Rumsfeld hadrons

An inspiring title for a preprint, indeed. Frank Close just published on the ArXiV (get your own copy  here) a short paper, Hep-ph/0706.2709, with that very title. The paper is just as inspiring, and it is worth a close look if you are interested in heavy hadron spectroscopy.

The reason of citing a war criminal in the title is made clear from the abstract:

Donald Rumsfeld, in attempt to excuse the inexcusable, once (in)famously said that “there are things that we know we know; there are things that we know we don’t know; and then there are things that we don’t know that we don’t know”. Recent discoveries about hadrons with heavy flavours fall into those categories. It is of course the third category that is the most tantalising, but lessons from the first two may help resolve the third.

I found the paper very interesting to read. It is, however, a bit too technical for me to attempt a discussion of it here. Maybe I can just quote the simplest example that Frank brings to explain what we really understand well in heavy hadrons, to stay in the spirit of the last sentence of his abstract.

The example of things we do know we know comes from the B_c meson. This peculiar particle is made by a bottom and a anti-charm quark jiggling around each other. The large mass of the two quarks makes the system non-relativistic to a good approximation (heavy things move slower!), so the mass of the object must be not too different from the mass of its constituents – to the extent that such a thing is well-defined.

Now, the mass of the B_c has been measured with precision by CDF (see plot on the left, which shows the distribution of reconstructed mass of the J/psi and pion system into which the B_c decayed), and is found to be M=6276.5+-4.8 MeV , in fair agreement with theoretical calculations based on lattice QCD (F.Allison et al., PRL 94, 172001 (2005): M=6304+-12+18-0 MeV), which are basically calculations approximating space with a grid of points and computing the interactions between quarks on this grid.

What can fortify beyond doubt our confidence that we do understand the (b anti-c) system is however not so much the good agreement with lattice QCD, but a “crackpottian coincidence”: take the mass of the fundamental mesons made of (c anti-c) [the psi] and (b anti-b) [the Upsilon], add them, divide by two, and – lo and behold – the value turns out to be 6278.6 MeV, less than one part per mille away from the B_c mass.

Duh! two c-quarks worth of dough, plus two b-quark worth of dough, divided by two, is a c-quark plus a b-quark worth of dough! Or, as Groucho Marx would put it, “A child of five could understand this. Go fetch a child of five!” (for some reason I feel very grouchian lately).

What the exercise tells us is that quarks may be mysterious things when their dynamics is involved, but as heavy static sources of color field they are much less mysterious. Close makes the point that he awaits the moment when excitations of the B_c meson will be found, because it is then that more interesting effects will start posing new puzzles.