Thursday, January 24, 2008

PS on GZK Cutoff

A somewhat belated answer to Eric Gisse's question to our earlier post Skymap of AGNs with Cosmic Ray Events about the GZK cutoff:
    "why is the limit imposed by pion pair production as opposed to electron pair production? the energies required for electron pair production is /significantly/ less than pion pair production."

I recently came across the figure below, which depicts the energy loss of a proton times 1/E (the relative energy loss per year), due to electron-positron pair production, and - at higher energies - pion production:

[Fig 1 (a) from V.Berezinsky, A.Z.Gazizov, S.I.Grigorieva "On astrophysical solution to ultra high energy cosmic rays", Phys.Rev. D74 (2006) 043005, arXiv:hep-ph/0204357]


As one sees, the electron-positron pair production leads to a loss and is the dominant contribution at energies below ≈ 1019 eV, but at higher energies pion production takes over, increasing the energy loss by a factor of ~ 100 which is the effect responsible for the cut-off in the spectrum.

Essentially the same is depicted differently in the figure below from Roberto Aloisio's talk, slide 2. I didn't hear the talk but a good guess is that the y axis shows the attenuation length of the protons in the CMB background. Again one sees the electron-positron pair production having an effect already at smaller energies, but it does not result in a sharp cut-off as the pion production: If energy loss would be caused by electron-positron production only, the proton could travel as far as a third the size of the observable universe.


For an excellent introduction into the physics of ultra-high-energetic air showers, I recommend Angela Olinto's recent PI colloquium, PIRSA: 08010000.

14 comments:

  1. Hi Bee,

    Does the present quantity/ratio of photons observed above the GZK cutoff suggest anything about conditions and outcomes in the early universe and its significance today? That is with average energies being so much higher then and the initial decay rate of protons above this threshold would be much higher then first thought as well. Does this suggest anything about the scarcity of matter in relation to dark matter and dark energy as it is now observed? I was going to say ordinary matter yet with things as they stand it should be referred to as extraordinary matter, if anything.

    Regards,

    Phil

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  2. Hi Bee,

    Sorry I meant present quantity/ratio of protons not photons :-/

    Best,

    Phil

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  3. a quantum diaries survivor1:18 PM, January 25, 2008

    Hi Bee,

    This post leaves me wanting. I acknowledge that the plots are compelling, but I would love to see some relativistic kinematics to explaing the onset of pion-pion production and its dominance over electron/positron production...

    I checked the talk you linked, but it is full of very pretty and colorful slides which explain little I did not know, at least at the speed at which i browsed them ;-)

    Cheers,
    T.

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  4. Hi Phil:

    I don't think so. I think it's more an astrophysics puzzle where these particles are coming from and how do they get their high energies.

    Hi Tommaso:

    Yeah. You're welcome to write a post on the matter. I promise you a link. I didn't find the paper I took the figure from too enlightening on the matter, and it's too far off my actual research to dig into it. As so often when hadrons are involved, energy dependence of cross-sections gets somewhat messy. If someone has an intuitive argument why the e+e- effect relates to the pion production the way it does, I'd be interested to hear. Best,

    B.

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  5. Way cool. Thanks for the response, Bee.

    I think this explains something I noticed and had no explanation for. If you plot the observed detection rates for cosmic rays of all energies, there are several distinct curves. Each part of the plot seems to obey a different power law, and this seems to be a compelling explanation as any.

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  6. I guess that means my intergalactic spaceship has a speed limit too, since my spaceship and I are made up of protons.

    If my protons can't have energy > 10^19, that's a gamma of about 10^10. So my speed can't go any higher than about 10^-20 less than the speed of light.

    Now, I'm bummed.

    andy.s

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  7. Dear Bee,


    thank you for digging out these plots, that's very interesting! I wasn't aware at all of this funny step-like attenuation behaviour at the onset of photo-pion production versus pair production!

    But I also share Tommaso's thoughts - it's a bit a pity that the paper doesn't show the actual cross sections and has not more details about the processes that are going on. That may help to better understand what happens and how come this difference.

    I mean, very naively, pionproduction is quark-pair production, just with a much higher threshold. It's not so clear to me why it should be so much stronger than electron pair production. Perhaps, the actual cross sections are not thatdifferent, just that pion production is a much more efficient channel to dissipate energy? I guess I will try to find out something about the cross sections ;-)...

    Best, Stefan

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  8. I like to see the answer to Tammaso's as well.:)

    The energy decay of particle showers and value would have produced "Cerenkov radiation" and we know how that is treated in IceCube?

    The higher energy values would have also accounted for "other curvatures recorded" in that collision processes. This would have been subject to the number of "high energy collisions" first seen in relation to the Fly's eye, and subsequent values determined in those collision processes and experiments today?

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  9. Exactly, an intuitive argument is what is needed here. I am surprised no commenter here know enough to explain it to us lazy off-field PhDs :)

    Bee, thank you for the virtual link, but I know less than you about the subject, and a post on it would require a lot of work on my part... I'm saturday-lazy.

    Cheers,
    T.

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  10. ...Unless it can be explained by the R ratio... sigma(hadrons)/sigma(ee) is large, and so the former happens much more frequently than the latter, given enough energy. But I think there is more to it...

    T.

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  11. a quantum diaries survivor6:26 AM, January 26, 2008

    hah, no - I found it. It is the delta resonance at 1236 MeV. The reaction is gamma p --> delta --> pi p.

    So it is not direct pion pair production, but single pion production!

    Cheers,
    T.

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  12. Peter Steinberg The creepy part of these kind of discussions is that one doesn't say that RHIC collisions "create" black holes, but that nucleus-nucleus collisions, and even proton-proton collisions, are in some sense black holes, albeit black holes in some sort of "dual" space which makes the theory easier.

    The interesting thing here is to consider the "crossover point?" You have Cerenkov radiation to consider? Well, "Muon production" as well in Gran Sasso as an addition to the LHC experiment.

    This sets the state of thinking here?

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  13. Hi Tommaso:

    Sure, it's the delta resonance, we explained that in the earlier post GZK cutoff. But how does that explain why the (relative) energy loss from pion production remains large for increasing energies, whereas the e+e- drops (at least that is how it looks in the figure)? Best,

    B.

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  14. OH. Shoot. Caught with my pants down :) Now I'll have to read your GKZ post three times to expiate.

    Now at the risk of adding blunder to blunder: I think I understand why ee production dies down. Think at branching fractions: when a very favorable channel opens up as you reach a threshold energy, the BR of all other decay processes simply shrink gradually, to reach the true high-energy asymptotic ratio, when phase space is not a factor anymore. Similarly here, as delta production starts playing a role, ee production becomes gradually less frequent.

    Or am I still misunderstanding something?

    Cheers,
    T.

    ReplyDelete

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