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There are some interactions that are forbidden by conservation laws, e.g. an electron cannot turn into a positron by conservation of charge and a photon cannot turn into a positron electron pair by conservation of momentum.

My question is if every interaction (between say up to 3 or 4 particles) that is consistent with all known conservation laws have been observed.

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    $\begingroup$ proton decay has not been observed $\endgroup$ – TROLLHUNTER Feb 20 '11 at 15:42
  • $\begingroup$ You should specify whether you are interested in Standard Model or also theories beyond it. There are lots of processes you are looking for also in SM but everything in "beyond the SM" is unobserved, pretty much by definition. $\endgroup$ – Marek Feb 20 '11 at 16:09
  • $\begingroup$ I guess I am mostly interested in examples that fall within the energies that accelerators are currently able to test (including things beyond the SM, but I was under the impression we don't have the energy to test any of those things yet). $\endgroup$ – Eric Feb 21 '11 at 20:32
  • $\begingroup$ Do you mean basic natural forces? (and not interactions between specific particles) $\endgroup$ – IljaBek Aug 15 '11 at 17:52
  • $\begingroup$ Great question, great answers! $\endgroup$ – Marton Trencseni Aug 16 '11 at 9:50
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  • proton decay is un-observed, and suspected on the basis of various Beyond the Standard Model theories
  • Nothing directly involving the Higgs had been published when the question was asked, but ATLAS and CMS have pretty definitive observations of the most easily measured channels. Some of the harder channels are still under invesitgation.
  • Neutrinoless double beta decay would be the signature of $\nu + \nu \to \text{::nothing::}$ (off-shell, of course) and would indicate that neutrinos are Majorana particles. There is a report of it, but the significance is limit and it is unconfirmed
  • Evidence for any kind of dark matter interactions outside of gravity is pretty sparse on the ground
  • No super-symmetric partners have been observed
  • I doubt anyone has seen $\nu_\tau + n \to \tau + p$, though this is required by the current electoweak formalism. Or at least, they haven't been able to show that this is what they saw

Basically lots of dark corners. Note that much of this is Beyond the Standard Model, so may or may not represent the real state of physics.

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  • $\begingroup$ "I doubt anyone has seen $\nu_\tau + n \to \tau + p$" - what about OPERA experiment? $\endgroup$ – voix Feb 20 '11 at 21:07
  • $\begingroup$ I stand corrected. Tough observation, and very much off-shell, as, too, as $E_\nu$ is about an order of magnitude below $m_\tau$. $\endgroup$ – dmckee♦ Feb 20 '11 at 21:19
  • $\begingroup$ Thanks for these answers! The wikipedia article says that models that predict proton decay say the half life is around 10^36 years. Considering this is so much longer than the age of the universe, how likely is it that this could be observed? And I'm guessing this 10^36 years is the average half-life of a proton, is it possible that some protons could have already decayed? Is it theoretically possible to speed up this decay by say elevating its energy or something? $\endgroup$ – Eric Feb 21 '11 at 20:31
  • $\begingroup$ @Eric, to search for proton decay you get kilotons of them in one place and watch them all, very, very closely. It's a random process like radioactive decay, so I few will go very early and a few very late. The current experimental limits is (according to the PDG) $\approx 10^{31}\text{ years}$ into any reasonable final state or $\approx 10^{29}\text{ years}$ into weird stuff. $\endgroup$ – dmckee♦ Feb 21 '11 at 20:39
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dmckee has given a good, thorough answer. I'd bet that there are lots of other interactions that haven't been seen. How about $\gamma+\gamma\to Z+\overline Z$, or $\gamma+\gamma\to t\overline t$? To see those reactions, you'd need high-energy photons, and the cross sections should be very low. I doubt that we've produced the right experimental setup for those reactions. Perhaps even better would be a ton of similar $\nu\overline\nu$ reactions: $\nu_\tau+\overline\nu_\tau\to t\overline t$, for instance.

All of these satisfy the conservation laws and are predicted to have nonzero cross sections in the standard model, but I'd be surprised if they've been observed.

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There are some extremely important reactions that have never been observed directly. My favorite example is p-p fusion,

$$\text{p} + \text{p} \rightarrow \text{d} + \text{e}^+ + \nu_e$$

which is the rate-determining step for the main fusion process in the Sun and all other small stars. But it is utterly impossible to observe this reaction in anything like today's accelerators, because the cross section is so tiny. It's only important in the Sun because there's such a large, dense collection of hot protons. (In fact the smallness of this cross section is the reason all the stars haven't burnt out yet.)

Other examples would be any reactions of two photons, or two neutrinos, as Ted Bunn said.

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  • $\begingroup$ The core of the Sun is over 10 million K, not 5800 K. Check your facts. $\endgroup$ – Keenan Pepper Aug 20 '11 at 11:08
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    $\begingroup$ possibly colliders today simply overshoot - the reaction is low-energy: with 1eV~11605K, kinetic energies of the particles in the core of the sun (some keV) hardly reach the colliders' energy (@Keenan: thx) $\endgroup$ – IljaBek Aug 20 '11 at 14:09

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