Kaluza-Klein modes June 5, 2006
Posted by dorigo in astronomy, mathematics, physics, science.trackback
I listened to a very interesting theory talk by Bogdan Dobrescu this morning at the CDF collaboration meeting. The speaker allowed me to understand a few things I had never bothered to grasp from the theory of Large Extra Dimensions.
I learned that you can combine Kaluza-Klein modes by conserving their quantum number in a way quite similar to the way you combine angular momentum of two reacting particles.
Ok, now that I've lost 95% of my readers with the above sentence, let me clarify for you survivors.
Do you remember Heisenberg's Uncertainty Principle ? The law that dictates that the spread in the possible values of momentum p of a body (momentum is how physicists call the mass times speed of a particle), multiplied by the spread in position x of the body, has to be larger than a certain quantity called Planck's constant, h? We write that as
Delta(x) * Delta(p) > h.
That law is the cornerstone of quantum mechanics. It not only puts a limit on the accuracy with which you can measure position and momentum of a particle. It basically says that if you constrain the position of a body within a certain interval, then you get specific vibration modes of well-defined (quantized) amounts of momentum. Just like normal modes of vibration of a string of a given length.
Kaluza-Klein modes are particles predicted by the theory of large extra dimensions. They can propagate in the extra dimension, which is limited spatially to a very small radius. That small radius - the thickness of the extra dimension - is a spatial limit and through Heisenberg's uncertainty principle it implies a discrete spectrum of possible momentum states for the propagating bodies, just like quantum mechanics dictates that a particle in a box has a discrete spectrum of definite energies.
This quantization of possible momentum states produces a spectrum of observable particles, that we may look for at particle colliders.
These KK particles are fun! You cannot produce a single KK particle in the lowest "mode", nor can you destroy one. That is very interesting, because the lightest KK particle is a very natural candidate for the dark matter we believe exists in the universe.
Astrophysicists have been intrigued by that riddle for a while now: we can compute the total mass of the universe by looking at the visible matter it contains (galaxies, that is), and we can compute its gravitational force by looking at the rate of expansion, but these do not match, unless they speculate that there exists a large amount of mass we cannot see, in the form of particles that do not interact with the ordinary matter.
That "dark matter" (dark because it does not emit light, nor does it interact with visible matter) could well be Kaluza-Klein particles…. By looking at our proton-antiproton collisions, we might just find out if that is the case!
Bogdan is a very good speaker, and I’m sure his talk was very interesting. Did he have any new ideas about signatures for extra dimensions at colliders? We currently look at final states with leptons, photons and jets + missing energies - which final state is favored depends on the particular extra-dimensional model you are considering. If he says something like: “..and you should also consider the X final state…” I would be most interested.
The Heisenberg Uncertainty relation does not lead to the quantization of mass states, nor of momenta. Quantization follows simply from the boundary conditions, and the common belief that this quantization is unique to quantum mechanics is a fallacy. The wave numbers (equiv. frequencies) of a wave guide or resonant cavity are quantized in exactly the same way as in the “particle in a box” problem, and this understanding of classical electro-magnetism certainly proceeded the advent of quantum mechanics.
What was interesting in the early “wave mechanics” was the quantization of the electron’s wave function in the azimuthal angle, phi, which allowed Bohr to explain, sort of, the stability of atomic orbits. It is this quantization in phi which is most analogous to the small extra-dimensions that Bogdan talks about.
Please send more pictures when you can. The sunset at dinner looks gorgeous!
Hi MIchael,
Bogdan indeed mentioned a few final states we should look at. If I recall correctly, one involves a “mode 2″ KK particle producing a signature with a top, a bottom quark, and two jets. This would be a signal in our W+4 jet sample where we find top-antitop events, and we would see a resonance in the mass of the t+b system, plus another resonance in the total mass of the tbjj system, much like the Mtt search except that one 3-jet system would not make the top mass.
And you are probably right, the connection of Heisenberg relation with the spatial limitation of the extra dimension is not the best way to explain quantization of energy levels. In my post I got two different issues mixed up.
T.