A Quantum Diaries Survivor

Spin-parity analysis of the X(3872) June 9, 2006

A few days ago, Michael Schmitt made the following comment here:

Ok, the collaboration meeting ends today, and I have a pretty clear idea of the most intruguing new measurement (new to me of course – I cannot follow everything that is done by my 700 CDF colleagues: that's the reason for following a collaboration meeting!) I heard about during this week. It is a good-old "angular distributions" kind of measurement, quite carefully carried out to investigate the properties of the X(3872) particle. The talk was given by our Karlsruhe collaborator Michael Feindt, and I owe him for some of the pictures and plots I am posting here.   The X was discovered at the e+ e- B factory BELLE in 2003, and was very shortly thereafter confirmed by CDF (who actually determined we had it in our dataset since quite a few years before, darn), D0 and BaBar. It is a funny little resonance, that can be observed in our data by selecting J/psi –> mu mu decays and associating to the J/psi a pair of charged pion tracks. Its characteristics are unknown as of yet, but its mass is unreasonably close to the sum of masses of two neutral charmed mesons, a D and a D*. This may indicate that the X is actually a sort of "molecular state" of those two particles. The graph above shows the peak in the invariant mass distribution of J/psi-pi-pi combinations, the X(3872) signal. About 2200 events sit on top of a large combinatioral background due to random associations of tracks. The more mundane explanation of the X is that it is a charmonium state, that is a bound state of a charm-anticharm pair. Charm quarks have a mass of about 1.5 GeV, and if they rotate around each other with sufficient angular momentum, the rest mass of the system may well be of the order of that of the X. However, the charmonium hypothesis has some shortcomings: other decay modes of the X are not observed as they should, and the observed one is not the one that should be preferred by a ccbar state at that mass. Also, the X lives quite long before decaying, a fact indicated by its narrowness (the longer an oscillation lives, the better determined its oscillation frequency is: the same goes with elementary particles, whose "oscillation frequency" is their mass). The two above explanations (molecule of D mesons or simple charmonium state), along with other hypotheses, can be discriminated by studying angular distributions in the particle decay. That is, when the X produces the J/psi and the two pions, it not only provides the decay products with momentum – in measure related to the difference between its own mass and the mass of the projectiles – but also with angular momentum, and the resulting relative motion of the projectiles tell us a lot about the quantum numbers of the X. The picture above shows the definition of the three angles one can experimentally measure from the decay products. They carry information on the spin-parity quantum numbers of the X. The measurement of the angular distributions in the decay of the X mesons observed by CDF is difficult, because the signal sits on top of a large, irreducible background (see first plot above). However, a careful statistical analysis can extract the distributions we need to fit. As the figure above shows, the data (black points) are divided in 12 bins as a function of the three angles describing the decay. Some of the possible spin-parity assignments are clearly incompatible with the data. Two possible spin-parity assignments of the X(3872) are equally probable: in particular, the X may be indeed a molecular bound state of two neutral D mesons (state J^(PC)=1^(++), that is a spin-one positive parity and charge conjugation state), or a charmonium state 2^(-+). Both are compatible with the data, with chisquared probabilities of 28% and 26%, respectively. Other explanations are ruled out by the analysis. More data will discriminate the two hypotheses. Also, it will be very important to search for this particle in other decay modes, and possibly search for a similar bound state decaying to a Upsilon and two pions – but there, things are experimetally even harder… Time will tell!