Since realistically we can only survey a tiny portion of the sky to the precision required to identify a Higgs boson, this quickly drops to much less than one a year.

So, trying to do any cosmic ray observations involving the Higgs boson are futile. Cosmic ray observations can be useful in the low energy regime (since there are many, many low energy cosmic rays hitting the earth every second) and the ultra-high energy regime (since those reach center of mass energies significantly beyond those reachable in the LHC), but they are not so useful in the middle regime. The LHC produces more than a billion collisions at $\sqrt{s}=13~\rm TeV$ every second, and has extremely precise instrumentation very close to the collision, allowing for much more data with much greater precision that an cosmic ray observatory could achieve.

• No...I was not implying cosmic rays...I meant trying to search for a 125GeV line in astrphysical events like Supernovae or galactic centers... – riemannium Jan 21 '18 at 2:23
• @riemannium Oh, that's hopeless then. The Higgs decays into two photons, so if anything it would be a $62.5~\rm GeV$ line. But since it's only created in ultra-relativistic collisions, those $62.5~\rm GeV$ gammas get Doppler shifted to basically any random old value. – Chris Jan 21 '18 at 2:31
• @Chris dopler shift would be no problem, if there was a non explained peak in a specific value. they find positron annihilation iopscience.iop.org/article/10.1088/1742-6596/703/1/012001/meta – anna v Jan 21 '18 at 5:38
• @annav By its nature, positron annihilation tends to occur pretty much at rest relative to the medium its in, so the Doppler shift is relatively quite mild: velocities on order $k_BT$ as opposed to velocities very, very close to $c$. Between that and the rarity of Higgs bosons you'd have to take observations for a long, long time to get any sort of peak in the spectrum. I suppose you'd also have problems with multiple scattering of any photons that were created that way. – Chris Jan 21 '18 at 5:52