Detecting negative energy products in particle accelerators Are the detectors in a typical particle accelerator experiment, either in Fermilab, or now in LHC, sensitive to negative energy particles?
How would a negative energy particle, (say, a negative energy $\gamma$-ray photon) be found in the data collected by those detectors? would it have to be detected by the missing momentum approach (just like neutrinos were found)?
If you wanted to look for traces of negative-energy particles in the on-shell, final, outgoing, asymptotic states in existing collision data, what strategy would you choose, that could be applied on existing HEP datasets?
Regarding Anna's answer about invariant mass measurement, I have a doubt, which is related to a few discussions by experimentalists regarding neutrinos possibly being tachyons due to the fact that the error bars of the squared-mass observable leaked a bit into negative territory, I bring that up because if squared-invariant-mass is the actual observable, instead of invariant-mass, then I'm not sure how that can be sensitive to the sign of the invariant mass.
But moving on to light particles (like an hypothetical negative-energy γ-ray, which I used as an example) that like neutrinos, have energy dispersion curves that are experimentally indistinguishable from $|E|=c|P|$. Does the situation change significantly when the invariant-mass is zero or nearly zero, but the time-like component of the four-momentum could be both very big, and pointing backwards? can 
we measure or at least infer such signed components?
Note: If someone has experience with Geant4, I'll appreciate some brief remarks about how to modify a gamma particle definition to simulate a negative energy photon hitting a detector volume, and/or how to add a reaction process that would produce it
 A: Interesting question!
This may not directly address your question, but I think it might be relevant, and it's too long to fit in a comment. Some questions that arise here are:


*

*What do we mean by a negative-energy object?

*Do we have any reason to think that they're worth searching for?

*If so, is there any method that we know should, at least in principle, be able to detect them (assuming they exist), or is this unknown?
I think relativity -- mostly classical relativity, in fact -- gives us ways of addressing these foundational/philosophical questions.
Answer #1. The definitional issue is pretty clear from a relativist's point of view. This would be an object that violates an energy condition.
Answer #2. Yes. In fact, we're pretty sure that all known energy conditions are violated.[Barcelo 2002] This is the only part where any nonclassical relativity creeps in; the arguments that some of the energy conditions can be violated are not purely classical arguments, they're arguments using semiclassical gravity (which I'm not sure I believe in).
Answer #3. At least in principle, yes, it's very clear that a violation of an energy condition is empirically measurable. The energy conditions are statements about the eigenvalues of the stress-energy tensor, and these are observable.
As a concrete example, we've (indirectly) detected dark energy, and dark energy violates various energy conditions.
IMO these arguments dispose of the issue of whether the question is silly, not well-posed, unknowable, undefined, or based on shaky foundations. It's not. On the other hand, I haven't even attempted to answer the question of what this would mean in terms of actual particle detectors.
Barcelo and Visser, "Twilight for the energy conditions?," 2002, http://arxiv.org/abs/gr-qc/0205066
A: How would you define a negative energy particle? Is that one that, when it hits your detector, takes a fixed amount of energy out of it? That's trivially forbidden by the third law of thermodynamics, otherwise you could construct a fridge that can make negative temperatures. The only way to escape that would be by requiring, that the particle can measure the temperature of the detector... and it would decouple when T becomes small. Is that what you mean? 
A: Within the limits of accuracy of the experiments, no negative energy particles, with negative invariant mass,  have been leaving a signature. 
Particle accelerators deliver beams at fixed energies. All the event ordering algorithms depend crucially on energy and momentum conservation, that is what missing energy and missing transverse momentum are all about. To balance the event to the input energy. Anomalies on these distributions would have been caught and studied if large enough. Anomalies would appear as deviations from the predicted by theory distributions as applied to the detector with Monte Carlo programs. The main attention of analysts of data is looking for anomalies, so if they were there with a strong enough signal they would have been seen.
That said, unless a specific mathematical model with negative mass particles generated in proton proton or electron positron scattering is proposed the answer above does not cover fine structure. (The mass should be negative since in its rest frame  that is the only energy available.) Considering that the standard model explains very well observations from the microcosm to the cosmos without the need for observable negative mass at rest frame particles, no need for such theories has arisen . 
p.s. tachyons may be imaginary mass particles but I assume the question above is not about tachyons. Similar arguments would apply for them too. Tachyons are searched for in cosmic rays.
