A Quantum Diaries Survivor

I read with pleasure today a recent preprint by CLEO-c, which describes their observation of the rare decay of mesons to three photons.

This is a process which we have known to occur ever since the November 1974 discovery of charmonium, because it is one predicted by quantum electrodynamics which does not violate any quantum-mechanical selection rule. Indeed, the charmonium system is very similar to ortho-positronium -a bound state of an electron and a positron carrying the very same quantum numbers, but made up of much lighter constituents. However, ortho-positronium decays to three photons almost exclusively, while the has many other ways to disintegrate which violate no rule: it does so by producing electron-positron pairs, or muon pairs, or light hadrons. Because of the wider choice of decay processes, some of which are mediated by strong interactions, the only decays to three photons once in about a hundred thousand times.

Actually, we have to give it to this intriguing meson: besides its historical importance -its detection marked the start of a new era in particle physics- its phenomenology is quite rich.

1. To begin with, the fact that the charm pair can only annihilate to an odd number of vector particles (since in quantum mechanics a state with angular momentum J=1 cannot be made up by combining even numbers of J=1 states) means that gluon mediation is rather suppressed: a decay mediated by one single gluon violates color conservation (the is of course colorless, while gluons aren’t), two is an even number, and so the simplest way for strong interactions to disintegrate the is through emission of three gluons, which is a process proportional to the third power of the strong coupling constant . This reduces the usual dominance of strong over electroweak decays, and makes the and processes not so infrequent (a few percent each). As far as the three-photon final state goes, it is suppressed by the third power of , or about .
2. mesons are invaluable tools in B-physics, because B hadrons often produce them in their decay. The subsequent leptonic decay of the allows to reconstruct exclusive final states with good accuracy, and identify them over the large QCD backgrounds. By this method, the meson was discovered by CDF a few years ago, and more recently the cascade baryon has been reconstructed in a spectacular decay chain by both CDF and D0. Further, decays are invaluable for measurements of the quark mixing matrix and other parameters in the B sector of the Standard Model, such as B lifetimes (1) (2) and a host of other quantities.
3. Through the study of production of mesons, the HERA experiments (colliding electrons with protons in Hamburg, at a center-of-mass energy of about 300 GeV) have performed very precise determinations of QCD processes.
4. decays to muon pairs are studied even in heavy ion collisions, where they are a probe of the creation of a hot “quark-gluon plasma“, which suppresses the leptonic decay of these bodies through enhanced hadronic interactions of the charm quarks.
5. And I am certainly forgetting to mention a large number of exquisite physics measurements where the meson is instrumental.

I wish I had more time to discuss the phenomenology of the remarkable meson. Maybe another time -we are by now deep in week-end time and I should devote more time to my family. Instead, let me just summarize in a line or two (really) the CLEO-c measurement.

CLEO studies electron-positron collisions yielding a meson (another charm-anticharm bound state with heavier mass, 3.68 GeV). When the decays to a pair of charged pions and a , the pions are easily recognizable, and the lack of any additional charged particle track from the suggests that the meson may have disappeared into photons. CLEO thus counts events with the tagging pions plus 2, 3, 4, and 5 photons, and they see a clear signal in the invariant mass of the pion recoil system, while no signal is seen in the other three categories. Below you can see the very nice mass peak obtained by reconstructing the meson mass.

From the number of observed decays and the total number of produced events, accounting for detector efficiencies and selection cuts, CLEO-c measures the branching fraction of to be . Congratulations to the collaboration!