Photons only couple to electromagnetically charged particles, regardless of how you rotation the space and time axis on a Feynman diagram of its couplings.
Now, since the Fermi exclusion principle doesn't apply to bosons, there is no problem with multiple Z bosons or photons or gluons being in the same place at the same time.
But, what about neutrinos? They can't occupy the same place at the same time, but it would seem by the reasoning above that a neutrino and an antineutrino to collide cannot annihilate into a photon, as that would be equivalent in Feynman diagram to neutrino-antineutrino pair production by a photon, which I have on good authority doesn't happen.
W boson interactions with neutrinos while common, and indeed the main reason that the rest of physics needs neutrinos, don't generally involve neutrino-antineutrino pairs. They involve the intersection in a Feynman diagram of a W boson, a charged lepton and an antineutrino, or a W boson, a charged antilepton and an ordinary neutrino. So, W boson interactions can't tell us what happens when a neutrino and antineutrino collide.
A Z boson does, of course, decay into neutrino and antineutrino pairs of exactly three types (electron, muon and tau). So, just as a Z boson decay could create a neutrino-antineutrino pair, a neutrino and antineutrino could annihilate into a Z boson. See, e.g. here:
Unless I'm mixed up, the most likely annihilation process creates
a virtual Z boson which can then decay into stuff with total charge
zero. If the neutrinos collide at sufficiently low energies,
the only final result allowed by conservation of energy is some
mix of photons, neutrinos and antineutrinos. One can't get just a
*single* photon, thanks to conservation of energy-momentum.
Conservation of parity and angular momentum put some other
limitations on what one can get.... but I'm too lazy to figure it out!
LEP did the reverse process: creation of neutrino-antineutrino
pairs! . . .
As the other posts have correctly stated, they do annihilate into a Z-zero
then whatever, but the cross section for neutrino-antineutrino annihilation
is tiny in the extreme, particularly at low energies. At low energy Z-zero
will just decay back to neutrinos, so you will see neutrino-neutrino
scattering (rotate the diagram by 90 degrees is the other option, so
multiply cross section by 2 if you want). Cross section is in region of
10^-45.
Incidentally it cannot decay into 1 photon, for energy/ momentum reasons,
and 2 photon's is a 3rd order rate so effectively impossible. The reason
being neutrinos cannot couple to photons, and neither can Z-zero, so we
need:
nu + nubar --> Z-zero
Z-zero --> W+ W-
W+ W- --> gamma gamma
Hence cross section surpressed by around 10^-20 . . .
Sorry that was wrong anyway should be of order 10^-36 and thats in m^2.
so 10^-8 mb if you prefer
i.e. v v small
I've also remembered that the single feynmann diagram needs multipliplying
by 4, one for the simple scattering and 3 from the three different neutrino
pairs that could be produced. Not that that makes much of a difference at
this level ==> 4 x 10^-8 mb . . .
Of course for few-MeV neutrinos that Z0 is
far off mass shell, which is partly why the cross-section is so tiny;
the coupling constant is also small for low energies.
But, given the fact that mass-energy is conserved and that energetic limitations can prevent otherwise possible couplings from happening, and that unlike photons, which despite Planck's constant can have very low energies via infrared wavelengths, there is a minimum mass-energy necessary to give rise to a Z boson (91.1 GeV/c^2).
Similarly, since weak force bosons operate only a short ranges (they promptly decay before they get too far), and simply emitting them is energetically limited, low energy neutrinos and antineutrinos might not even be able to interact with each other via the weak force. Yet, since they are fermions, there must be some sort of contact force that prevents them from occupying the same space.
One possibility to prevent this problem from arising would be that the chain of neutrino production is such that every neutrino and antineutrino has at least half of the Z boson mass-energy, which is definitionally true in the case of neutrinos and antineutrinos produced in Z boson decay that have not emitted Z bosons of their own. But, this is manifestly not the case when neutrinos are produced by W bosons and there are neutrinos in the literature with mass-energies in the 10 MeV range, far less than necessary to produce a Z boson upon contact with its antiparticle. (Stable heavy neutrinos are also disfavored by cosmology data in certain mass ranges and by LEP data under certain assumptions.)
Another possibility is that neutrinos and antineutrinos could interact in some way, either a neutral current interactions or in an annihilation event, that would seem to be energetically prohibited via some sort of quantum tunnelling or virtual particle interaction. Perhaps a neutrino and antineutrino could give rise to a virtual Z boson which could decay to a virtual electron-positron pair which could in turn decay to an energetically permitted photon or something like that. (This sounds like what the block quote implies, but I'm not really clear on it.)
But, I'm not certain that there are any experiments that directly look at same type neutrino and antineutrino collisions, or, in particular, collisions of neutrinos and antineutrions sufficiently low in energy to energetically prohibit the formation of a Z boson. Given the limited about of interaction that a neutrino has with everything else, trying to make that kind of collision happen would have a herding cats element to it. Indeed, the whole discussion of the source of neutrino mass fundamentally has at its root a lack of clarity concerning the way that neutrinos and antineutrinos are related.
Another concern along the same lines is that it isn't clear if a low kinetic energy neutrino, even if it had enough kinetic energy to energetically allow it to oscillate into another generation of neutrino, would be energetically limited in a way that prevented that from happening if it lacked the energy to emit a W or Z boson.
If neutrinos can oscillate when it has less than 80 GeV of combined kinetic energy and rest mass, does it follow that (1) oscillations only derived from aborbsion of a weak force boson from some other source, followed by emission of a weak force boson, (2) oscillations are made possible by quantum tunnelling with virtual particles between end states that are not subject to energetic limitations or that can overcome energetic limitations as a result of the uncertainty principle, or (3) that oscillations of neutrinos involve some beyond the Standard Model process other than W or Z boson mediated interactions.
There has been some theoretical exploration of what happens near black holes, in exploding stars, and for high kinetic energy neutrinos in cosmic rays (also here) via Z boson decay, but the low energy, non-relativistic regime is really more interesting than the high energy, relativistic regime from the theoretical perspective, and there seems to be at least one paper from 1992 on the subject of 17 keV neutrino annihilations. See also here (abstract only) and here and here.
There may be well established, textbook answers to some of these questions, but I don't know them.
No comments:
Post a Comment