The .pdf file can be found here
An external link to the paper is here.
The DOI is 10.1103/PhysRevLett.83.268
Some brief last-minute answers (or attempts at least):
Heirarchy Problem in this case means the huge difference in the energy scales for the Electroweak Unification and the “Super Unification,” where gravity becomes of comperable strength to other fundamental forces. There are approximately 17 orders of magnitude separating those scales, which some people think is a lot or perhaps even too much.
M is the energy (or mass) scale on which graviational interactions become “strong.” It is determined, above all else, by the magnitude of gravitational coupling, which we normaly know as G. Since G is really small (on particle scale), one needs to go to huge energies to make gravity matter. This paper then tries to see if we can exploit a loophole where the presence of small additional dimensions actually allows G not to be so small at very short distances.
D-branes are String Theorist voodoo. What we care about is simply the fact that normal particles that we know and love live in our good-old 4-D space, and don't see the supposed extra dimensions (because they are too cool for such things!)
As far as I know, we have not seen any other effects associated with gravitons, virtual or otherwise. For them to begin to matter, we wouls still have to be conducting our experiments at the TeV scale, which we are now doing at the LHC, but at least as of last week's presentation, have not seen anything either.
I believe that the type I supernovae start out below the critical mass, and munch up their fat neighbors until they get heavy enough to explode. Type II are fatties to begin with, and once they run out of nuclear fuel, their core just collapses and the outsides go boom!
It's not so much that the reaction in (2) has to be mediated by the strong force, as that this is the main contribution, as at those energies, which are relatively low compared to the “Strong Scale” (~300MeV), strong force is, well, strong, about 137 times stronger than electromagnetism, so the exchange of mesons will be by far the most common way to interact. They also don't have to emmit gravitons in this case, but they might, and we want to put a limit on how often they can do it by watching for missing energy from nearby supernovae.
As I understand it, their bound is “Model-independent” because they useda very generic Lagrangian for the interaction of gravitons with matter, which has no notin built into it about what really goes on, so it can only be used for order-of-magnitude estimates.
To see how high energies relate to small distances, consider the example of light. To look at really small things, one needs shorter wavelengths, and shorter wavelengths are associated with more energy. This is essentially true of all other particles as well. (Also, length has dimensions of inverse energy, so more energy naturally implies smaller length.)
…Whew. I most likely lied profusely about somethings here, so if anyone bothers to read this before the actual meeting, feel free to call me out on it there.
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